How many moles of oxygen gas (O_2) are present in 33.6 L of the gas at 1 atm and 0°C?

• A. 32
• B. 22.4
• C. 2
• D. 1.5

Answer: (C)

Verified step by step guidance

1. Identify the given information: volume of oxygen gas \(V = 33.6\ \text{L}\), pressure \(P = 1\ \text{atm}\), and temperature \(T = 0^\circ\text{C} = 273\ \text{K}\) (convert Celsius to Kelvin by adding 273).
2. Recall the ideal gas law equation: \(PV = nRT\), where \(n\) is the number of moles, \(R\) is the ideal gas constant, \(P\) is pressure, \(V\) is volume, and \(T\) is temperature in Kelvin.
3. Use the ideal gas constant \(R = 0.0821\ \text{L}\cdot\text{atm}/\text{mol}\cdot\text{K}\), which matches the units of pressure in atm and volume in liters.
4. Rearrange the ideal gas law to solve for moles \(n\): \(n = \frac{PV}{RT}\).
5. Substitute the known values into the equation: \(n = \frac{(1\ \text{atm})(33.6\ \text{L})}{(0.0821\ \text{L}\cdot\text{atm}/\text{mol}\cdot\text{K})(273\ \text{K})}\), then simplify to find the number of moles.