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CHXI06:THERMODYNAMICS

369493 The heat of formation of \(\mathrm{\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}_{(\mathrm{l})}}\) is \({\rm{ - 66}}\,{\rm{k}}\,{\rm{cal/}}\) mol. The heat of combustion of \(\mathrm{\mathrm{CH}_{3} \mathrm{OCH}_{3(\mathrm{~g})}}\) is \({\rm{ - 348}}\,{\rm{k}}\,{\rm{cal/mol}}{\rm{.}}\) \({\rm{\Delta }}{{\rm{H}}_{\rm{f}}}\) for \(\mathrm{\mathrm{H}_{2} \mathrm{O}}\) and \(\mathrm{\mathrm{CO}_{2}}\) are \({\rm{ - 68}}\)\(\mathrm{\mathrm{kcal} / \mathrm{mol}}\) and \({\rm{ - 94}}\,{\rm{k}}\,{\rm{cal/mol}}\), respectively. Then, \(\mathrm{\Delta H}\) for the isomerisation reaction \(\mathrm{\mathrm{CH}_{3} \mathrm{OCH}_{3(\mathrm{~g})}}\) is

1 \({\rm{18}}\,{\rm{k}}\,{\rm{cal/mol}}\)

2 \({\rm{95}}\,{\rm{k}}\,{\rm{cal/mol}}\)

3 \({\rm{22}}\,{\rm{k}}\,{\rm{cal/mol}}\)

4 \({\rm{30}}{\mkern 1mu} {\rm{k}}{\mkern 1mu} {\rm{cal/mol}}\)

CHXI06:THERMODYNAMICS

369494 Given,
\({{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})}\)\( \rightleftharpoons \)\({{\rm{NC}}{{\rm{l}}_3}(\;{\rm{g}}) + 3{\rm{HCl}}({\rm{g}});}\)
\({ - {\rm{\Delta }}{{\rm{H}}_1}}\)
\({{{\rm{N}}_2}({\rm{g}}) + 3{{\rm{H}}_2}({\rm{g}})}\)\( \rightleftharpoons \)\({2{\rm{N}}{{\rm{H}}_3}({\rm{g}});}\)
\({ - {\rm{\Delta }}{{\rm{H}}_2}}\)
\({{\rm{H}}_{\rm{2}}}{\rm{(g)}} + {\rm{C}}{{\rm{l}}_{\rm{2}}}{\rm{(g)}}\)\( \rightleftharpoons \)\(2{\rm{HCl(g)}};\)
\({\rm{\Delta }}{{\rm{H}}_{\rm{3}}}\)
The heat of formation of \(\mathrm{NCl}_{3}(\mathrm{~g})\)
in terms of \(\Delta \mathrm{H}_{1}, \Delta \mathrm{H}_{2}\) and \(\Delta \mathrm{H}_{3}\) is

1 \(\Delta \mathrm{H}_{\mathrm{f}}=-\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}-\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

2 \(\Delta \mathrm{H}_{\mathrm{f}}=\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}-\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

3 \(\Delta \mathrm{H}_{\mathrm{f}}=\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}+\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

4 None of the above

Explanation:

\({\rm{I}}.{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}({\rm{g}})\)\( \rightleftharpoons \)\({\rm{NC}}{{\rm{l}}_3}(\;{\rm{g}}) + 3{\rm{HCl}}({\rm{g}}),\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - {\rm{\Delta }}{{\rm{H}}_1}(1)\)
\({\rm{II}}.{{\rm{N}}_2}({\rm{g}}) + 3{{\rm{H}}_2}({\rm{g}})\)\( \rightleftharpoons \)\(2{\rm{N}}{{\rm{H}}_3}({\rm{g}}),\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - {\rm{\Delta }}{{\rm{H}}_2}(2){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\({\rm{III}}.{{\rm{H}}_2}({\rm{g}}) + {\rm{C}}{{\rm{l}}_2}({\rm{g}})\)\( \rightleftharpoons \)\(2{\rm{HCl}}({\rm{g}}),{\mkern 1mu} {\mkern 1mu} \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{\Delta }}{{\rm{H}}_3}{\mkern 1mu} (3){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\({\rm{On}}{\mkern 1mu} \,{\rm{multiplying}}\,{\mkern 1mu} {\rm{Eq}}{\rm{.}}{\mkern 1mu} {\rm{(3)by}}{\mkern 1mu} {\rm{3,we}}\,{\mkern 1mu} {\rm{get}}\)
\(3{{\rm{H}}_2}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})\)\( \rightleftharpoons \)\(6{\rm{HCl}}({\rm{g}});{\mkern 1mu} {\mkern 1mu} \)
\({\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 \times \Delta {{\rm{H}}_3}{\mkern 1mu} {\mkern 1mu} (4)\)
\({\rm{On}}{\mkern 1mu} \,{\rm{inverting}}\,{\mkern 1mu} {\rm{Eq}}{\rm{.(4),we}}{\mkern 1mu} {\mkern 1mu} {\rm{get}}\)
\({6{\rm{HCl}}({\rm{g}})}\)\( \rightleftharpoons \)\({3{{\rm{H}}_2}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})}\)
\({{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 3 \times \Delta {{\rm{H}}_3}(5)}\)
\({\rm{On}}\,{\mkern 1mu} {\rm{Multiplying}}{\mkern 1mu} \,{\rm{Eq}}{\rm{.(1)}}{\mkern 1mu} \,{\rm{with}}\,{\mkern 1mu} {\rm{(2),we}}\,{\mkern 1mu} {\rm{get}}\)
\(2{\rm{N}}{{\rm{H}}_3} + 6{\rm{C}}{{\rm{l}}_2}\)\( \rightleftharpoons \)\(2{\rm{NC}}{{\rm{l}}_3} + 6{\rm{HCl}}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 2 \times {\rm{\Delta }}{{\rm{H}}_1}(6)\)
\({\rm{On}}\,{\rm{adding}}\,\,{\rm{Eq}}.({\rm{2}}),({\rm{5}}){\rm{and}}({\rm{6}}),{\rm{we}}{\mkern 1mu} \,{\rm{get}}\)
\({{\rm{N}}_2} + 3{\rm{C}}{{\rm{l}}_2}\)\( \rightleftharpoons \)\(2{\rm{NC}}{{\rm{l}}_3};\)
\({{\rm{\Delta }}{{\rm{H}}_{\rm{r}}} = - {\rm{\Delta }}{{\rm{H}}_2} - 3 \times {\rm{\Delta }}{{\rm{H}}_3} - 2 \times {\rm{\Delta }}{{\rm{H}}_1}}\)
\({\therefore {\rm{\Delta }}{{\rm{H}}_{\rm{f}}} = \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{r}}}}}{{\rm{2}}} = - \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{2}}}}}{{\rm{2}}} - \frac{3}{2}{\rm{\Delta }}{{\rm{H}}_3} - {\rm{\Delta }}{{\rm{H}}_1}}\)
\({ = - {\rm{\Delta }}{{\rm{H}}_1} - \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{2}}}}}{{\rm{2}}} - \frac{3}{2}{\rm{\Delta }}{{\rm{H}}_3}}\)

CHXI06:THERMODYNAMICS

369495 In the reaction,
\({\rm{S + }}\frac{{\rm{3}}}{{\rm{2}}}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{3}}}{\rm{ + 2xkJ}}\) and \({\rm{S}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}\frac{{\rm{1}}}{{\rm{2}}}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{3}}}{\rm{ + ykJ}}\)
heat of formation of \(\mathrm{\mathrm{SO}_{2}}\) is

1 \(\mathrm{x-y}\)

2 \(\mathrm{2 x+y}\)

3 \(\mathrm{x+y}\)

4 \(\mathrm{y-2 x}\)

CHXI06:THERMODYNAMICS

369496 Given
\({\rm{C + 2}}\;{\rm{S}} \to {\rm{C}}{{\rm{S}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = + 117}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
\({\rm{C + }}{{\rm{O}}_{\rm{2}}} \to {\rm{C}}{{\rm{O}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = - 393}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
\(\;{\rm{S + }}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = - 297}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
The heat of combustion of
\(\mathrm{\mathrm{CS}_{2}+3 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{SO}_{2}}\) is

1 \(\mathrm{-807 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

2 \(\mathrm{-1104 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

3 \(\mathrm{+1104 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

4 \(\mathrm{+807 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

CHXI06:THERMODYNAMICS

369497 A sample of gas changes from \({{\rm{p}}_{\rm{1}}}{\rm{,}}\) \({{\rm{V}}_{\rm{1}}}\) and \({{\rm{T}}_{\rm{1}}}\) to \({{\rm{p}}_{\rm{2}}}{\rm{,}}\) \({{\rm{V}}_{\rm{2}}}\) and \({{\rm{T}}_{\rm{2}}}\) by one path and then back to \({{\rm{p}}_{\rm{1}}}{\rm{,}}\) \({{\rm{V}}_{\rm{1}}}\) and \({{\rm{T}}_{\rm{1}}}\) by another path. How many of the following must be zero for the gas in this cycle?
\(\Delta {\rm{T}},\Delta \,{\rm{p}},\Delta {\rm{V}},\,\,{\rm{q}}{\rm{.}}\,\,{\rm{W}}\) and \(\Delta \,{\rm{E}},\)

1 1

2 2

3 3

4 4

CHXI06:THERMODYNAMICS

369493 The heat of formation of \(\mathrm{\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}_{(\mathrm{l})}}\) is \({\rm{ - 66}}\,{\rm{k}}\,{\rm{cal/}}\) mol. The heat of combustion of \(\mathrm{\mathrm{CH}_{3} \mathrm{OCH}_{3(\mathrm{~g})}}\) is \({\rm{ - 348}}\,{\rm{k}}\,{\rm{cal/mol}}{\rm{.}}\) \({\rm{\Delta }}{{\rm{H}}_{\rm{f}}}\) for \(\mathrm{\mathrm{H}_{2} \mathrm{O}}\) and \(\mathrm{\mathrm{CO}_{2}}\) are \({\rm{ - 68}}\)\(\mathrm{\mathrm{kcal} / \mathrm{mol}}\) and \({\rm{ - 94}}\,{\rm{k}}\,{\rm{cal/mol}}\), respectively. Then, \(\mathrm{\Delta H}\) for the isomerisation reaction \(\mathrm{\mathrm{CH}_{3} \mathrm{OCH}_{3(\mathrm{~g})}}\) is

1 \({\rm{18}}\,{\rm{k}}\,{\rm{cal/mol}}\)

2 \({\rm{95}}\,{\rm{k}}\,{\rm{cal/mol}}\)

3 \({\rm{22}}\,{\rm{k}}\,{\rm{cal/mol}}\)

4 \({\rm{30}}{\mkern 1mu} {\rm{k}}{\mkern 1mu} {\rm{cal/mol}}\)

CHXI06:THERMODYNAMICS

369494 Given,
\({{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})}\)\( \rightleftharpoons \)\({{\rm{NC}}{{\rm{l}}_3}(\;{\rm{g}}) + 3{\rm{HCl}}({\rm{g}});}\)
\({ - {\rm{\Delta }}{{\rm{H}}_1}}\)
\({{{\rm{N}}_2}({\rm{g}}) + 3{{\rm{H}}_2}({\rm{g}})}\)\( \rightleftharpoons \)\({2{\rm{N}}{{\rm{H}}_3}({\rm{g}});}\)
\({ - {\rm{\Delta }}{{\rm{H}}_2}}\)
\({{\rm{H}}_{\rm{2}}}{\rm{(g)}} + {\rm{C}}{{\rm{l}}_{\rm{2}}}{\rm{(g)}}\)\( \rightleftharpoons \)\(2{\rm{HCl(g)}};\)
\({\rm{\Delta }}{{\rm{H}}_{\rm{3}}}\)
The heat of formation of \(\mathrm{NCl}_{3}(\mathrm{~g})\)
in terms of \(\Delta \mathrm{H}_{1}, \Delta \mathrm{H}_{2}\) and \(\Delta \mathrm{H}_{3}\) is

1 \(\Delta \mathrm{H}_{\mathrm{f}}=-\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}-\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

2 \(\Delta \mathrm{H}_{\mathrm{f}}=\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}-\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

3 \(\Delta \mathrm{H}_{\mathrm{f}}=\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}+\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

4 None of the above

Explanation:

\({\rm{I}}.{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}({\rm{g}})\)\( \rightleftharpoons \)\({\rm{NC}}{{\rm{l}}_3}(\;{\rm{g}}) + 3{\rm{HCl}}({\rm{g}}),\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - {\rm{\Delta }}{{\rm{H}}_1}(1)\)
\({\rm{II}}.{{\rm{N}}_2}({\rm{g}}) + 3{{\rm{H}}_2}({\rm{g}})\)\( \rightleftharpoons \)\(2{\rm{N}}{{\rm{H}}_3}({\rm{g}}),\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - {\rm{\Delta }}{{\rm{H}}_2}(2){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\({\rm{III}}.{{\rm{H}}_2}({\rm{g}}) + {\rm{C}}{{\rm{l}}_2}({\rm{g}})\)\( \rightleftharpoons \)\(2{\rm{HCl}}({\rm{g}}),{\mkern 1mu} {\mkern 1mu} \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{\Delta }}{{\rm{H}}_3}{\mkern 1mu} (3){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\({\rm{On}}{\mkern 1mu} \,{\rm{multiplying}}\,{\mkern 1mu} {\rm{Eq}}{\rm{.}}{\mkern 1mu} {\rm{(3)by}}{\mkern 1mu} {\rm{3,we}}\,{\mkern 1mu} {\rm{get}}\)
\(3{{\rm{H}}_2}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})\)\( \rightleftharpoons \)\(6{\rm{HCl}}({\rm{g}});{\mkern 1mu} {\mkern 1mu} \)
\({\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 \times \Delta {{\rm{H}}_3}{\mkern 1mu} {\mkern 1mu} (4)\)
\({\rm{On}}{\mkern 1mu} \,{\rm{inverting}}\,{\mkern 1mu} {\rm{Eq}}{\rm{.(4),we}}{\mkern 1mu} {\mkern 1mu} {\rm{get}}\)
\({6{\rm{HCl}}({\rm{g}})}\)\( \rightleftharpoons \)\({3{{\rm{H}}_2}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})}\)
\({{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 3 \times \Delta {{\rm{H}}_3}(5)}\)
\({\rm{On}}\,{\mkern 1mu} {\rm{Multiplying}}{\mkern 1mu} \,{\rm{Eq}}{\rm{.(1)}}{\mkern 1mu} \,{\rm{with}}\,{\mkern 1mu} {\rm{(2),we}}\,{\mkern 1mu} {\rm{get}}\)
\(2{\rm{N}}{{\rm{H}}_3} + 6{\rm{C}}{{\rm{l}}_2}\)\( \rightleftharpoons \)\(2{\rm{NC}}{{\rm{l}}_3} + 6{\rm{HCl}}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 2 \times {\rm{\Delta }}{{\rm{H}}_1}(6)\)
\({\rm{On}}\,{\rm{adding}}\,\,{\rm{Eq}}.({\rm{2}}),({\rm{5}}){\rm{and}}({\rm{6}}),{\rm{we}}{\mkern 1mu} \,{\rm{get}}\)
\({{\rm{N}}_2} + 3{\rm{C}}{{\rm{l}}_2}\)\( \rightleftharpoons \)\(2{\rm{NC}}{{\rm{l}}_3};\)
\({{\rm{\Delta }}{{\rm{H}}_{\rm{r}}} = - {\rm{\Delta }}{{\rm{H}}_2} - 3 \times {\rm{\Delta }}{{\rm{H}}_3} - 2 \times {\rm{\Delta }}{{\rm{H}}_1}}\)
\({\therefore {\rm{\Delta }}{{\rm{H}}_{\rm{f}}} = \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{r}}}}}{{\rm{2}}} = - \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{2}}}}}{{\rm{2}}} - \frac{3}{2}{\rm{\Delta }}{{\rm{H}}_3} - {\rm{\Delta }}{{\rm{H}}_1}}\)
\({ = - {\rm{\Delta }}{{\rm{H}}_1} - \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{2}}}}}{{\rm{2}}} - \frac{3}{2}{\rm{\Delta }}{{\rm{H}}_3}}\)

CHXI06:THERMODYNAMICS

369495 In the reaction,
\({\rm{S + }}\frac{{\rm{3}}}{{\rm{2}}}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{3}}}{\rm{ + 2xkJ}}\) and \({\rm{S}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}\frac{{\rm{1}}}{{\rm{2}}}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{3}}}{\rm{ + ykJ}}\)
heat of formation of \(\mathrm{\mathrm{SO}_{2}}\) is

1 \(\mathrm{x-y}\)

2 \(\mathrm{2 x+y}\)

3 \(\mathrm{x+y}\)

4 \(\mathrm{y-2 x}\)

CHXI06:THERMODYNAMICS

369496 Given
\({\rm{C + 2}}\;{\rm{S}} \to {\rm{C}}{{\rm{S}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = + 117}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
\({\rm{C + }}{{\rm{O}}_{\rm{2}}} \to {\rm{C}}{{\rm{O}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = - 393}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
\(\;{\rm{S + }}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = - 297}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
The heat of combustion of
\(\mathrm{\mathrm{CS}_{2}+3 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{SO}_{2}}\) is

1 \(\mathrm{-807 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

2 \(\mathrm{-1104 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

3 \(\mathrm{+1104 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

4 \(\mathrm{+807 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

CHXI06:THERMODYNAMICS

369497 A sample of gas changes from \({{\rm{p}}_{\rm{1}}}{\rm{,}}\) \({{\rm{V}}_{\rm{1}}}\) and \({{\rm{T}}_{\rm{1}}}\) to \({{\rm{p}}_{\rm{2}}}{\rm{,}}\) \({{\rm{V}}_{\rm{2}}}\) and \({{\rm{T}}_{\rm{2}}}\) by one path and then back to \({{\rm{p}}_{\rm{1}}}{\rm{,}}\) \({{\rm{V}}_{\rm{1}}}\) and \({{\rm{T}}_{\rm{1}}}\) by another path. How many of the following must be zero for the gas in this cycle?
\(\Delta {\rm{T}},\Delta \,{\rm{p}},\Delta {\rm{V}},\,\,{\rm{q}}{\rm{.}}\,\,{\rm{W}}\) and \(\Delta \,{\rm{E}},\)

1 1

2 2

3 3

4 4

CHXI06:THERMODYNAMICS

369493 The heat of formation of \(\mathrm{\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}_{(\mathrm{l})}}\) is \({\rm{ - 66}}\,{\rm{k}}\,{\rm{cal/}}\) mol. The heat of combustion of \(\mathrm{\mathrm{CH}_{3} \mathrm{OCH}_{3(\mathrm{~g})}}\) is \({\rm{ - 348}}\,{\rm{k}}\,{\rm{cal/mol}}{\rm{.}}\) \({\rm{\Delta }}{{\rm{H}}_{\rm{f}}}\) for \(\mathrm{\mathrm{H}_{2} \mathrm{O}}\) and \(\mathrm{\mathrm{CO}_{2}}\) are \({\rm{ - 68}}\)\(\mathrm{\mathrm{kcal} / \mathrm{mol}}\) and \({\rm{ - 94}}\,{\rm{k}}\,{\rm{cal/mol}}\), respectively. Then, \(\mathrm{\Delta H}\) for the isomerisation reaction \(\mathrm{\mathrm{CH}_{3} \mathrm{OCH}_{3(\mathrm{~g})}}\) is

1 \({\rm{18}}\,{\rm{k}}\,{\rm{cal/mol}}\)

2 \({\rm{95}}\,{\rm{k}}\,{\rm{cal/mol}}\)

3 \({\rm{22}}\,{\rm{k}}\,{\rm{cal/mol}}\)

4 \({\rm{30}}{\mkern 1mu} {\rm{k}}{\mkern 1mu} {\rm{cal/mol}}\)

CHXI06:THERMODYNAMICS

369494 Given,
\({{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})}\)\( \rightleftharpoons \)\({{\rm{NC}}{{\rm{l}}_3}(\;{\rm{g}}) + 3{\rm{HCl}}({\rm{g}});}\)
\({ - {\rm{\Delta }}{{\rm{H}}_1}}\)
\({{{\rm{N}}_2}({\rm{g}}) + 3{{\rm{H}}_2}({\rm{g}})}\)\( \rightleftharpoons \)\({2{\rm{N}}{{\rm{H}}_3}({\rm{g}});}\)
\({ - {\rm{\Delta }}{{\rm{H}}_2}}\)
\({{\rm{H}}_{\rm{2}}}{\rm{(g)}} + {\rm{C}}{{\rm{l}}_{\rm{2}}}{\rm{(g)}}\)\( \rightleftharpoons \)\(2{\rm{HCl(g)}};\)
\({\rm{\Delta }}{{\rm{H}}_{\rm{3}}}\)
The heat of formation of \(\mathrm{NCl}_{3}(\mathrm{~g})\)
in terms of \(\Delta \mathrm{H}_{1}, \Delta \mathrm{H}_{2}\) and \(\Delta \mathrm{H}_{3}\) is

1 \(\Delta \mathrm{H}_{\mathrm{f}}=-\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}-\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

2 \(\Delta \mathrm{H}_{\mathrm{f}}=\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}-\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

3 \(\Delta \mathrm{H}_{\mathrm{f}}=\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}+\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

4 None of the above

Explanation:

\({\rm{I}}.{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}({\rm{g}})\)\( \rightleftharpoons \)\({\rm{NC}}{{\rm{l}}_3}(\;{\rm{g}}) + 3{\rm{HCl}}({\rm{g}}),\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - {\rm{\Delta }}{{\rm{H}}_1}(1)\)
\({\rm{II}}.{{\rm{N}}_2}({\rm{g}}) + 3{{\rm{H}}_2}({\rm{g}})\)\( \rightleftharpoons \)\(2{\rm{N}}{{\rm{H}}_3}({\rm{g}}),\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - {\rm{\Delta }}{{\rm{H}}_2}(2){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\({\rm{III}}.{{\rm{H}}_2}({\rm{g}}) + {\rm{C}}{{\rm{l}}_2}({\rm{g}})\)\( \rightleftharpoons \)\(2{\rm{HCl}}({\rm{g}}),{\mkern 1mu} {\mkern 1mu} \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{\Delta }}{{\rm{H}}_3}{\mkern 1mu} (3){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\({\rm{On}}{\mkern 1mu} \,{\rm{multiplying}}\,{\mkern 1mu} {\rm{Eq}}{\rm{.}}{\mkern 1mu} {\rm{(3)by}}{\mkern 1mu} {\rm{3,we}}\,{\mkern 1mu} {\rm{get}}\)
\(3{{\rm{H}}_2}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})\)\( \rightleftharpoons \)\(6{\rm{HCl}}({\rm{g}});{\mkern 1mu} {\mkern 1mu} \)
\({\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 \times \Delta {{\rm{H}}_3}{\mkern 1mu} {\mkern 1mu} (4)\)
\({\rm{On}}{\mkern 1mu} \,{\rm{inverting}}\,{\mkern 1mu} {\rm{Eq}}{\rm{.(4),we}}{\mkern 1mu} {\mkern 1mu} {\rm{get}}\)
\({6{\rm{HCl}}({\rm{g}})}\)\( \rightleftharpoons \)\({3{{\rm{H}}_2}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})}\)
\({{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 3 \times \Delta {{\rm{H}}_3}(5)}\)
\({\rm{On}}\,{\mkern 1mu} {\rm{Multiplying}}{\mkern 1mu} \,{\rm{Eq}}{\rm{.(1)}}{\mkern 1mu} \,{\rm{with}}\,{\mkern 1mu} {\rm{(2),we}}\,{\mkern 1mu} {\rm{get}}\)
\(2{\rm{N}}{{\rm{H}}_3} + 6{\rm{C}}{{\rm{l}}_2}\)\( \rightleftharpoons \)\(2{\rm{NC}}{{\rm{l}}_3} + 6{\rm{HCl}}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 2 \times {\rm{\Delta }}{{\rm{H}}_1}(6)\)
\({\rm{On}}\,{\rm{adding}}\,\,{\rm{Eq}}.({\rm{2}}),({\rm{5}}){\rm{and}}({\rm{6}}),{\rm{we}}{\mkern 1mu} \,{\rm{get}}\)
\({{\rm{N}}_2} + 3{\rm{C}}{{\rm{l}}_2}\)\( \rightleftharpoons \)\(2{\rm{NC}}{{\rm{l}}_3};\)
\({{\rm{\Delta }}{{\rm{H}}_{\rm{r}}} = - {\rm{\Delta }}{{\rm{H}}_2} - 3 \times {\rm{\Delta }}{{\rm{H}}_3} - 2 \times {\rm{\Delta }}{{\rm{H}}_1}}\)
\({\therefore {\rm{\Delta }}{{\rm{H}}_{\rm{f}}} = \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{r}}}}}{{\rm{2}}} = - \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{2}}}}}{{\rm{2}}} - \frac{3}{2}{\rm{\Delta }}{{\rm{H}}_3} - {\rm{\Delta }}{{\rm{H}}_1}}\)
\({ = - {\rm{\Delta }}{{\rm{H}}_1} - \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{2}}}}}{{\rm{2}}} - \frac{3}{2}{\rm{\Delta }}{{\rm{H}}_3}}\)

CHXI06:THERMODYNAMICS

369495 In the reaction,
\({\rm{S + }}\frac{{\rm{3}}}{{\rm{2}}}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{3}}}{\rm{ + 2xkJ}}\) and \({\rm{S}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}\frac{{\rm{1}}}{{\rm{2}}}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{3}}}{\rm{ + ykJ}}\)
heat of formation of \(\mathrm{\mathrm{SO}_{2}}\) is

1 \(\mathrm{x-y}\)

2 \(\mathrm{2 x+y}\)

3 \(\mathrm{x+y}\)

4 \(\mathrm{y-2 x}\)

CHXI06:THERMODYNAMICS

369496 Given
\({\rm{C + 2}}\;{\rm{S}} \to {\rm{C}}{{\rm{S}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = + 117}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
\({\rm{C + }}{{\rm{O}}_{\rm{2}}} \to {\rm{C}}{{\rm{O}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = - 393}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
\(\;{\rm{S + }}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = - 297}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
The heat of combustion of
\(\mathrm{\mathrm{CS}_{2}+3 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{SO}_{2}}\) is

1 \(\mathrm{-807 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

2 \(\mathrm{-1104 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

3 \(\mathrm{+1104 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

4 \(\mathrm{+807 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

CHXI06:THERMODYNAMICS

369497 A sample of gas changes from \({{\rm{p}}_{\rm{1}}}{\rm{,}}\) \({{\rm{V}}_{\rm{1}}}\) and \({{\rm{T}}_{\rm{1}}}\) to \({{\rm{p}}_{\rm{2}}}{\rm{,}}\) \({{\rm{V}}_{\rm{2}}}\) and \({{\rm{T}}_{\rm{2}}}\) by one path and then back to \({{\rm{p}}_{\rm{1}}}{\rm{,}}\) \({{\rm{V}}_{\rm{1}}}\) and \({{\rm{T}}_{\rm{1}}}\) by another path. How many of the following must be zero for the gas in this cycle?
\(\Delta {\rm{T}},\Delta \,{\rm{p}},\Delta {\rm{V}},\,\,{\rm{q}}{\rm{.}}\,\,{\rm{W}}\) and \(\Delta \,{\rm{E}},\)

1 1

2 2

3 3

4 4

CHXI06:THERMODYNAMICS

369493 The heat of formation of \(\mathrm{\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}_{(\mathrm{l})}}\) is \({\rm{ - 66}}\,{\rm{k}}\,{\rm{cal/}}\) mol. The heat of combustion of \(\mathrm{\mathrm{CH}_{3} \mathrm{OCH}_{3(\mathrm{~g})}}\) is \({\rm{ - 348}}\,{\rm{k}}\,{\rm{cal/mol}}{\rm{.}}\) \({\rm{\Delta }}{{\rm{H}}_{\rm{f}}}\) for \(\mathrm{\mathrm{H}_{2} \mathrm{O}}\) and \(\mathrm{\mathrm{CO}_{2}}\) are \({\rm{ - 68}}\)\(\mathrm{\mathrm{kcal} / \mathrm{mol}}\) and \({\rm{ - 94}}\,{\rm{k}}\,{\rm{cal/mol}}\), respectively. Then, \(\mathrm{\Delta H}\) for the isomerisation reaction \(\mathrm{\mathrm{CH}_{3} \mathrm{OCH}_{3(\mathrm{~g})}}\) is

1 \({\rm{18}}\,{\rm{k}}\,{\rm{cal/mol}}\)

2 \({\rm{95}}\,{\rm{k}}\,{\rm{cal/mol}}\)

3 \({\rm{22}}\,{\rm{k}}\,{\rm{cal/mol}}\)

4 \({\rm{30}}{\mkern 1mu} {\rm{k}}{\mkern 1mu} {\rm{cal/mol}}\)

CHXI06:THERMODYNAMICS

369494 Given,
\({{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})}\)\( \rightleftharpoons \)\({{\rm{NC}}{{\rm{l}}_3}(\;{\rm{g}}) + 3{\rm{HCl}}({\rm{g}});}\)
\({ - {\rm{\Delta }}{{\rm{H}}_1}}\)
\({{{\rm{N}}_2}({\rm{g}}) + 3{{\rm{H}}_2}({\rm{g}})}\)\( \rightleftharpoons \)\({2{\rm{N}}{{\rm{H}}_3}({\rm{g}});}\)
\({ - {\rm{\Delta }}{{\rm{H}}_2}}\)
\({{\rm{H}}_{\rm{2}}}{\rm{(g)}} + {\rm{C}}{{\rm{l}}_{\rm{2}}}{\rm{(g)}}\)\( \rightleftharpoons \)\(2{\rm{HCl(g)}};\)
\({\rm{\Delta }}{{\rm{H}}_{\rm{3}}}\)
The heat of formation of \(\mathrm{NCl}_{3}(\mathrm{~g})\)
in terms of \(\Delta \mathrm{H}_{1}, \Delta \mathrm{H}_{2}\) and \(\Delta \mathrm{H}_{3}\) is

1 \(\Delta \mathrm{H}_{\mathrm{f}}=-\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}-\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

2 \(\Delta \mathrm{H}_{\mathrm{f}}=\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}-\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

3 \(\Delta \mathrm{H}_{\mathrm{f}}=\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}+\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

4 None of the above

Explanation:

\({\rm{I}}.{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}({\rm{g}})\)\( \rightleftharpoons \)\({\rm{NC}}{{\rm{l}}_3}(\;{\rm{g}}) + 3{\rm{HCl}}({\rm{g}}),\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - {\rm{\Delta }}{{\rm{H}}_1}(1)\)
\({\rm{II}}.{{\rm{N}}_2}({\rm{g}}) + 3{{\rm{H}}_2}({\rm{g}})\)\( \rightleftharpoons \)\(2{\rm{N}}{{\rm{H}}_3}({\rm{g}}),\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - {\rm{\Delta }}{{\rm{H}}_2}(2){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\({\rm{III}}.{{\rm{H}}_2}({\rm{g}}) + {\rm{C}}{{\rm{l}}_2}({\rm{g}})\)\( \rightleftharpoons \)\(2{\rm{HCl}}({\rm{g}}),{\mkern 1mu} {\mkern 1mu} \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{\Delta }}{{\rm{H}}_3}{\mkern 1mu} (3){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\({\rm{On}}{\mkern 1mu} \,{\rm{multiplying}}\,{\mkern 1mu} {\rm{Eq}}{\rm{.}}{\mkern 1mu} {\rm{(3)by}}{\mkern 1mu} {\rm{3,we}}\,{\mkern 1mu} {\rm{get}}\)
\(3{{\rm{H}}_2}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})\)\( \rightleftharpoons \)\(6{\rm{HCl}}({\rm{g}});{\mkern 1mu} {\mkern 1mu} \)
\({\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 \times \Delta {{\rm{H}}_3}{\mkern 1mu} {\mkern 1mu} (4)\)
\({\rm{On}}{\mkern 1mu} \,{\rm{inverting}}\,{\mkern 1mu} {\rm{Eq}}{\rm{.(4),we}}{\mkern 1mu} {\mkern 1mu} {\rm{get}}\)
\({6{\rm{HCl}}({\rm{g}})}\)\( \rightleftharpoons \)\({3{{\rm{H}}_2}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})}\)
\({{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 3 \times \Delta {{\rm{H}}_3}(5)}\)
\({\rm{On}}\,{\mkern 1mu} {\rm{Multiplying}}{\mkern 1mu} \,{\rm{Eq}}{\rm{.(1)}}{\mkern 1mu} \,{\rm{with}}\,{\mkern 1mu} {\rm{(2),we}}\,{\mkern 1mu} {\rm{get}}\)
\(2{\rm{N}}{{\rm{H}}_3} + 6{\rm{C}}{{\rm{l}}_2}\)\( \rightleftharpoons \)\(2{\rm{NC}}{{\rm{l}}_3} + 6{\rm{HCl}}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 2 \times {\rm{\Delta }}{{\rm{H}}_1}(6)\)
\({\rm{On}}\,{\rm{adding}}\,\,{\rm{Eq}}.({\rm{2}}),({\rm{5}}){\rm{and}}({\rm{6}}),{\rm{we}}{\mkern 1mu} \,{\rm{get}}\)
\({{\rm{N}}_2} + 3{\rm{C}}{{\rm{l}}_2}\)\( \rightleftharpoons \)\(2{\rm{NC}}{{\rm{l}}_3};\)
\({{\rm{\Delta }}{{\rm{H}}_{\rm{r}}} = - {\rm{\Delta }}{{\rm{H}}_2} - 3 \times {\rm{\Delta }}{{\rm{H}}_3} - 2 \times {\rm{\Delta }}{{\rm{H}}_1}}\)
\({\therefore {\rm{\Delta }}{{\rm{H}}_{\rm{f}}} = \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{r}}}}}{{\rm{2}}} = - \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{2}}}}}{{\rm{2}}} - \frac{3}{2}{\rm{\Delta }}{{\rm{H}}_3} - {\rm{\Delta }}{{\rm{H}}_1}}\)
\({ = - {\rm{\Delta }}{{\rm{H}}_1} - \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{2}}}}}{{\rm{2}}} - \frac{3}{2}{\rm{\Delta }}{{\rm{H}}_3}}\)

CHXI06:THERMODYNAMICS

369495 In the reaction,
\({\rm{S + }}\frac{{\rm{3}}}{{\rm{2}}}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{3}}}{\rm{ + 2xkJ}}\) and \({\rm{S}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}\frac{{\rm{1}}}{{\rm{2}}}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{3}}}{\rm{ + ykJ}}\)
heat of formation of \(\mathrm{\mathrm{SO}_{2}}\) is

1 \(\mathrm{x-y}\)

2 \(\mathrm{2 x+y}\)

3 \(\mathrm{x+y}\)

4 \(\mathrm{y-2 x}\)

CHXI06:THERMODYNAMICS

369496 Given
\({\rm{C + 2}}\;{\rm{S}} \to {\rm{C}}{{\rm{S}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = + 117}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
\({\rm{C + }}{{\rm{O}}_{\rm{2}}} \to {\rm{C}}{{\rm{O}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = - 393}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
\(\;{\rm{S + }}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = - 297}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
The heat of combustion of
\(\mathrm{\mathrm{CS}_{2}+3 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{SO}_{2}}\) is

1 \(\mathrm{-807 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

2 \(\mathrm{-1104 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

3 \(\mathrm{+1104 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

4 \(\mathrm{+807 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

CHXI06:THERMODYNAMICS

369497 A sample of gas changes from \({{\rm{p}}_{\rm{1}}}{\rm{,}}\) \({{\rm{V}}_{\rm{1}}}\) and \({{\rm{T}}_{\rm{1}}}\) to \({{\rm{p}}_{\rm{2}}}{\rm{,}}\) \({{\rm{V}}_{\rm{2}}}\) and \({{\rm{T}}_{\rm{2}}}\) by one path and then back to \({{\rm{p}}_{\rm{1}}}{\rm{,}}\) \({{\rm{V}}_{\rm{1}}}\) and \({{\rm{T}}_{\rm{1}}}\) by another path. How many of the following must be zero for the gas in this cycle?
\(\Delta {\rm{T}},\Delta \,{\rm{p}},\Delta {\rm{V}},\,\,{\rm{q}}{\rm{.}}\,\,{\rm{W}}\) and \(\Delta \,{\rm{E}},\)

1 1

2 2

3 3

4 4

CHXI06:THERMODYNAMICS

369493 The heat of formation of \(\mathrm{\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}_{(\mathrm{l})}}\) is \({\rm{ - 66}}\,{\rm{k}}\,{\rm{cal/}}\) mol. The heat of combustion of \(\mathrm{\mathrm{CH}_{3} \mathrm{OCH}_{3(\mathrm{~g})}}\) is \({\rm{ - 348}}\,{\rm{k}}\,{\rm{cal/mol}}{\rm{.}}\) \({\rm{\Delta }}{{\rm{H}}_{\rm{f}}}\) for \(\mathrm{\mathrm{H}_{2} \mathrm{O}}\) and \(\mathrm{\mathrm{CO}_{2}}\) are \({\rm{ - 68}}\)\(\mathrm{\mathrm{kcal} / \mathrm{mol}}\) and \({\rm{ - 94}}\,{\rm{k}}\,{\rm{cal/mol}}\), respectively. Then, \(\mathrm{\Delta H}\) for the isomerisation reaction \(\mathrm{\mathrm{CH}_{3} \mathrm{OCH}_{3(\mathrm{~g})}}\) is

1 \({\rm{18}}\,{\rm{k}}\,{\rm{cal/mol}}\)

2 \({\rm{95}}\,{\rm{k}}\,{\rm{cal/mol}}\)

3 \({\rm{22}}\,{\rm{k}}\,{\rm{cal/mol}}\)

4 \({\rm{30}}{\mkern 1mu} {\rm{k}}{\mkern 1mu} {\rm{cal/mol}}\)

CHXI06:THERMODYNAMICS

369494 Given,
\({{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})}\)\( \rightleftharpoons \)\({{\rm{NC}}{{\rm{l}}_3}(\;{\rm{g}}) + 3{\rm{HCl}}({\rm{g}});}\)
\({ - {\rm{\Delta }}{{\rm{H}}_1}}\)
\({{{\rm{N}}_2}({\rm{g}}) + 3{{\rm{H}}_2}({\rm{g}})}\)\( \rightleftharpoons \)\({2{\rm{N}}{{\rm{H}}_3}({\rm{g}});}\)
\({ - {\rm{\Delta }}{{\rm{H}}_2}}\)
\({{\rm{H}}_{\rm{2}}}{\rm{(g)}} + {\rm{C}}{{\rm{l}}_{\rm{2}}}{\rm{(g)}}\)\( \rightleftharpoons \)\(2{\rm{HCl(g)}};\)
\({\rm{\Delta }}{{\rm{H}}_{\rm{3}}}\)
The heat of formation of \(\mathrm{NCl}_{3}(\mathrm{~g})\)
in terms of \(\Delta \mathrm{H}_{1}, \Delta \mathrm{H}_{2}\) and \(\Delta \mathrm{H}_{3}\) is

1 \(\Delta \mathrm{H}_{\mathrm{f}}=-\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}-\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

2 \(\Delta \mathrm{H}_{\mathrm{f}}=\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}-\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

3 \(\Delta \mathrm{H}_{\mathrm{f}}=\Delta \mathrm{H}_{1}+\dfrac{\Delta \mathrm{H}_{2}}{2}+\dfrac{3}{2} \Delta \mathrm{H}_{3}\)

4 None of the above

Explanation:

\({\rm{I}}.{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}({\rm{g}})\)\( \rightleftharpoons \)\({\rm{NC}}{{\rm{l}}_3}(\;{\rm{g}}) + 3{\rm{HCl}}({\rm{g}}),\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - {\rm{\Delta }}{{\rm{H}}_1}(1)\)
\({\rm{II}}.{{\rm{N}}_2}({\rm{g}}) + 3{{\rm{H}}_2}({\rm{g}})\)\( \rightleftharpoons \)\(2{\rm{N}}{{\rm{H}}_3}({\rm{g}}),\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - {\rm{\Delta }}{{\rm{H}}_2}(2){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\({\rm{III}}.{{\rm{H}}_2}({\rm{g}}) + {\rm{C}}{{\rm{l}}_2}({\rm{g}})\)\( \rightleftharpoons \)\(2{\rm{HCl}}({\rm{g}}),{\mkern 1mu} {\mkern 1mu} \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{\Delta }}{{\rm{H}}_3}{\mkern 1mu} (3){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\({\rm{On}}{\mkern 1mu} \,{\rm{multiplying}}\,{\mkern 1mu} {\rm{Eq}}{\rm{.}}{\mkern 1mu} {\rm{(3)by}}{\mkern 1mu} {\rm{3,we}}\,{\mkern 1mu} {\rm{get}}\)
\(3{{\rm{H}}_2}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})\)\( \rightleftharpoons \)\(6{\rm{HCl}}({\rm{g}});{\mkern 1mu} {\mkern 1mu} \)
\({\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 \times \Delta {{\rm{H}}_3}{\mkern 1mu} {\mkern 1mu} (4)\)
\({\rm{On}}{\mkern 1mu} \,{\rm{inverting}}\,{\mkern 1mu} {\rm{Eq}}{\rm{.(4),we}}{\mkern 1mu} {\mkern 1mu} {\rm{get}}\)
\({6{\rm{HCl}}({\rm{g}})}\)\( \rightleftharpoons \)\({3{{\rm{H}}_2}(\;{\rm{g}}) + 3{\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})}\)
\({{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 3 \times \Delta {{\rm{H}}_3}(5)}\)
\({\rm{On}}\,{\mkern 1mu} {\rm{Multiplying}}{\mkern 1mu} \,{\rm{Eq}}{\rm{.(1)}}{\mkern 1mu} \,{\rm{with}}\,{\mkern 1mu} {\rm{(2),we}}\,{\mkern 1mu} {\rm{get}}\)
\(2{\rm{N}}{{\rm{H}}_3} + 6{\rm{C}}{{\rm{l}}_2}\)\( \rightleftharpoons \)\(2{\rm{NC}}{{\rm{l}}_3} + 6{\rm{HCl}}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 2 \times {\rm{\Delta }}{{\rm{H}}_1}(6)\)
\({\rm{On}}\,{\rm{adding}}\,\,{\rm{Eq}}.({\rm{2}}),({\rm{5}}){\rm{and}}({\rm{6}}),{\rm{we}}{\mkern 1mu} \,{\rm{get}}\)
\({{\rm{N}}_2} + 3{\rm{C}}{{\rm{l}}_2}\)\( \rightleftharpoons \)\(2{\rm{NC}}{{\rm{l}}_3};\)
\({{\rm{\Delta }}{{\rm{H}}_{\rm{r}}} = - {\rm{\Delta }}{{\rm{H}}_2} - 3 \times {\rm{\Delta }}{{\rm{H}}_3} - 2 \times {\rm{\Delta }}{{\rm{H}}_1}}\)
\({\therefore {\rm{\Delta }}{{\rm{H}}_{\rm{f}}} = \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{r}}}}}{{\rm{2}}} = - \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{2}}}}}{{\rm{2}}} - \frac{3}{2}{\rm{\Delta }}{{\rm{H}}_3} - {\rm{\Delta }}{{\rm{H}}_1}}\)
\({ = - {\rm{\Delta }}{{\rm{H}}_1} - \frac{{{\rm{\Delta }}{{\rm{H}}_{\rm{2}}}}}{{\rm{2}}} - \frac{3}{2}{\rm{\Delta }}{{\rm{H}}_3}}\)

CHXI06:THERMODYNAMICS

369495 In the reaction,
\({\rm{S + }}\frac{{\rm{3}}}{{\rm{2}}}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{3}}}{\rm{ + 2xkJ}}\) and \({\rm{S}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}\frac{{\rm{1}}}{{\rm{2}}}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{3}}}{\rm{ + ykJ}}\)
heat of formation of \(\mathrm{\mathrm{SO}_{2}}\) is

1 \(\mathrm{x-y}\)

2 \(\mathrm{2 x+y}\)

3 \(\mathrm{x+y}\)

4 \(\mathrm{y-2 x}\)

CHXI06:THERMODYNAMICS

369496 Given
\({\rm{C + 2}}\;{\rm{S}} \to {\rm{C}}{{\rm{S}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = + 117}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
\({\rm{C + }}{{\rm{O}}_{\rm{2}}} \to {\rm{C}}{{\rm{O}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = - 393}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
\(\;{\rm{S + }}{{\rm{O}}_{\rm{2}}} \to {\rm{S}}{{\rm{O}}_{\rm{2}}},{\Delta _{\rm{f}}}{\rm{H}}^\circ {\rm{ = - 297}}.{\rm{0}}\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\)
The heat of combustion of
\(\mathrm{\mathrm{CS}_{2}+3 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{SO}_{2}}\) is

1 \(\mathrm{-807 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

2 \(\mathrm{-1104 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

3 \(\mathrm{+1104 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

4 \(\mathrm{+807 \mathrm{~kJ} \mathrm{~mol}^{-1}}\)

CHXI06:THERMODYNAMICS

369497 A sample of gas changes from \({{\rm{p}}_{\rm{1}}}{\rm{,}}\) \({{\rm{V}}_{\rm{1}}}\) and \({{\rm{T}}_{\rm{1}}}\) to \({{\rm{p}}_{\rm{2}}}{\rm{,}}\) \({{\rm{V}}_{\rm{2}}}\) and \({{\rm{T}}_{\rm{2}}}\) by one path and then back to \({{\rm{p}}_{\rm{1}}}{\rm{,}}\) \({{\rm{V}}_{\rm{1}}}\) and \({{\rm{T}}_{\rm{1}}}\) by another path. How many of the following must be zero for the gas in this cycle?
\(\Delta {\rm{T}},\Delta \,{\rm{p}},\Delta {\rm{V}},\,\,{\rm{q}}{\rm{.}}\,\,{\rm{W}}\) and \(\Delta \,{\rm{E}},\)

1 1

2 2

3 3

4 4