The rate constant of a reaction is 1.25 x 10^4 mol^-1 s^-1. If the initial concentration of the reactant is 0.25 mol L^-1, the total time (in seconds) required for complete convers... The rate constant of a reaction is 1.25 x 10^4 mol^-1 s^-1. If the initial concentration of the reactant is 0.25 mol L^-1, the total time (in seconds) required for complete conversion is __________? Read more

Steps to Solve

1. Identify the rate law and constants

Given data:

• Rate constant, $k = 1.25 \times 10^4 , \text{mol}^{-1}\text{L}^{-1}\text{s}^{-1}$
• Initial concentration of the reactant, $[A]_0 = 0.25 , \text{mol/L}$

Since the rate constant has units indicating a second-order reaction, we can use the integrated rate law for a second-order reaction.

2. Write the integrated rate equation

The integrated rate equation for a second-order reaction is given by:

$$ \frac{1}{[A]} - \frac{1}{[A]_0} = kt $$

where:

• $[A]$ is the concentration at time $t$,
• $[A]_0$ is the initial concentration,
• $k$ is the rate constant,
• $t$ is the time.

3. Set the concentration for complete conversion

For complete conversion, the concentration of the reactant $[A]$ will approach $0$. Therefore, we can set up the equation as follows:

$$ \frac{1}{0} - \frac{1}{0.25} = (1.25 \times 10^4) t $$

This simplifies to:

$$ -\frac{1}{0.25} = (1.25 \times 10^4) t $$

4. Solve for time $t$

From the equation:

$$ -4 = (1.25 \times 10^4) t $$

Now, solving for $t$ gives us:

$$ t = \frac{-4}{1.25 \times 10^4} $$

Calculating this provides the total time required for complete conversion.