Finding Moles of Gas from Pressure and Volume

\[ PV = nRT \]

Where:

• P = Pressure of the gas (in atm)
• V = Volume of the gas (in liters)
• n = Number of moles of gas
• R = Ideal gas constant (0.0821 L·atm/(K·mol))
• T = Temperature in Kelvin (K)

To find the number of moles (n), we can rearrange the equation:

\[ n = \frac{PV}{RT} \]

Example 1: Calculating Moles from Known Pressure and Volume

Problem Statement:

A gas occupies a volume of 10.0 liters at a pressure of 2.0 atm and a temperature of 300 K. How many moles of gas are present?

Solution:

1. Identify given values:

   • P = 2.0 atm
   • V = 10.0 L
   • T = 300 K
   • R = 0.0821 L·atm/(K·mol)

2. Plug the values into the rearranged Ideal Gas Law:
   \[ n = \frac{PV}{RT} = \frac{(2.0 \, \text{atm})(10.0 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)})(300 \, K)} \]

3. Calculate:
   \[ n = \frac{20.0 \, \text{atm·L}}{24.63 \, \text{L·atm/(K·mol)}} \approx 0.812 \, \text{mol} \]

Conclusion:

Approximately 0.812 moles of gas are present in the sample.

Example 2: Determining Moles with Different Conditions

Problem Statement:

A 5.0 L container holds a gas at a pressure of 1.5 atm and a temperature of 273 K. How many moles of gas does the container hold?

Solution:

1. Identify given values:

   • P = 1.5 atm
   • V = 5.0 L
   • T = 273 K
   • R = 0.0821 L·atm/(K·mol)

2. Use the Ideal Gas Law:
   \[ n = \frac{PV}{RT} = \frac{(1.5 \, \text{atm})(5.0 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)})(273 \, K)} \]

3. Calculate:
   \[ n = \frac{7.5 \, \text{atm·L}}{22.41 \, \text{L·atm/(K·mol)}} \approx 0.334 \, \text{mol} \]

Conclusion:

There are approximately 0.334 moles of gas in the container under these conditions.

Key Takeaways

• The Ideal Gas Law is a powerful tool for calculating the number of moles of a gas based on its pressure, volume, and temperature.
• By rearranging the formula, you can easily solve for moles when provided with sufficient information.
• Practice with different scenarios to solidify your understanding of the relationship between pressure, volume, and moles.