Question

From the data given below, determine the rate expression and calculate the rate constant for the reaction. $A\to 2B$

[A] (mol/L)	rate (mol/L.s)
0.250	$3.40\times {10}^2$
0.500	$1.36\times {10}^3$
1.00	$5.44\times {10}^3$

• A. Rate = $5.44\times {10}^3{\left[A\right]}^2$
• B. Rate = $1.36\times {10}^3{\left[A\right]}^2$
• C. Rate = $5.44\times {10}^3\left[A\right]$
• D. Rate = $1.36\times {10}^3\left[A\right]$

Answer 1

The correct option is A Rate = $5.44\times {10}^3{\left[A\right]}^2$

When$\left[A\right]$ is doubled from $0.250$ M to $0.500$ M, the rate increases four times from $3.40\times {10}^2$ to $1.36\times {10}^3$. Hence, the order of the reaction with respect to $A$ is $2$.

Similarly, when $\left[A\right]$ is doubled from $0.500$ M to $1.00$ M, the rate increases four times from $1.36\times {10}^3$ to $5.44\times {10}^3$. Hence, the order of the reaction with respect to $A$ is $2$.

The rate expression is ,

$rate=k[A{]}^2$

When $\left[A\right]=1.00$ M, rate is $5.44\times {10}^3$.

Substitute this in rate expression.

$5.44\times {10}^3=k(1.00{)}^2$.

Hence, the rate constant $k=5.44\times {10}^{3}L/mol/s$