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CHXII04:CHEMICAL KINETICS

320519 For a reaction, the dimensions of rate constant are same as that of rate, hence order of reaction is

1 0

2 1

3 2

4 3

CHXII04:CHEMICAL KINETICS

320520 What will be the order of reaction and rate constant for a chemical change having \({\text{log}}\,{{\text{t}}_{{\text{50\% }}}}\) versus log concentration of ( 1\()\) curves as?
supporting img

1 \(0, \dfrac{1}{2}\)

2 1,1

3 2,2

4 3,1

CHXII04:CHEMICAL KINETICS

320521 For the reaction \({\mathrm{A+2 B \longrightarrow C}}\), the reaction rate is doubled if the concentration of A is doubled. The rate is increased by four times when concentrations of both A and B are increased by four times. The order of the reaction is ____.

1 1

2 \( - 1\)

3 0

4 2

Explanation:

Rate of the given reaction is doubled when concentration of ' A ' is doubled and it is quadrupled when concentrations of ' A ' and ' B ' are raised four times.
Let the rate, \({\rm{R = k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\,\,\,\,(1)\)
\({\mathrm{\therefore}}\) When concentration of \({\mathrm{A}}\) is doubled, the new rate \({\mathrm{\left(R_{1}\right)}}\) will be
\({{\rm{R}}_{\rm{1}}}{\rm{ = k}}{[{\rm{2A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\)
But \({\mathrm{\mathrm{R}_{1}=2 \mathrm{R}}}\)
\(\therefore \,\,\,{\rm{k}}{[{\rm{2A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}{\rm{ = 2k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\mkern 1mu} [{\rm{From(1)}}{\mkern 1mu} {\rm{and }}({\rm{2}})]\)
\({\mathrm{\therefore k 2^{\mathrm{x}}[A]^{\mathrm{x}}[B]^{\mathrm{y}}=2 \mathrm{k}[\mathrm{A}]^{\mathrm{x}}[B]^{\mathrm{y}}}}\)
\({\mathrm{\therefore \quad 2^{x}=2}}\) and thus \({\mathrm{x=1}}\)
Similarly, when concentrations of both \({\mathrm{A}}\) and \({\mathrm{B}}\) are quadrupled, the new rate \({\mathrm{\left(\mathrm{R}_{2}\right)}}\) will be\({{\rm{R}}_{\rm{2}}}{\rm{ = k}}{[{\rm{4}}\;{\rm{A}}]^{\rm{x}}}{[{\rm{4}}\;{\rm{B}}]^{\rm{y}}}\,\,\,\,\,\,\,\,\,\,\,\,(3)\)
But \({\mathrm{\mathrm{R}_{2}=4 \mathrm{R}}}\)
\(\therefore \,\,{\rm{k}}{[{\rm{4}}\;{\rm{A}}]^{\rm{x}}}{[{\rm{4}}\;{\rm{B}}]^{\rm{y}}}{\rm{ = 4k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\quad \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[From(1)\,and\,(3)]\)
\({\mathrm{K 4^{x}[A]^{x} 4^{y}[B]^{y}=4 k[A]^{x}[B]^{y}}}\)
\({\mathrm{\therefore 4^{x} \cdot 4^{y}=4}}\)
\({\mathrm{\therefore \quad 4.4^{\mathrm{y}}=4 \quad(\because \mathrm{x}=1)}}\)
\({\mathrm{\therefore \quad 4^{y}=1}}\) and thus \({\mathrm{y=0}}\)
Substituting the values of \({\mathrm{x}}\) and \({\mathrm{y}}\) in (1), the rate expression for the given reaction is
rate, \({\mathrm{\mathrm{R}=\mathrm{k}[\mathrm{A}]^{1}[\mathrm{~B}]^{0} \quad \therefore \quad \mathrm{R}=\mathrm{k}[\mathrm{A}]}}\)
Thus, the overall order of the given reaction is 1 .

CHXII04:CHEMICAL KINETICS

320522 \(\mathrm{A}+\mathrm{B} \rightarrow\) Product, \(\frac{{{\text{dx}}}}{{{\text{dt}}}} = {\text{k}}{[{\text{A}}]^{\text{a}}}{[{\text{B}}]^{\text{b}}}\). If \(\left( {\frac{{{\rm{dx}}}}{{{\rm{dt}}}}} \right) = {\rm{k}},\) then order of reaction is

1 4

2 3

3 1

4 0

CHXII04:CHEMICAL KINETICS

320519 For a reaction, the dimensions of rate constant are same as that of rate, hence order of reaction is

1 0

2 1

3 2

4 3

CHXII04:CHEMICAL KINETICS

320520 What will be the order of reaction and rate constant for a chemical change having \({\text{log}}\,{{\text{t}}_{{\text{50\% }}}}\) versus log concentration of ( 1\()\) curves as?
supporting img

1 \(0, \dfrac{1}{2}\)

2 1,1

3 2,2

4 3,1

CHXII04:CHEMICAL KINETICS

320521 For the reaction \({\mathrm{A+2 B \longrightarrow C}}\), the reaction rate is doubled if the concentration of A is doubled. The rate is increased by four times when concentrations of both A and B are increased by four times. The order of the reaction is ____.

1 1

2 \( - 1\)

3 0

4 2

Explanation:

Rate of the given reaction is doubled when concentration of ' A ' is doubled and it is quadrupled when concentrations of ' A ' and ' B ' are raised four times.
Let the rate, \({\rm{R = k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\,\,\,\,(1)\)
\({\mathrm{\therefore}}\) When concentration of \({\mathrm{A}}\) is doubled, the new rate \({\mathrm{\left(R_{1}\right)}}\) will be
\({{\rm{R}}_{\rm{1}}}{\rm{ = k}}{[{\rm{2A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\)
But \({\mathrm{\mathrm{R}_{1}=2 \mathrm{R}}}\)
\(\therefore \,\,\,{\rm{k}}{[{\rm{2A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}{\rm{ = 2k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\mkern 1mu} [{\rm{From(1)}}{\mkern 1mu} {\rm{and }}({\rm{2}})]\)
\({\mathrm{\therefore k 2^{\mathrm{x}}[A]^{\mathrm{x}}[B]^{\mathrm{y}}=2 \mathrm{k}[\mathrm{A}]^{\mathrm{x}}[B]^{\mathrm{y}}}}\)
\({\mathrm{\therefore \quad 2^{x}=2}}\) and thus \({\mathrm{x=1}}\)
Similarly, when concentrations of both \({\mathrm{A}}\) and \({\mathrm{B}}\) are quadrupled, the new rate \({\mathrm{\left(\mathrm{R}_{2}\right)}}\) will be\({{\rm{R}}_{\rm{2}}}{\rm{ = k}}{[{\rm{4}}\;{\rm{A}}]^{\rm{x}}}{[{\rm{4}}\;{\rm{B}}]^{\rm{y}}}\,\,\,\,\,\,\,\,\,\,\,\,(3)\)
But \({\mathrm{\mathrm{R}_{2}=4 \mathrm{R}}}\)
\(\therefore \,\,{\rm{k}}{[{\rm{4}}\;{\rm{A}}]^{\rm{x}}}{[{\rm{4}}\;{\rm{B}}]^{\rm{y}}}{\rm{ = 4k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\quad \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[From(1)\,and\,(3)]\)
\({\mathrm{K 4^{x}[A]^{x} 4^{y}[B]^{y}=4 k[A]^{x}[B]^{y}}}\)
\({\mathrm{\therefore 4^{x} \cdot 4^{y}=4}}\)
\({\mathrm{\therefore \quad 4.4^{\mathrm{y}}=4 \quad(\because \mathrm{x}=1)}}\)
\({\mathrm{\therefore \quad 4^{y}=1}}\) and thus \({\mathrm{y=0}}\)
Substituting the values of \({\mathrm{x}}\) and \({\mathrm{y}}\) in (1), the rate expression for the given reaction is
rate, \({\mathrm{\mathrm{R}=\mathrm{k}[\mathrm{A}]^{1}[\mathrm{~B}]^{0} \quad \therefore \quad \mathrm{R}=\mathrm{k}[\mathrm{A}]}}\)
Thus, the overall order of the given reaction is 1 .

CHXII04:CHEMICAL KINETICS

320522 \(\mathrm{A}+\mathrm{B} \rightarrow\) Product, \(\frac{{{\text{dx}}}}{{{\text{dt}}}} = {\text{k}}{[{\text{A}}]^{\text{a}}}{[{\text{B}}]^{\text{b}}}\). If \(\left( {\frac{{{\rm{dx}}}}{{{\rm{dt}}}}} \right) = {\rm{k}},\) then order of reaction is

1 4

2 3

3 1

4 0

CHXII04:CHEMICAL KINETICS

320519 For a reaction, the dimensions of rate constant are same as that of rate, hence order of reaction is

1 0

2 1

3 2

4 3

CHXII04:CHEMICAL KINETICS

320520 What will be the order of reaction and rate constant for a chemical change having \({\text{log}}\,{{\text{t}}_{{\text{50\% }}}}\) versus log concentration of ( 1\()\) curves as?
supporting img

1 \(0, \dfrac{1}{2}\)

2 1,1

3 2,2

4 3,1

CHXII04:CHEMICAL KINETICS

320521 For the reaction \({\mathrm{A+2 B \longrightarrow C}}\), the reaction rate is doubled if the concentration of A is doubled. The rate is increased by four times when concentrations of both A and B are increased by four times. The order of the reaction is ____.

1 1

2 \( - 1\)

3 0

4 2

Explanation:

Rate of the given reaction is doubled when concentration of ' A ' is doubled and it is quadrupled when concentrations of ' A ' and ' B ' are raised four times.
Let the rate, \({\rm{R = k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\,\,\,\,(1)\)
\({\mathrm{\therefore}}\) When concentration of \({\mathrm{A}}\) is doubled, the new rate \({\mathrm{\left(R_{1}\right)}}\) will be
\({{\rm{R}}_{\rm{1}}}{\rm{ = k}}{[{\rm{2A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\)
But \({\mathrm{\mathrm{R}_{1}=2 \mathrm{R}}}\)
\(\therefore \,\,\,{\rm{k}}{[{\rm{2A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}{\rm{ = 2k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\mkern 1mu} [{\rm{From(1)}}{\mkern 1mu} {\rm{and }}({\rm{2}})]\)
\({\mathrm{\therefore k 2^{\mathrm{x}}[A]^{\mathrm{x}}[B]^{\mathrm{y}}=2 \mathrm{k}[\mathrm{A}]^{\mathrm{x}}[B]^{\mathrm{y}}}}\)
\({\mathrm{\therefore \quad 2^{x}=2}}\) and thus \({\mathrm{x=1}}\)
Similarly, when concentrations of both \({\mathrm{A}}\) and \({\mathrm{B}}\) are quadrupled, the new rate \({\mathrm{\left(\mathrm{R}_{2}\right)}}\) will be\({{\rm{R}}_{\rm{2}}}{\rm{ = k}}{[{\rm{4}}\;{\rm{A}}]^{\rm{x}}}{[{\rm{4}}\;{\rm{B}}]^{\rm{y}}}\,\,\,\,\,\,\,\,\,\,\,\,(3)\)
But \({\mathrm{\mathrm{R}_{2}=4 \mathrm{R}}}\)
\(\therefore \,\,{\rm{k}}{[{\rm{4}}\;{\rm{A}}]^{\rm{x}}}{[{\rm{4}}\;{\rm{B}}]^{\rm{y}}}{\rm{ = 4k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\quad \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[From(1)\,and\,(3)]\)
\({\mathrm{K 4^{x}[A]^{x} 4^{y}[B]^{y}=4 k[A]^{x}[B]^{y}}}\)
\({\mathrm{\therefore 4^{x} \cdot 4^{y}=4}}\)
\({\mathrm{\therefore \quad 4.4^{\mathrm{y}}=4 \quad(\because \mathrm{x}=1)}}\)
\({\mathrm{\therefore \quad 4^{y}=1}}\) and thus \({\mathrm{y=0}}\)
Substituting the values of \({\mathrm{x}}\) and \({\mathrm{y}}\) in (1), the rate expression for the given reaction is
rate, \({\mathrm{\mathrm{R}=\mathrm{k}[\mathrm{A}]^{1}[\mathrm{~B}]^{0} \quad \therefore \quad \mathrm{R}=\mathrm{k}[\mathrm{A}]}}\)
Thus, the overall order of the given reaction is 1 .

CHXII04:CHEMICAL KINETICS

320522 \(\mathrm{A}+\mathrm{B} \rightarrow\) Product, \(\frac{{{\text{dx}}}}{{{\text{dt}}}} = {\text{k}}{[{\text{A}}]^{\text{a}}}{[{\text{B}}]^{\text{b}}}\). If \(\left( {\frac{{{\rm{dx}}}}{{{\rm{dt}}}}} \right) = {\rm{k}},\) then order of reaction is

1 4

2 3

3 1

4 0

CHXII04:CHEMICAL KINETICS

320519 For a reaction, the dimensions of rate constant are same as that of rate, hence order of reaction is

1 0

2 1

3 2

4 3

CHXII04:CHEMICAL KINETICS

320520 What will be the order of reaction and rate constant for a chemical change having \({\text{log}}\,{{\text{t}}_{{\text{50\% }}}}\) versus log concentration of ( 1\()\) curves as?
supporting img

1 \(0, \dfrac{1}{2}\)

2 1,1

3 2,2

4 3,1

CHXII04:CHEMICAL KINETICS

320521 For the reaction \({\mathrm{A+2 B \longrightarrow C}}\), the reaction rate is doubled if the concentration of A is doubled. The rate is increased by four times when concentrations of both A and B are increased by four times. The order of the reaction is ____.

1 1

2 \( - 1\)

3 0

4 2

Explanation:

Rate of the given reaction is doubled when concentration of ' A ' is doubled and it is quadrupled when concentrations of ' A ' and ' B ' are raised four times.
Let the rate, \({\rm{R = k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\,\,\,\,(1)\)
\({\mathrm{\therefore}}\) When concentration of \({\mathrm{A}}\) is doubled, the new rate \({\mathrm{\left(R_{1}\right)}}\) will be
\({{\rm{R}}_{\rm{1}}}{\rm{ = k}}{[{\rm{2A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\)
But \({\mathrm{\mathrm{R}_{1}=2 \mathrm{R}}}\)
\(\therefore \,\,\,{\rm{k}}{[{\rm{2A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}{\rm{ = 2k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\mkern 1mu} [{\rm{From(1)}}{\mkern 1mu} {\rm{and }}({\rm{2}})]\)
\({\mathrm{\therefore k 2^{\mathrm{x}}[A]^{\mathrm{x}}[B]^{\mathrm{y}}=2 \mathrm{k}[\mathrm{A}]^{\mathrm{x}}[B]^{\mathrm{y}}}}\)
\({\mathrm{\therefore \quad 2^{x}=2}}\) and thus \({\mathrm{x=1}}\)
Similarly, when concentrations of both \({\mathrm{A}}\) and \({\mathrm{B}}\) are quadrupled, the new rate \({\mathrm{\left(\mathrm{R}_{2}\right)}}\) will be\({{\rm{R}}_{\rm{2}}}{\rm{ = k}}{[{\rm{4}}\;{\rm{A}}]^{\rm{x}}}{[{\rm{4}}\;{\rm{B}}]^{\rm{y}}}\,\,\,\,\,\,\,\,\,\,\,\,(3)\)
But \({\mathrm{\mathrm{R}_{2}=4 \mathrm{R}}}\)
\(\therefore \,\,{\rm{k}}{[{\rm{4}}\;{\rm{A}}]^{\rm{x}}}{[{\rm{4}}\;{\rm{B}}]^{\rm{y}}}{\rm{ = 4k}}{[{\rm{A}}]^{\rm{x}}}{[{\rm{B}}]^{\rm{y}}}\quad \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[From(1)\,and\,(3)]\)
\({\mathrm{K 4^{x}[A]^{x} 4^{y}[B]^{y}=4 k[A]^{x}[B]^{y}}}\)
\({\mathrm{\therefore 4^{x} \cdot 4^{y}=4}}\)
\({\mathrm{\therefore \quad 4.4^{\mathrm{y}}=4 \quad(\because \mathrm{x}=1)}}\)
\({\mathrm{\therefore \quad 4^{y}=1}}\) and thus \({\mathrm{y=0}}\)
Substituting the values of \({\mathrm{x}}\) and \({\mathrm{y}}\) in (1), the rate expression for the given reaction is
rate, \({\mathrm{\mathrm{R}=\mathrm{k}[\mathrm{A}]^{1}[\mathrm{~B}]^{0} \quad \therefore \quad \mathrm{R}=\mathrm{k}[\mathrm{A}]}}\)
Thus, the overall order of the given reaction is 1 .

CHXII04:CHEMICAL KINETICS

320522 \(\mathrm{A}+\mathrm{B} \rightarrow\) Product, \(\frac{{{\text{dx}}}}{{{\text{dt}}}} = {\text{k}}{[{\text{A}}]^{\text{a}}}{[{\text{B}}]^{\text{b}}}\). If \(\left( {\frac{{{\rm{dx}}}}{{{\rm{dt}}}}} \right) = {\rm{k}},\) then order of reaction is

1 4

2 3

3 1

4 0