Question

For the given first order reaction A → B, the half-life of the reaction is 0.3010 min. The ratio of the initial concentration of reactant to the concentration of reactant at time 2.0 min will be equal to ______. (Nearest integer)

Answer 1

Correct Answer: 100

To solve for the ratio of the initial concentration of reactant [A]₀ to the concentration of reactant [A] at time 2.0 min for a first-order reaction, we use the half-life formula and rate equation for first-order kinetics.

Step 1: Understand the relationship for first-order reactions. The rate equation is given by:

[A]=[A]₀e^-kt

Where:

• [A]₀ is the initial concentration of the reactant.
• [A] is the concentration at time t.
• k is the rate constant.
• t is the time.

Step 2: Calculate the rate constant k. The half-life (t_1/2) of a first-order reaction is related to the rate constant by:

t_1/2=0.693/k

Given t_1/2=0.3010 min, solve for k:

k=0.693/0.3010=2.302 min^-1

Step 3: Use the first-order rate equation to find the ratio. At time t=2.0 min:

[A]=[A]₀e^{-(2.302)(2.0)}

Calculate e^{-(2.302)(2.0)}:

[A]=[A]₀e^-4.604

The exponential term evaluates to:

e^-4.604≈0.010

Therefore, [A]≈0.010[A]₀.

Step 4: Calculate the ratio [A]₀/[A].

[A]₀/[A]=1/0.010=100

Conclusion: The ratio of the initial concentration to the concentration at 2.0 min is approximately 100, which fits the provided range of 100,100.