Question

The conversion of molecule X to Y follows second order kinetics. If the concentration of X is increased to three times then the rate of formation of Y will be:
A) Increased by 8 times.
B) Increased by 9 times.
C) Increased by 6 times.
D) Decreased by 8 times.

Answer 1

Hint: The answer to this question lies in the fact that the rate of a reaction is directly proportional to the concentration of the reactants and this fact will lead you to the correct answer.

Complete step by step solution:
We have studied about the thermodynamics chapter that comes under the physical chemistry part that basically deals with the rate of a reaction and also the parameters that are associated with the rate like, temperature, concentration, enthalpy etc.
Now, let us go through what is the meaning of the order of the reaction and deduce the correct answer.
- Order of a reaction is the power dependence of the rate on the concentrations of each of the reactants.
- For first order reactions, the rate of reaction is dependent on the concentration of one reactant.
- Order of a reaction is determined by adding up the powers of the concentration of reactants that yields the product and the concentration is independent for the molecules like water that do not participate in the reaction.
- Now, in the above question since the order of reaction is second order the concentration of species X will be according to rate law as,
$Rate=k{{[X]}^{2}}={{r}_{1}}$……(1)
And now, if concentration is increased to three times that is 3X then the rate law becomes,
${{r}_{2}}=k{{[3X]}^{2}}=9{{[X]}^{2}}$……..(2)
Now, the ratio will be$\dfrac{{{r}_{2}}}{{{r}_{1}}}=\dfrac{9k{{[X]}^{2}}}{k{{[X]}^{2}}}$
\[\Rightarrow \dfrac{{{r}_{2}}}{{{r}_{1}}}=9\]
Therefore, ${{r}_{2}}=9{{r}_{1}}$
This means that the rate of reaction becomes nine times from the actual rate of reaction.

This implies that the rate of formation of $Y[X\to Y]$ will be nine times if the concentration is increased to three times. So the answer is option (B).

Note: Order of a reaction and molecularity of reaction are two different entities and do not be confused because order of reaction is dependent on the total concentration of the reactant and molecularity is the total molecules involved in the reaction even if it does not take part in chemical reaction.