Question

In the chemical reaction A $\rightarrow$ B, what is the order of the reaction? Given that, the rate of reaction doubles if the concentration of A is increased four times.

• A. 2
• B. 1.5
• C. 0.5
• D. 1

Hint:

The order of a reaction can be determined experimentally using the given rate conditions by applying logarithmic methods to compare relative rate changes.

Answer 1

The Correct Option is C

Step 1: Rate Law Definition
The reaction rate is defined as: \[ r = k[A]^n \] where \( k \) represents the rate constant, \( [A] \) denotes the reactant concentration, and \( n \) signifies the reaction order.
Step 2: Incorporating Given Data 
When reactant \( A \)'s concentration quadruples, the reaction rate doubles. This can be expressed as: \[ 2r_1 = k[4A]^n \] The initial rate equation is: \[ r_1 = k[A]^n \] 
Step 3: Equation Division 
Dividing the two equations yields: \[ \frac{2r_1}{r_1} = \frac{k(4[A])^n}{k[A]^n} \] This simplifies to: \[ 2 = 4^n \] 
Step 4: Determining Reaction Order 
Applying logarithms to both sides: \[ \log 2 = n \log 4 \] Substituting \( \log 4 = 2 \log 2 \): \[ \log 2 = n (2 \log 2) \] Solving for \( n \): \[ n = \frac{\log 2}{2 \log 2} = \frac{1}{2} = 0.5 \] 
Final Determination: The reaction order is 0.5.