A sample of 3.51 g argon and an unknown amount of oxygen are mixed in a container at room temperature. The partial pressure of argon was calculated as 71.0 torr and the partial pressure of oxygen as 188 torr. What is the mass of the oxygen within the container?

• A. 4.27 g
• B. 6.18 g
• C. 7.44 g
• D. 9.16 g
• E. 15.2 g

Answer: (C)

Verified step by step guidance

1. First, understand that the problem involves a mixture of gases, and we need to use the concept of partial pressures and the ideal gas law to find the mass of oxygen.
2. Use the ideal gas law in the form \( PV = nRT \) to find the number of moles of argon. Here, \( P \) is the partial pressure of argon, \( V \) is the volume of the container, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
3. Calculate the number of moles of argon using its given mass and molar mass. The molar mass of argon is approximately 39.95 g/mol. Use the formula \( n = \frac{\text{mass}}{\text{molar mass}} \).
4. Since the volume \( V \) and temperature \( T \) are constant for both gases, use the ratio of partial pressures to find the moles of oxygen. The ratio of moles of oxygen to moles of argon is the same as the ratio of their partial pressures: \( \frac{n_{\text{O}_2}}{n_{\text{Ar}}} = \frac{P_{\text{O}_2}}{P_{\text{Ar}}} \).
5. Finally, calculate the mass of oxygen using the number of moles of oxygen and its molar mass (approximately 32.00 g/mol). Use the formula \( \text{mass} = n \times \text{molar mass} \).