The density of hydrogen gas, H_2(g), at STP has been measured to be 0.08988 g/L.

Question

The density of hydrogen gas, H_2(g), at STP has been measured to be 0.08988 g/L. Calculating the molar volume of this gas at STP. Calculate the percent deviation of this value from the molar volume of an ideal gas, 22.414 L. Assuming Charles law to be valid calculate the molar volume of gas at 1.000 atm and 25.00 degree C. Assuming the molecules of the gas "occupy" equal fractions of the total gas volume, and that the sum of the volumes "occupied" (assigned) to each molecule equals the total volume of the container. Calculate the average volume "occupied by" (associated with) a single molecule of this gas at STP. (Note that this average "occupied" volume includes both the volume actually physically occupied by a molecule of hydrogen plus the fraction of the "dead" - actually empty- volume in the container associated with (assigned to) it.)

Explanation / Answer

density = mass/ volume

Molar mass of H2 = 2 gm/mol

Molar volume = molar mass / density = (2gm/mol)/0.08988g/L = 22.252 L

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% deviation = [(22.414-22.252) /22.414]*100 = 0.72 %

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According to Charles law : V1*T2 = V2*T1

V1=22.252 L, T1 =273K, V2=?, T2 = 298 K

V2 = 22.252 L*298K /273K = 24.289 L

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1 mole of gas = 6.023*10^23 molecules

Let the volume of each molecule = x

6.023*10^23 * x = 22.252

or x = 3.69*10^-23 L

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