| For the reaction \[RX+Mg\xrightarrow[{}]{{}}RMgX\]products it is observed that |
| (1) On doubling the initial concentration of A only the rate of reaction is also doubled and. |
| (2) On doubling the initial concentrations of both A and B there is a change by a factor of 8 in the rate of the reaction. |
| The rate of this reaction is given by [AIPMT (S) 2009] |
A) rate\[\text{mo}{{\text{l}}^{\text{-1}}}\]
B) rate\[\text{mo}{{\text{l}}^{\text{-1}}}\]
C) rate\[\text{mo}{{\text{l}}^{\text{-1}}}\]
D) rate\[\text{mo}{{\text{l}}^{\text{-1}}}\]
Correct Answer: B
Solution :
| [b] For the reaction, \[\underset{\begin{smallmatrix} \text{ }\!\!|\!\!\text{ } \\ \text{H} \end{smallmatrix}}{\overset{\begin{smallmatrix} \text{H} \\ \text{ }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}}\,=\underset{\begin{smallmatrix} \text{ }\!\!|\!\!\text{ } \\ \text{H} \end{smallmatrix}}{\overset{\begin{smallmatrix} \text{H} \\ \text{ }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}}\,+\text{H}-\xrightarrow[{}]{{}}\text{H}-\underset{\begin{smallmatrix} \text{ }\!\!|\!\!\text{ } \\ \text{H} \end{smallmatrix}}{\overset{\begin{smallmatrix} \text{H} \\ \text{ }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}}\,-\underset{\begin{smallmatrix} \text{ }\!\!|\!\!\text{ } \\ \text{H} \end{smallmatrix}}{\overset{\begin{smallmatrix} \text{H} \\ \text{ }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}}\,-\text{H}\]Products |
| On doubling the initial concentration of A only, the rate of reaction is also doubled, therefore |
| Rat\[\text{mo}{{\text{l}}^{\text{-1}}}\] ...(i) |
| Let initially rate law is |
| Rate\[\text{mo}{{\text{l}}^{\text{-1}}}\] ...(ii) |
| If concentration of A and B both are doubled, the rate gets changed by a factor of 8. |
| \[\text{mo}{{\text{l}}^{\text{-1}}}\] (iii) |
| \[\text{mo}{{\text{l}}^{\text{-1}}}\] |
| Dividing Eq. (iii) by Eq. (ii), |
| \[1.77\times {{10}^{-5}}\] |
| \[5.65\times {{10}^{-10}}\] |
| \[6.50\times {{10}^{-12}}\]\[5.65\times {{10}^{-13}}\] |
| Hence, rate law is, rate\[5.65\times {{10}^{-12}}\] |
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