Read the passage carefully and answer the questions.
The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation \( r = k[A]^x[B]^y \), where \( x \) and \( y \) are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is \( x + y \). The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.
If the rate of reaction becomes twenty-seven times upon increasing the concentration of reactant by three times, the order of this reaction is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3
For a reaction with rate \( = k[\mathrm{A}]^{n} \), the rate depends on the concentration raised to the power n, the order of the reaction. If the concentration is multiplied by a factor, the rate is multiplied by that factor raised to the power n:
\( \displaystyle \frac{r_2}{r_1} = \left(\frac{[\mathrm{A}]_2}{[\mathrm{A}]_1}\right)^{n} \)
Here the concentration is made three times and the rate becomes twenty-seven times:
\( \displaystyle 27 = 3^{n} \)
\( \displaystyle 3^{3} = 3^{n} \Rightarrow n = 3 \)
So the reaction is of third order.