Given a molecular view of a gaseous mixture, which statement best explains how the Ideal Gas Law applies to the mixture?

• A. The gases in the mixture react with each other, so the Ideal Gas Law cannot be used.
• B. The volume occupied by each gas is different, so the Ideal Gas Law must be applied separately to each gas.
• C. The temperature of each gas in the mixture is different, so the Ideal Gas Law does not apply.
• D. Each gas in the mixture behaves independently, and the total pressure is the sum of the partial pressures of each gas.

Answer: (D)

Verified step by step guidance

1. Understand that the Ideal Gas Law, given by \(P V = n R T\), relates the pressure (\(P\)), volume (\(V\)), number of moles (\(n\)), gas constant (\(R\)), and temperature (\(T\)) for an ideal gas.
2. Recognize that in a gaseous mixture, each gas behaves independently and exerts its own partial pressure as if it alone occupied the entire volume at the mixture's temperature.
3. Recall Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas: \(P_{total} = P_1 + P_2 + \dots + P_n\).
4. Apply the Ideal Gas Law to each gas separately to find its partial pressure: \(P_i = \frac{n_i R T}{V}\), where \(n_i\) is the number of moles of gas \(i\).
5. Combine these partial pressures to find the total pressure of the mixture, confirming that the Ideal Gas Law applies to the mixture through the sum of independent gas behaviors.