Medium
$A$ reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is $(i)$ doubled $(ii)$ reduced to half?
(N/A) Let the initial concentration of the reactant be $[A] = a$.
The rate of reaction is given by $R = k[A]^2 = ka^2$.
$(i)$ If the concentration is doubled,$[A] = 2a$:
$R' = k(2a)^2 = 4ka^2 = 4R$.
Thus,the rate of reaction increases by $4$ times.
$(ii)$ If the concentration is reduced to half,$[A] = \frac{1}{2}a$:
$R'' = k(\frac{1}{2}a)^2 = \frac{1}{4}ka^2 = \frac{1}{4}R$.
Thus,the rate of reaction is reduced to $\frac{1}{4}$ of its initial value.
The rate of reaction is given by $R = k[A]^2 = ka^2$.
$(i)$ If the concentration is doubled,$[A] = 2a$:
$R' = k(2a)^2 = 4ka^2 = 4R$.
Thus,the rate of reaction increases by $4$ times.
$(ii)$ If the concentration is reduced to half,$[A] = \frac{1}{2}a$:
$R'' = k(\frac{1}{2}a)^2 = \frac{1}{4}ka^2 = \frac{1}{4}R$.
Thus,the rate of reaction is reduced to $\frac{1}{4}$ of its initial value.
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Similar Questions
The reaction of hydrogen and iodine monochloride is given as
$H_{2(g)} + 2ICl_{(g)} \to 2HCl_{(g)} + I_{2(g)}$
This reaction is of first order with respect to $H_{2(g)}$ and $ICl_{(g)}$. Which of the following mechanisms is consistent with the given information?
Mechanism $A$:
$H_{2(g)} + 2ICl_{(g)} \to 2HCl_{(g)} + I_{2(g)}$
Mechanism $B$:
$H_{2(g)} + ICl_{(g)} \to HCl_{(g)} + HI_{(g)}$ (Slow)
$HI_{(g)} + ICl_{(g)} \to HCl_{(g)} + I_{2(g)}$ (Fast)
$H_{2(g)} + 2ICl_{(g)} \to 2HCl_{(g)} + I_{2(g)}$
This reaction is of first order with respect to $H_{2(g)}$ and $ICl_{(g)}$. Which of the following mechanisms is consistent with the given information?
Mechanism $A$:
$H_{2(g)} + 2ICl_{(g)} \to 2HCl_{(g)} + I_{2(g)}$
Mechanism $B$:
$H_{2(g)} + ICl_{(g)} \to HCl_{(g)} + HI_{(g)}$ (Slow)
$HI_{(g)} + ICl_{(g)} \to HCl_{(g)} + I_{2(g)}$ (Fast)
Consider the kinetic data given in the following table for the reaction $A + B + C \rightarrow$ Product.
Experiment No.
$[A] \ (mol \ dm^{-3})$
$[B] \ (mol \ dm^{-3})$
$[C] \ (mol \ dm^{-3})$
Rate of reaction $(mol \ dm^{-3} \ s^{-1})$
$1$
$0.2$
$0.1$
$0.1$
$6.0 \times 10^{-5}$
$2$
$0.2$
$0.2$
$0.1$
$6.0 \times 10^{-5}$
$3$
$0.2$
$0.1$
$0.2$
$1.2 \times 10^{-4}$
$4$
$0.3$
$0.1$
$0.1$
$9.0 \times 10^{-5}$
The rate of the reaction for $[A]=0.15 \ mol \ dm^{-3}, [B]=0.25 \ mol \ dm^{-3}$ and $[C]=0.15 \ mol \ dm^{-3}$ is found to be $Y \times 10^{-5} \ mol \ dm^{-3} \ s^{-1}$. The value of $Y$ is . . . . . .
| Experiment No. | $[A] \ (mol \ dm^{-3})$ | $[B] \ (mol \ dm^{-3})$ | $[C] \ (mol \ dm^{-3})$ | Rate of reaction $(mol \ dm^{-3} \ s^{-1})$ |
| $1$ | $0.2$ | $0.1$ | $0.1$ | $6.0 \times 10^{-5}$ |
| $2$ | $0.2$ | $0.2$ | $0.1$ | $6.0 \times 10^{-5}$ |
| $3$ | $0.2$ | $0.1$ | $0.2$ | $1.2 \times 10^{-4}$ |
| $4$ | $0.3$ | $0.1$ | $0.1$ | $9.0 \times 10^{-5}$ |
The rate of the reaction for $[A]=0.15 \ mol \ dm^{-3}, [B]=0.25 \ mol \ dm^{-3}$ and $[C]=0.15 \ mol \ dm^{-3}$ is found to be $Y \times 10^{-5} \ mol \ dm^{-3} \ s^{-1}$. The value of $Y$ is . . . . . .
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