Question

The density of hydrogen of hydrogen gas, H:8) at STP has been measured to be 0.08988 Calculate the molar volume of this gas at STP (b) Calculate the per cent deviation of this value from the molar volume of an ideal gas, 22.414 L (c) Assuming Charles' law to be valid, calculate the molar volume of this gas at 1,000 atm and 25.00*C. (d) 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.) Whe er the volume 6. [The following calculations are optional.] (a) Assuming the hydrogen molecule to be a sphere with a diameter of 130 pm, use the formula of a sphere, V (4/3) , to calculate the physical volume of one hydrogen molecule. make the weddie (b) Determine the percentage of the total occupied" volume per molecule at STP (as calculated in 5(d)) that is actually occupied by the H, molecule, assuming the H, molecule can be approximated by a sphere of diameter 130 pm. The difference between this percentage and one hundred percent is the percentage of "dead" or empty space in the gas sample. (c) Determine the average center-to-center distance between nearest neighbor molecules in a sample of H, gas at STP. (To do this calculation, it is useful to imagine the sample of gas is a cube which in turn is divided into smaller cubes of equal volume each with one molecule the center of it)

Answer 1

5.a)

density is 0.8988 g/L.

molar mass of Hydrogen = 2 g/mol

hence, volume of 1 mole Hydrogen

=
IL 0.08988 g
×  $\frac{2\: g}{1 \:mol}$

= 22.252 (g/mL).

b,)

Percent deviation

= ( exact difference ×100)/ theoretical value.

= [ (22.414 -22.252)×100/22.414]

= 0.723 %.

c)

at STP , T₁ = 0⁰ C = 273 K, V₁ = 22.252 L

now at T₂ = 25^oc = 25+273 = 298 K , V₂ is unknown.

by charles law

$\frac{V_1}{V_2}$ = $\frac{T_1}{T_2}$

or,
22.252 V2
=  $\frac{273}{298}$

or, V₂ = (22.252×298)/(273)

or, V₂ = 24.289 L

d)

Number of Hydrogen molecule in 1 mole hydrogen = 6.02×10²³.

average occupied volume of each molecule at STP

=
22.252(L) 1(mol)
×
1(mol) 6.02 x 1023

= 3.696×10^-23 L .