A gas mixture with a total pressure of 745 mmHg contains each of the following gases at the indicated partial pressures: CO2, 112 mmHg; Ar, 225 mmHg; and O2, 114 mmHg. The mixture also contains helium gas. What is the partial pressure of the helium gas? What mass of helium gas is present in a 12.0-L sample of this mixture at 273 K?

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Identify the total pressure of the gas mixture, which is given as 745 mmHg.

List the partial pressures of the known gases: CO2 (112 mmHg), Ar (225 mmHg), and O2 (114 mmHg).

Use Dalton's Law of Partial Pressures to find the partial pressure of helium: \( P_{\text{total}} = P_{\text{CO}_2} + P_{\text{Ar}} + P_{\text{O}_2} + P_{\text{He}} \). Rearrange to solve for \( P_{\text{He}} \).

Calculate the partial pressure of helium by subtracting the sum of the known partial pressures from the total pressure: \( P_{\text{He}} = 745 \text{ mmHg} - (112 \text{ mmHg} + 225 \text{ mmHg} + 114 \text{ mmHg}) \).

Use the ideal gas law \( PV = nRT \) to find the mass of helium. First, solve for \( n \) (moles of He) using \( P = P_{\text{He}} \), \( V = 12.0 \text{ L} \), \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \), and \( T = 273 \text{ K} \). Then, convert moles to grams using the molar mass of helium (4.00 g/mol).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 partial pressure of an unknown gas in a mixture by subtracting the known partial pressures from the total pressure.

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 present in a given volume and temperature, allowing us to determine the mass of helium 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). For helium, the molar mass is approximately 4.00 g/mol. Knowing the molar mass is crucial for converting the number of moles of helium gas, calculated from the Ideal Gas Law, into mass.

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