How can separate 1L samples of O2 and H2 have the same average velocity/
The kinetic energy of gaseous molecules is proportional to the temperature. At the same temperature, the kinetic energy is the same for any gas.
K.E. = 1/2 mv2. Therefore, at the same T, the average velocity of the lighter molecules will be higher, the heavier molecules will be slower. Having O2 and H2 at different temperatures will allow the average velocity to be the same
To answer your question, it is important to note that the average velocity of gas particles is directly proportional to the square root of the temperature, and inversely proportional to the square root of the molar mass.
Given that oxygen (O2) and hydrogen(H2) have different molar masses, they will have different average velocities at the same temperature. However, if the condition of the question assumes both gases to be at the same temperature, then it would not be possible for them to have the same average velocity.
If you have any other questions, feel free to ask!
To determine if separate 1-liter samples of oxygen (O2) and hydrogen (H2) have the same average velocity, we need to consider their molecular masses and temperature. The average velocity of a gas depends on the root-mean-square (RMS) velocity formula:
v_rms = √(3RT / M)
where:
- v_rms is the root-mean-square velocity
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (K)
- M is the molar mass of the gas in kilograms per mole (kg/mol)
Since we have separate samples of O2 and H2, we can compare their average velocities using this formula. However, we need to assume that the temperature is the same for both gases.
Let's calculate the average velocities step by step:
Step 1: Determine the molecular masses of O2 and H2:
- Molecular mass of O2 = 32 g/mol (16 g/mol per oxygen atom)
- Molecular mass of H2 = 2 g/mol (1 g/mol per hydrogen atom)
Step 2: Convert the molecular masses to kilograms per mole:
- Molecular mass of O2 = 0.032 kg/mol
- Molecular mass of H2 = 0.002 kg/mol
Step 3: Assume a temperature for the samples (in Kelvin). Let's say T = 273 K.
Step 4: Plug the values into the RMS velocity formula to calculate the average velocities:
For O2:
v_rms_O2 = √(3 * 8.314 J/(mol·K) * 273 K / 0.032 kg/mol)
For H2:
v_rms_H2 = √(3 * 8.314 J/(mol·K) * 273 K / 0.002 kg/mol)
Perform the calculations for each gas to find their respective average velocities. If the results are the same, the separate 1-liter samples of O2 and H2 will have the same average velocity.