What is the pressure in a 10.0 L cylinder filled with 0.448 mol of nitrogen gas at a temperature of 315 K?

Verified step by step guidance

1. Identify the ideal gas law equation: \( PV = nRT \).
2. Rearrange the equation to solve for pressure \( P \): \( P = \frac{nRT}{V} \).
3. Identify the values given in the problem: \( n = 0.448 \text{ mol} \), \( V = 10.0 \text{ L} \), \( T = 315 \text{ K} \).
4. Use the ideal gas constant \( R = 0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1} \).
5. Substitute the values into the equation: \( P = \frac{(0.448 \text{ mol})(0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1})(315 \text{ K})}{10.0 \text{ L}} \).

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 of the variables if the others are known.

Units of Measurement

Understanding the units of measurement is crucial when applying the Ideal Gas Law. Pressure is typically measured in atmospheres (atm) or pascals (Pa), volume in liters (L), temperature in Kelvin (K), and the amount of substance in moles (mol). Ensuring that all units are consistent is essential for accurate calculations.

Gas Constant (R)

The gas constant (R) is a proportionality constant in the Ideal Gas Law that relates the energy scale to the temperature scale. Its value depends on the units used; for example, R = 0.0821 L·atm/(K·mol) when pressure is in atmospheres and volume in liters. Knowing the correct value of R is necessary for solving gas law problems accurately.