What is the pressure in a 15.0-L cylinder filled with 32.7 g of oxygen gas at a temperature of 302 K?

Verified step by step guidance

1. Identify the ideal gas law equation: \( PV = nRT \).
2. Calculate the number of moles \( n \) of oxygen gas using its molar mass (\( \text{O}_2 \) has a molar mass of approximately 32.00 g/mol): \( n = \frac{\text{mass}}{\text{molar mass}} \).
3. Substitute the given values into the ideal gas law equation: \( P = \frac{nRT}{V} \), where \( R \) is the ideal gas constant (0.0821 L·atm/mol·K).
4. Use the given volume \( V = 15.0 \) L, temperature \( T = 302 \) K, and the calculated moles \( n \) to solve for pressure \( P \).
5. Perform the calculation to find the pressure \( P \) in atmospheres.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate one property of a gas if the others are known.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For oxygen (O2), the molar mass is approximately 32.00 g/mol. Understanding molar mass is essential for converting grams of a substance to moles, which is necessary for using the Ideal Gas Law.

Gas Constant (R)

The gas constant (R) is a proportionality constant in the Ideal Gas Law, with a value of 0.0821 L·atm/(K·mol) when pressure is measured in atmospheres and volume in liters. It serves as a bridge between the physical properties of gases and their behavior under various conditions. Knowing the correct value of R is crucial for accurate calculations in gas law problems.