Assuming the hydrogen molecule to be a sphere with a diameter of 130 pm, use the

Question

Assuming the hydrogen molecule to be a sphere with a diameter of 130 pm, use the formula of a sphere. V_molecule = (4/3)pi r^3, to calculate the physical volume of one hydrogen molecule. Determine the percentage of the total "occupied" volume per molecule at STP (as calculated in 5(d)) that is actually occupied by the H_2 molecule, assuming the H_2 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. Determine the average center-to-center distance between nearest neighbor molecules in a sample of H_2 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 at the center of it.)

Explanation / Answer

a) Volume = (4/3)*Pi*r^3

Volume = 1.15*10^-30 m^3

b) at STP, 1 Mole =22.4 L

1 molecule =22.4/avogadro constant. = 3.719*10^-26 m^3

% occupied = (1.15*10^-30 /3.719*10^-26 )*100= 0.00309 %

c) length of 1 side of 1 single small cube= 3.33 nm

a distance between two molecules(center to center) = 3.33 nm.

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