Question

Consider a first order reaction 𝐴 → 𝐵. The initial concentration of 𝐴 is $100 mol L^{-1}$ and the value of first order rate constant is 0.01 $min^{-1}$. The concentration of 𝐴 after 10 min of reaction is ____ $ mol L^{-1}$ (rounded off to one decimal place).

Answer 1

Correct Answer: 90.4

To determine the concentration of 𝐴 after 10 minutes for a first order reaction 𝐴 → 𝐵, we utilize the integrated rate equation for a first order reaction: 
[A] = [A]₀e^-kt.  
Here, [A]₀ is the initial concentration, k is the rate constant, and t is the time. Given: [A]₀ = 100 mol L^-1, k = 0.01 min^-1, and t = 10 min. 
Substituting into the formula: [A] = 100 e^-0.01×10 = 100 e^-0.1. 
Calculating e^-0.1 ≈ 0.9048. 
Thus, [A] = 100 × 0.9048 = 90.48 mol L^-1. 
Rounding off to one decimal place, the concentration of 𝐴 after 10 min is 90.5 mol L^-1. 
This value is verified to fall within the expected range of 90.4.