A mixture of nitrogen (N₂) and helium has a volume of 365 mL at 30 °C and a total pressure of 745 mmHg. (8.5, 8.6, 8.7)
a. If the partial pressure of helium is 65 mmHg, what is the partial pressure of the nitrogen?

Verified step by step guidance

1. Step 1: Understand 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. Mathematically, this can be expressed as: $P$_total = P_He + P_N2, where $P$_total is the total pressure, $P$_He is the partial pressure of helium, and $P$_N2 is the partial pressure of nitrogen.
2. Step 2: Identify the given values from the problem. The total pressure of the gas mixture is $745$ mmHg, and the partial pressure of helium is $65$ mmHg.
3. Step 3: Rearrange Dalton's Law equation to solve for the partial pressure of nitrogen: $P$_N2 = P_total - P_He.
4. Step 4: Substitute the known values into the equation: $P$_N2 = 745 - 65 mmHg.
5. Step 5: Perform the subtraction to find the partial pressure of nitrogen. This will give you the value of $P$_N2.

Key Concepts

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. This principle is crucial for solving problems involving gas mixtures, as it allows us to isolate the contribution of each gas to the overall pressure.

Partial Pressure

Partial pressure refers to the pressure that a single gas in a mixture would exert if it occupied the entire volume alone at the same temperature. Understanding partial pressures is essential for calculating the individual contributions of gases in a mixture, particularly when using Dalton's Law.

Ideal Gas Law

The Ideal Gas Law (PV=nRT) relates the pressure, volume, temperature, and number of moles of a gas. While not directly needed for this specific question, it provides a foundational understanding of gas behavior and can be useful in broader contexts involving gas calculations.