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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.
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|constant||elastic||Graham’s Law of Diffusion|
Click on each ? below to check your answers.
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 =
NH3: d2 =
6. Calculate the ratio d1/d2 =
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 =
NH3: m2 =
8. Calculate the ratio:
√(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)?
Yes. Although 0.722 does not equal 0.682, the values are close enough to be considered the same experimentally.