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 sphere V_absolute = (4/3)pi r^2, to calculate the physical volume of one hydrogen molecule. Determine the percentage of the total "occupied" volume gas 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 as the center of it.)

Explanation / Answer

Ans. a. Physical volume of 1 H2 molecule = 4/3 pi r3                                [radius, r = ½ diameter]

                                                                = 4/3 pi (65 pm)3

                                                                = 1150346.50998946 pm3

                                                                = 1.150 x 106 pm3

Ans. b. Volume of 1 mole H2 molecule = volume of 1 molecule x Avogadro number

                                    = 1.150 x 106 pm3 x 6.022140857 x 1023 mol-1

                                                = 6.92755 x 1029 pm3 mol-1

Thus, the physical volume of 1 mole of H2 molecules = 6.92755 x 1029 pm3

                                                = 6.92755 x 1029 pm3 x 10-33 L                       [1 L = 1033 pm3]

                                                = 6.92755 x 10-4 L

% physical volume occupied by H2 molecules =

(physical volume of 1 mol H2 molecules / volume of 1 mol gas at STP) x 100

= (6.92755 x 10-4 L / 22.4 L) x 100 = 0.00309 %

Note: Volume of 1 mole of a gas at STP = 22.4L

Ans. c. Assume, the whole 22.4 L volume of a gas at STP is occupies by 1 mole H2 moles (cubes)

Volume of a cube = a3       ; where a= length of a side

Volume of 1 mole H2 molecules (6.022140857 x 1023 molecules) at STP = 22.4 L

Volume of 1 H2 molecule (cube) = 22.4 L / 6.022140857 x 1023

                                                                = 3.71960745 x 10-23 L

                                                                = 3.7196 x 10-23 x 1033 pm3

                                                                = 3.7196 x 1011 pm3

Now, a3 = 3.7196 x 1011 pm3

Or, a = 7.191 x 103 pm

Thus, the length of 1 cube = 7.191 x 103 pm

Distance between center of two cubes = 7.191 x 103 pm

Two cubes attached together has a distance between their centers equal to their arms’ length.

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