A gas has an RMS speed of 500 m/s. If the molar mass of the gas is 0.02 kg/mol,
Practice Questions
Q1
A gas has an RMS speed of 500 m/s. If the molar mass of the gas is 0.02 kg/mol, what is the temperature of the gas?
250 K
500 K
1000 K
2000 K
Questions & Step-by-Step Solutions
A gas has an RMS speed of 500 m/s. If the molar mass of the gas is 0.02 kg/mol, what is the temperature of the gas?
Step 1: Write down the formula for RMS speed: v_rms = sqrt((3RT)/M).
Step 2: Rearrange the formula to solve for temperature (T): T = (v_rms^2 * M) / (3R).
Step 3: Identify the values needed: v_rms = 500 m/s and M = 0.02 kg/mol.
Step 4: Use the value of the gas constant R = 8.314 J/(mol·K).
Step 5: Substitute the values into the rearranged formula: T = (500^2 * 0.02) / (3 * 8.314).
Step 6: Calculate 500^2 = 250000.
Step 7: Multiply 250000 by 0.02 to get 5000.
Step 8: Calculate 3 * 8.314 = 24.942.
Step 9: Divide 5000 by 24.942 to find T: T = 200.5 K.
Step 10: Round the temperature to the nearest whole number: T = 201 K.
RMS Speed and Temperature Relationship – The relationship between the root mean square speed of gas molecules, their molar mass, and the temperature of the gas, as described by the equation v_rms = sqrt((3RT)/M).
Gas Laws – Understanding the ideal gas law and how it relates to molecular speed and temperature.
