A gas mixture contains each of the following gases at the indicated partial pressures: N2, 111 torr; O2, 213 torr; and He, 102 torr. What is the total pressure of the mixture? What mass of each gas is present in a 1.55-L sample of this mixture at 25.0°C?

Verified step by step guidance

1. Step 1: To find the total pressure of the gas mixture, use Dalton's Law of Partial Pressures, which states that the total pressure is the sum of the partial pressures of each gas. Calculate the total pressure by adding the partial pressures of N2, O2, and He.
2. Step 2: Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. This is necessary for using the ideal gas law.
3. Step 3: Use the ideal gas law, PV = nRT, to find the number of moles (n) of each gas. Rearrange the equation to solve for n: n = PV / RT. Use the partial pressure of each gas, the volume of the container, the ideal gas constant (R = 0.0821 L·atm/mol·K), and the temperature in Kelvin.
4. Step 4: Calculate the mass of each gas using the number of moles obtained in Step 3 and the molar mass of each gas. The molar mass of N2 is approximately 28.02 g/mol, O2 is approximately 32.00 g/mol, and He is approximately 4.00 g/mol. Use the formula: mass = moles × molar mass.
5. Step 5: Summarize the results by stating the total pressure of the gas mixture and the mass of each gas present in the 1.55-L sample.

Key Concepts

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. This principle allows us to calculate the total pressure by simply adding the partial pressures of the gases present in the mixture.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the amount of gas in a given volume and temperature, allowing us to determine the mass of each gas in the mixture.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). Knowing the molar mass of each gas in the mixture is crucial for converting the number of moles calculated from the Ideal Gas Law into mass, enabling us to find the mass of each gas present in the sample.