What is the concentration of a CO₂ in a container after 4 half-lives if 0.325 mol of CO2 is initially placed into a 5.0 L reaction vessel?

• A. 0.020 M
• B. 4.06×10^–3 M
• C. 8.1×10^–3 M
• D. 0.325 M

Answer: (B)

Verified step by step guidance

1. Determine the initial concentration of CO2 by dividing the initial moles by the volume of the container. Use the formula: \( \text{Initial Concentration} = \frac{\text{Initial Moles}}{\text{Volume}} \).
2. Calculate the initial concentration: \( \text{Initial Concentration} = \frac{0.325 \text{ mol}}{5.0 \text{ L}} \).
3. Understand that after each half-life, the concentration of the substance is halved. Therefore, after 4 half-lives, the concentration will be \( \frac{1}{2^4} \) of the initial concentration.
4. Calculate the concentration after 4 half-lives using the formula: \( \text{Concentration after 4 half-lives} = \text{Initial Concentration} \times \frac{1}{2^4} \).
5. Substitute the initial concentration value into the formula to find the concentration after 4 half-lives.