Question

In a certain reaction 10% of the reactant decomposes in one hour, 20% in two hours, 30% in three hours and so on. Dimension of the velocity constant (rate constant) are:
A.$h{r^{ - 1}}$
B.$Mol{L^{ - 1}}h{r^{ - 1}}$
C.$Lmo{l^{ - 1}}{s^{ - 1}}$
D.\[Mol{s^{ - 1}}\]

Answer 1

Hint:We have to know that for a zero-order reaction, increasing the concentration of the reacting species will not speed up the rate of the reaction.
Complete step by step answer:In a certain reaction 10% of the reactant decomposes in one hour, 20% in two hours, 30% in three hours and continues. Since rate is not dependent on concentration, we can say the reaction follows zero order.
A reaction which contains that independent of the reactant(s) concentration is known as zero order reaction. When we increase (or) decrease the reacting species concentration, the rate of the reaction would either slow down (or) speed up.
We can write the rate law for a zero order reaction as,
$Rate = k{\left[ A \right]^ \circ }$
Here, k is the rate constant and A is the concentration of the reactant species.
For the question we can understand that ${t_{1/2}}\alpha a$. The dimension of the reaction will be,
$k = mo{l^{ - 1}}{L^{ - 1}}h{r^{ - 1}}$
For a zero order reaction, we can say $t = \dfrac{x}{k}$ (or) $k = \dfrac{x}{t}$
If take the value of t as 10%, ${t_{10\% }} = 10\min $, x=10
Then k the value of is equal to, $k = \dfrac{{10}}{{10}} = 1mol{L^{ - 1}}{t^{ - 1}}$
If take the value of t as 20%, ${t_{20\% }} = 20\min $, x=20
Then k the value of is equal to, $k = \dfrac{{20}}{{20}} = 1mol{L^{ - 1}}{t^{ - 1}}$
If take the value of t as 30%, ${t_{30\% }} = 30\min $, x=30
Then k the value of is equal to, $k = \dfrac{{30}}{{30}} = 1mol{L^{ - 1}}{t^{ - 1}}$ and it goes on.
Thus, the reaction follows zero-order kinetics.

Therefore, Option (B) is correct.


Note: An alternate method to determine the rate of the reaction is a graphical method. We can plot a graph of percent decomposition to time, and can obtain a straight line plot. The straight line plot indicates the reaction is zero order. The unit of zero order reaction can also be $mol{L^{ - 1}}{\sec ^{ - 1}}$ (or) $M/\sec $. We can find zero-order reactions when a substance that is needed for the reaction to proceed, like a surface or a catalyst, is saturated by the reactants.