According to the ideal gas law the total pressure of a system is indepenent of w

Question

According to the ideal gas law the total pressure of a system is indepenent of what gas we are dealing with as long as they behave 'ideal'. Therefore 0.250 moles of H2 should have the same pressure as 0.250 moles of CO2. However these molecules have different masses, so to achieve the same force when hitting the walls of the container they need to travel at different speeds. For a 0.250 mole sample of these gases in a 0.500 L container, find:

1. Determine the mass of H2 in kg/molecule

2. Determine the mass of CO2 in kg/molecule

3. Determine the average molecular speed of H2 at 298.15 K, P=6.197 bar

4. Determine the average molecular speed of CO2 at 298.15 K, P=6.197 bar

5. Determine the average molecular speed of H2 at 400.00 K, P=8.41446 bar

6. Determine the average molecular speed of CO2 at 400.00 K, P=8.31446 bar

Explanation / Answer

1. The mass of H2 in Kg / molecule

Mass of 6.023 X 10^23 molecules = 2g = 2 X 10^-3 Kg

Mass of 1 molecule = 2 X 10^-3 / 6.023 X 10^23 Kg = 3.32 X 10^-27 Kg

2. Mass of one mole of CO2 or 6.023 X 10^23 molecules = 44g = 44 X 10^-3 Kg

Mass of 1 molecule = 44 X 10^-3 / 6.023 X 10^23 Kg = 7.31 X 10^-26 Kg

3. The average speed = (3R T / M)1/2

R= gas constant = 8.314

T = 298.15 K

M = 2 X 10^-3 Kg / mole

Average speed of H2 = (3 X 8.314 X 298.15 / 2 X 10^-3)^1/2 = 1928.27 m/s

4) average molecular speed of CO2 = (3 X 8.314 X 298.15 / 44 X 10^-3)^1/2 = 411.11 m/s

5) average molecular speed of H2 at 400K and P = 8.41446

Average speed of H2 = (3 X 8.314 X 400 / 2 X 10^-3)^1/2 =2233.47 m /s

6) average molecular speed of CO2 at 400K = (3 X 8.314 X 400 / 44 X 10^-3)^1/2 = 476.18 m /s

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