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

Question

According to the ideal gas law the total pressure of a system is independent 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. Find the average molecular speed for H2 at 298.15 K, P=6.197 bar

4. Find the average molecular speed for CO2 at 298.15 K, P=6.197 bar

5. Find the molecular speed for H2 at 400.00 K, P=8.31446 bar

6. Find the molecular speed for CO2 at 400.00 K, P=8.31446 bar

(I do know in the equation the velocity is squared)

Explanation / Answer

1. Mass of H2 in kg/molecule-

0.250 mole sample of H2 gas in a 0.500 L container

Use Avogadro's number to convert moles into molecules

Mass of 1mole of H2 = 2.01g

Mass of 1.505 x 1023 molecules (0.250mole) of H2 = 2.01g/mole x 0.250mole = 0.5025g

Mass of 1molecules of H2 = 0.5025g /1.505 x 1023 molecules =3.338 x10-24g

Mass of 1molecules of H2 = 3.338 x10-24g/ 1000 = 3.338 x 10-27 Kg/molecule.

2. Determine the mass of CO2 in kg/molecule.

0.250 mole sample of CO2 gas in a 0.500 L container

Use Avogadro's number to convert moles into molecules:

0.250 mol × 6.02×1023 molecules/mol = 1.505 × 1023molecules

Mass of 1mole of CO2= 44.01g

Mass of 1.505 x 1023 molecules (0.250mole) of CO2 = 44.01g/mole x 0.250mole = 11.0025g

Mass of 1molecules of CO2 = 11.0025g /1.505 x 1023 molecules =7.31 x10-23g

Mass of 1molecules of CO2 = 7.31 x 10-26 Kg/molecule

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