Using the ideal gas law, what is the pressure (in atm) in a 5.80 L container that contains 0.545 moles of oxygen gas at 22.0 °C?

• A. 2.29 atm
• B. 4.51 atm
• C. 0.37 atm
• D. 1.12 atm

Answer: (A)

Verified step by step guidance

1. Identify the known variables from the problem: number of moles \(n = 0.545\) mol, volume \(V = 5.80\) L, and temperature \(T = 22.0\ ^\circ\mathrm{C}\).
2. Convert the temperature from Celsius to Kelvin using the formula \(T(K) = T(^\circ\mathrm{C}) + 273.15\). This is necessary because the ideal gas law requires temperature in Kelvin.
3. Recall the ideal gas law equation: \(P V = n R T\), where \(P\) is pressure in atm, \(V\) is volume in liters, \(n\) is moles of gas, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.
4. Use the value of the ideal gas constant \(R = 0.0821\ \mathrm{L \cdot atm / mol \cdot K}\), which is appropriate for pressure in atm and volume in liters.
5. Rearrange the ideal gas law to solve for pressure: \(P = \frac{n R T}{V}\). Substitute the known values of \(n\), \(R\), \(T\), and \(V\) into this equation to calculate the pressure.