Integrated Rate Equations
CHXII04:CHEMICAL KINETICS

320322 In a first order reaction the \(\frac{{\rm{a}}}{{{\rm{a - x}}}}\) was found to be 9 after 10 minute. The rate constant is

1 \(\dfrac{3 \times 2.303}{10} \log 2\)
2 \(\dfrac{2.303 \times 2}{10} \log 3\)
3 \(\dfrac{3 \ln 2}{10}\)
4 Both (1) and (3)
CHXII04:CHEMICAL KINETICS

320323 For a homogeneous gaseous reaction \({\rm{A}} \to {\rm{B}} + {\rm{C}} + {\rm{D}}\), the initial pressure was \({{\rm{P}}_{\rm{0}}}\) while pressure after time 't' was P if \(\left( {{\rm{P > }}{{\rm{P}}_{\rm{0}}}} \right)\). The expression for the rate constant k is

1 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{2}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{3}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
2 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{3}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{2}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
3 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{{\rm{P}}_{\rm{0}}}}}{{{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
4 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{2}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{4}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
CHXII04:CHEMICAL KINETICS

320324 The decomposition of a substance follows first order kinetics. If its concentration is reduced to 1/8th of its initial value, in 24 minutes, the rate constant of decomposition process is

1 \(\frac{{\rm{1}}}{{{\rm{24}}}}{\rm{mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
2 \(\frac{{{\rm{0}}{\rm{.692}}}}{{{\rm{24}}}}{\rm{\;mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
3 \(\left( {\frac{{{\rm{2}}{\rm{.303}}}}{{{\rm{24}}}}} \right){\rm{log}}\left( {\frac{{\rm{1}}}{{\rm{8}}}} \right){\rm{mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
4 \(\left( {\frac{{{\rm{2}}{\rm{.303}}}}{{{\rm{24}}}}} \right){\rm{log(8)mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
CHXII04:CHEMICAL KINETICS

320325 A first order reaction is \(20 \%\) complete in 10 minutes. The rate constant of the reaction is

1 \(0.223 \mathrm{~min}^{-1}\)
2 \(0.0223 \mathrm{~min}^{-1}\)
3 \(2.23 \mathrm{~min}^{-1}\)
4 \(22.3 \mathrm{~min}^{-1}\)
CHXII04:CHEMICAL KINETICS

320322 In a first order reaction the \(\frac{{\rm{a}}}{{{\rm{a - x}}}}\) was found to be 9 after 10 minute. The rate constant is

1 \(\dfrac{3 \times 2.303}{10} \log 2\)
2 \(\dfrac{2.303 \times 2}{10} \log 3\)
3 \(\dfrac{3 \ln 2}{10}\)
4 Both (1) and (3)
CHXII04:CHEMICAL KINETICS

320323 For a homogeneous gaseous reaction \({\rm{A}} \to {\rm{B}} + {\rm{C}} + {\rm{D}}\), the initial pressure was \({{\rm{P}}_{\rm{0}}}\) while pressure after time 't' was P if \(\left( {{\rm{P > }}{{\rm{P}}_{\rm{0}}}} \right)\). The expression for the rate constant k is

1 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{2}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{3}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
2 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{3}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{2}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
3 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{{\rm{P}}_{\rm{0}}}}}{{{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
4 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{2}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{4}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
CHXII04:CHEMICAL KINETICS

320324 The decomposition of a substance follows first order kinetics. If its concentration is reduced to 1/8th of its initial value, in 24 minutes, the rate constant of decomposition process is

1 \(\frac{{\rm{1}}}{{{\rm{24}}}}{\rm{mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
2 \(\frac{{{\rm{0}}{\rm{.692}}}}{{{\rm{24}}}}{\rm{\;mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
3 \(\left( {\frac{{{\rm{2}}{\rm{.303}}}}{{{\rm{24}}}}} \right){\rm{log}}\left( {\frac{{\rm{1}}}{{\rm{8}}}} \right){\rm{mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
4 \(\left( {\frac{{{\rm{2}}{\rm{.303}}}}{{{\rm{24}}}}} \right){\rm{log(8)mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
CHXII04:CHEMICAL KINETICS

320325 A first order reaction is \(20 \%\) complete in 10 minutes. The rate constant of the reaction is

1 \(0.223 \mathrm{~min}^{-1}\)
2 \(0.0223 \mathrm{~min}^{-1}\)
3 \(2.23 \mathrm{~min}^{-1}\)
4 \(22.3 \mathrm{~min}^{-1}\)
CHXII04:CHEMICAL KINETICS

320322 In a first order reaction the \(\frac{{\rm{a}}}{{{\rm{a - x}}}}\) was found to be 9 after 10 minute. The rate constant is

1 \(\dfrac{3 \times 2.303}{10} \log 2\)
2 \(\dfrac{2.303 \times 2}{10} \log 3\)
3 \(\dfrac{3 \ln 2}{10}\)
4 Both (1) and (3)
CHXII04:CHEMICAL KINETICS

320323 For a homogeneous gaseous reaction \({\rm{A}} \to {\rm{B}} + {\rm{C}} + {\rm{D}}\), the initial pressure was \({{\rm{P}}_{\rm{0}}}\) while pressure after time 't' was P if \(\left( {{\rm{P > }}{{\rm{P}}_{\rm{0}}}} \right)\). The expression for the rate constant k is

1 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{2}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{3}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
2 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{3}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{2}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
3 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{{\rm{P}}_{\rm{0}}}}}{{{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
4 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{2}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{4}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
CHXII04:CHEMICAL KINETICS

320324 The decomposition of a substance follows first order kinetics. If its concentration is reduced to 1/8th of its initial value, in 24 minutes, the rate constant of decomposition process is

1 \(\frac{{\rm{1}}}{{{\rm{24}}}}{\rm{mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
2 \(\frac{{{\rm{0}}{\rm{.692}}}}{{{\rm{24}}}}{\rm{\;mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
3 \(\left( {\frac{{{\rm{2}}{\rm{.303}}}}{{{\rm{24}}}}} \right){\rm{log}}\left( {\frac{{\rm{1}}}{{\rm{8}}}} \right){\rm{mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
4 \(\left( {\frac{{{\rm{2}}{\rm{.303}}}}{{{\rm{24}}}}} \right){\rm{log(8)mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
CHXII04:CHEMICAL KINETICS

320325 A first order reaction is \(20 \%\) complete in 10 minutes. The rate constant of the reaction is

1 \(0.223 \mathrm{~min}^{-1}\)
2 \(0.0223 \mathrm{~min}^{-1}\)
3 \(2.23 \mathrm{~min}^{-1}\)
4 \(22.3 \mathrm{~min}^{-1}\)
CHXII04:CHEMICAL KINETICS

320322 In a first order reaction the \(\frac{{\rm{a}}}{{{\rm{a - x}}}}\) was found to be 9 after 10 minute. The rate constant is

1 \(\dfrac{3 \times 2.303}{10} \log 2\)
2 \(\dfrac{2.303 \times 2}{10} \log 3\)
3 \(\dfrac{3 \ln 2}{10}\)
4 Both (1) and (3)
CHXII04:CHEMICAL KINETICS

320323 For a homogeneous gaseous reaction \({\rm{A}} \to {\rm{B}} + {\rm{C}} + {\rm{D}}\), the initial pressure was \({{\rm{P}}_{\rm{0}}}\) while pressure after time 't' was P if \(\left( {{\rm{P > }}{{\rm{P}}_{\rm{0}}}} \right)\). The expression for the rate constant k is

1 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{2}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{3}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
2 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{3}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{2}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
3 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{{\rm{P}}_{\rm{0}}}}}{{{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
4 \({\rm{k = }}\frac{{{\rm{2}}{\rm{.303}}}}{{\rm{t}}}{\rm{log}}\left( {\frac{{{\rm{2}}{{\rm{P}}_{\rm{0}}}}}{{{\rm{4}}{{\rm{P}}_{\rm{0}}}{\rm{ - P}}}}} \right)\)
CHXII04:CHEMICAL KINETICS

320324 The decomposition of a substance follows first order kinetics. If its concentration is reduced to 1/8th of its initial value, in 24 minutes, the rate constant of decomposition process is

1 \(\frac{{\rm{1}}}{{{\rm{24}}}}{\rm{mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
2 \(\frac{{{\rm{0}}{\rm{.692}}}}{{{\rm{24}}}}{\rm{\;mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
3 \(\left( {\frac{{{\rm{2}}{\rm{.303}}}}{{{\rm{24}}}}} \right){\rm{log}}\left( {\frac{{\rm{1}}}{{\rm{8}}}} \right){\rm{mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
4 \(\left( {\frac{{{\rm{2}}{\rm{.303}}}}{{{\rm{24}}}}} \right){\rm{log(8)mi}}{{\rm{n}}^{{\rm{ - 1}}}}\)
CHXII04:CHEMICAL KINETICS

320325 A first order reaction is \(20 \%\) complete in 10 minutes. The rate constant of the reaction is

1 \(0.223 \mathrm{~min}^{-1}\)
2 \(0.0223 \mathrm{~min}^{-1}\)
3 \(2.23 \mathrm{~min}^{-1}\)
4 \(22.3 \mathrm{~min}^{-1}\)