If the RMS speed of a gas is 400 m/s, what is the kinetic energy per molecule at 300 K?
Practice Questions
1 question
Q1
If the RMS speed of a gas is 400 m/s, what is the kinetic energy per molecule at 300 K?
0.5 mJ
0.4 mJ
0.2 mJ
0.1 mJ
Kinetic energy per molecule = (1/2)mv^2. Using v = 400 m/s and m = M/N_A, we find KE = 0.5 mJ.
Questions & Step-by-step Solutions
1 item
Q
Q: If the RMS speed of a gas is 400 m/s, what is the kinetic energy per molecule at 300 K?
Solution: Kinetic energy per molecule = (1/2)mv^2. Using v = 400 m/s and m = M/N_A, we find KE = 0.5 mJ.
Steps: 5
Step 1: Understand that the kinetic energy (KE) of a molecule can be calculated using the formula KE = (1/2)mv^2, where m is the mass of the molecule and v is the speed.
Step 2: Identify the given values. The RMS speed (v) is 400 m/s.
Step 3: Find the mass of one molecule (m). To do this, use the formula m = M/N_A, where M is the molar mass of the gas and N_A is Avogadro's number (approximately 6.022 x 10^23 mol^-1).
Step 4: Substitute the values into the kinetic energy formula. You will need to calculate (1/2) * m * (400 m/s)^2.
Step 5: Calculate the kinetic energy per molecule. After substituting the values and performing the calculations, you will find that KE is approximately 0.5 mJ.
