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According to the kinetic theory, gas molecules are in constant motion, hitting each other and the sides of their container with perfectly elastic collisions. The temperature of a gas is a measure of the average kinetic energy of the molecules. The equation for calculating this energy is: KE = ½ mv2 If two gases are at the same temperature, the molecules have the same average kinetic energy. This makes KE a constant. This means that m and v2 are inversely proportional. Heavier molecules move slower than light molecules at the same temperature.
Mathematically, the relationship can be stated as:
m1v12 = m2v22 which equals v12 / v22 = m2 / m1 which equals The last equation is known as Graham’s Law of Diffusion.

Word Bank (some words may be used more than once)

 constant elastic Graham’s Law of Diffusion inversely kinetic slower

Procedure:

1. A drop of concentrated hydrochloric acid (a source of HCl fumes) was placed on a cotton swab. A drop of concentrated aqueous ammonia was placed on another cotton swab.

2. The swabs were simultaneously inserted into opposite ends of a glass tube.

3. The glass tube was left undisturbed for two minutes.

4. After two minutes, a white ring was located and the center of the ring was marked.

5. The distance from each end of the tube to the mark was measured.

HCl : d1 =

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10.9 cm

NH3: d2 =

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15.1 cm

6. Calculate the ratio d1/d2 =

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0.722 cm

This is also the ratio of the velocities of the molecules, v1/v2.

v1 / v2 = 0.722

7. Calculate the molar masses of the molecules:

HCl : m1 =

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36.5 g/mol

NH3: m2 =

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17.0 g/mol

8. Calculate the ratio:

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√(M2/M1) = 0.682

9. Within bounds of experimental error, does V1 (calculated in number 6) equal √(M2/M1) (the ratio is calculated in number 8)?

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Yes. Although 0.722 does not equal 0.682, the values are close enough to be considered the same experimentally.

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