The rate constant of a zero order reaction is $$2.0 \times 10^{-2}$$ mol L$$^{-1}$$ s$$^{-1}$$. If the concentration of the reactant after 25 seconds is 0.5M. What is the initial concentration?

For a zero-order reaction, the rate of reaction is constant and independent of the concentration of the reactant. The integrated rate law for a zero-order reaction is given by:

$$ [A]_t = [A]_0 - kt $$

where:

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

We are given:

• Rate constant $$ k = 2.0 \times 10^{-2} $$ mol L$$^{-1}$$ s$$^{-1}$$,
• Time $$ t = 25 $$ seconds,
• Concentration at time $$ t $$, $$ [A]_t = 0.5 $$ M (which is equivalent to mol L$$^{-1}$$).

We need to find the initial concentration $$ [A]_0 $$.

Substitute the given values into the equation:

$$ 0.5 = [A]_0 - (2.0 \times 10^{-2}) \times 25 $$

First, calculate the value of $$ kt $$:

$$ kt = (2.0 \times 10^{-2}) \times 25 $$

Multiply 2.0 by 25:

$$ 2.0 \times 25 = 50 $$

Now, since $$ 2.0 \times 10^{-2} = 0.02 $$, we have:

$$ kt = 0.02 \times 25 = 0.5 $$

Alternatively, using scientific notation:

$$ 2.0 \times 10^{-2} = 0.02 $$

$$ 0.02 \times 25 = 0.5 $$

So, $$ kt = 0.5 $$ mol L$$^{-1}$$.

Now, substitute back into the equation:

$$ 0.5 = [A]_0 - 0.5 $$

To solve for $$ [A]_0 $$, add 0.5 to both sides:

$$ 0.5 + 0.5 = [A]_0 $$

$$ 1.0 = [A]_0 $$

Therefore, the initial concentration is 1.0 M.

Comparing with the options:

• A. 0.5M
• B. 1.25M
• C. 12.5M
• D. 1.0M

Hence, the correct answer is Option D.