A cylinder contains 28.5 L of oxygen gas at a pressure of 1.8 atm and a temperature of 298 K. How much gas (in moles) is in the cylinder?

Verified step by step guidance

1. Identify the ideal gas law equation: \( PV = nRT \).
2. List the known values: Pressure \( P = 1.8 \text{ atm} \), Volume \( V = 28.5 \text{ L} \), Temperature \( T = 298 \text{ K} \), and the ideal gas constant \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \).
3. Rearrange the ideal gas law equation to solve for the number of moles \( n \): \( n = \frac{PV}{RT} \).
4. Substitute the known values into the rearranged equation: \( n = \frac{(1.8 \text{ atm})(28.5 \text{ L})}{(0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1})(298 \text{ K})} \).
5. Calculate the value of \( n \) to find the number of moles of gas in the cylinder.

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 the amount of gas present under specific conditions.

Units of Measurement

Understanding the units of measurement is crucial when applying the Ideal Gas Law. Pressure is typically measured in atmospheres (atm), volume in liters (L), and temperature in Kelvin (K). The ideal gas constant R can be expressed in different units, so it is important to ensure consistency in units when performing calculations to avoid errors.

Molar Volume of a Gas

The molar volume of a gas at standard temperature and pressure (STP) is approximately 22.4 L/mol. This concept helps in understanding how many moles of gas occupy a certain volume under specific conditions. While the question does not ask for STP, knowing the molar volume can provide a reference point for gas behavior and calculations.