What is the kinetic energy of 2 moles of gas at 300K?
Understand the Problem
The question is asking for the calculation of the kinetic energy of a gas under specific conditions (2 moles at a temperature of 300K). This involves using the formula for kinetic energy in terms of temperature, which relates to the average kinetic energy of gas molecules.
Answer
The total kinetic energy of the gas is \( 7482.6 \, \text{J} \).
Answer for screen readers
The total kinetic energy of the gas is ( 7482.6 , \text{J} ).
Steps to Solve
- Identify the relevant formula
To calculate the average kinetic energy of gas molecules, we use the formula: $$ KE = \frac{3}{2} nRT $$ where:
- ( KE ) is the total kinetic energy,
- ( n ) is the number of moles of the gas,
- ( R ) is the ideal gas constant, approximately ( 8.314 , \text{J/(mol K)} ),
- ( T ) is the absolute temperature in Kelvin.
- Substitute the known values
Given that ( n = 2 ) moles and ( T = 300 ) K, we can substitute these values into the formula: $$ KE = \frac{3}{2} \cdot 2 \cdot 8.314 \cdot 300 $$
- Perform the multiplication
Calculate the kinetic energy step by step:
- First, compute ( 2 \cdot 8.314 ): $$ 2 \cdot 8.314 = 16.628 $$
- Next, multiply the result by ( 300 ): $$ 16.628 \cdot 300 = 4988.4 $$
- Finally, multiply by ( \frac{3}{2} ): $$ KE = \frac{3}{2} \cdot 4988.4 = 7482.6 , \text{J} $$
The total kinetic energy of the gas is ( 7482.6 , \text{J} ).
More Information
The average kinetic energy of gas molecules can be understood as a measure of the energy due to their motion. The higher the temperature or the number of moles, the greater the kinetic energy.
Tips
- Forgetting to convert the ideal gas constant when using different units, leading to incorrect answers.
- Not using Kelvin for temperature; temperatures must always be in Kelvin for this formula.
