Diffusion in a Tube

Introduction

One gaseous substance can diffuse through another due simply to their random motion. The speed of diffusion of molecules depends on their mass. Heavy molecules diffuse more slowly than light molecules. The mathematical relationship is as follows.

RA/RB = (MB/MA)^0.5

RA = rate of diffusion of gas A

RB = rate of diffusion of gas B

MA = molar mass of gas A

MB = molar mass of gas B

The distance traveled by a gas is proportional to the rate. If dA represents the distance traveled on the average by gas a during a given period of time, and dB the corresponding quantity for gas B, then

(dA/dB) = (MB/MA)^0.5

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1. Obtain a Beral pipet containing concentrated HCl at the hood. Place 2 drops of HCl in well 1 of a 12-well strip.
2. Obtain a Beral pipet containing concentrated NH₃ solution at the hood. Place 2 drops of NH₃ in well 12 of a 12-well strip.
3. Return to the work station. Grasping the middle of the capillary tube, quickly dip one end into the HCl and then the other end in the NH₃ solution. Place the tube on the black table top. Measure immediately the distance from the innermost edge of the HCl to the innermost edge of the NH₃ solution. (This is the length of the tube of air trapped between the 2 liquids.) Record this distance in part A on the Data Table.
4. The gases will begin to diffuse through the air in the tube. Where the two gases meet, a white ring will begin to form on the tube because NH₃ and HCl react to form the solid NH₄Cl.
5. As soon as the white ring forms in the capillary tube, mark the spot with the china marker. Measure how far from the NH3 end the two gases actually met on your capillary tube. Record the value in part C on the Data Table. Using the equation in the introduction, calculate the distance where the gases were expected to meet. Show your work below and then record your value in part D on the Data Table.

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1. Total length of trapped air in capillary tube
2. Calculated ratio of distance traveled by ammonia to distance traveled by hydrogen chloride:
3. Distance from the NH₃ end that the gases actually met?
4. How far from the NH₃ end do you predict the gases will meet?
5. Difference between actual and predicted?

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Questions

Explain why the gases did not meet exactly halfway between the two liquids.

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1. Find the rate of diffusion of N₂ compared to O₂.

   (RN₂/RO₂) = √(MO₂ / MN₂) = √(32/28)

   Nitrogen diffuses 1.07 times as fast as Oxygen.

2. Suppose nitrogen gas and oxygen gas, both at 25 °C, were injected into opposite ends of a tube filled with neon gas. If the tube is 100 cm long, at what point will the N₂ and O₂ meet?

   

   You may calculate the distance from either end. We chose the end where N₂ was introduced.

   x / (100 - x) = dN₂/dO₂ = √ (MO₂/MN₂) = 1.07

   Solving for x,

   x = 51.7 cm and 100 - x = 48.3 cm

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Safety

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Ammonia is lighter than hydrogen chloride and so the average speed of ammonia molecules is greater than that of hydrogen chloride molecules at the same temperature.

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• Beral pipet filled with concentrated HCl (store in hood)
• Beral pipet filled with concentrated ammonia (store in hood)
• 6-8 cm capillary tube
• 12-well strip
• metric ruler
• China marker

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The Woodrow Wilson microscale version of this lesson was developed by:

Donna Deen
Pauls Valley High School
111 Maxwell Drive
Pauls Valley, OK 73075

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