Graham's Law of Diffusion

Graham's Law of Diffusion

Description

Hydrogen chloride and ammonia diffuse from opposite ends of a long tube. They meet and react to produce ammonium chloride, a white solid powder. The distances of the white powder from either end of the tube are measured, and the ratio compared with a predicted ratio from Graham's Law. The experiment is not expected to give close quantitative agreement between calculated and observed values, but the ammonia does diffuse faster than the HCl, as expected.

Set

Diffusion is the spreading of gases to occupy all the space available to them. A gas will diffuse even if another gas is present in the same space. The molecules of gases are far enough apart to allow other gas molecules to fit in between. The rate at which a gas diffuses is directly proportional to the average speed of its molecules: the faster molecules diffuse at a faster rate. The rates depend on the molar masses.
At a given temperature, the average kinetic energy (KE) of all gas molecules is the same:

KE = (1/2) mc²

where m=mass of molecule and c = speed of molecule so that:

KE (HCl(g)) = KE (NH₃(g))
(1/2) (mHCl) (cHCl)2=(1/2) (mNH3) (cNH3)2
(mHCl) / (mNH₃) = (cNH₃)² / (cHCl)²)
[ (cNH₃) / (cHCl) ] = √ [ (mHCl) / (mNH₃) ]

Since speed = distance/time, and the time is the same for both kinds of molecules in this experiment,

[ Distance NH₃ / Distance HCl ] = √ [ (mHCl) / (mNH₃) ]
The distance traveled by the heavier gas (gas with the greater molar mass) will be less then that traveled by the lighter gas in the same period of time.

Hazards

HCl and NH₃ are toxic by ingestion or inhalation, and corrosive to skin and eyes. They are irritating, especially to the eyes. They are also potentially fatal respiratory hazards.

Precautions

Dispense the chemicals in a hood. Have an eye wash accessible. Caution should be employed when saturating the cotton with the liquids. Do not inhale the vapors; provide adequate ventilation.

Procedure

Microscale Procedure

Under a hood, one drop of concentrated hydrochloric acid is placed in well-1 of a 12-well strip. A drop of 6 M ammonia is placed in well-12 of the same strip. The strip serves as a source of reagents. These small amounts may be moved to a student's desk. A glass capillary is dipped one end into the hydrochloric acid, and then the other end into the ammonia. In each case, capillary action draws a small amount of liquid into the capillary. The capillary is placed flat against a dark surface. In just a few moments, a white solid forms inside the capillary. Use a millimeter rule to measure the distance between the boundary of each liquid in the capillary and the white solid.

Demonstration

Clamp a long tube (20 to 25 mm in diameter) horizontally.
Place drops of the chemicals on cotton wads set on watch glasses. Have two students assist you. Using tweezers, insert these wads into the open ends of the glass tube. Stopper the ends. Note which end contains the ammonia.
Wait. It takes 5 to 10 minutes for the reaction to take place to a noticeable extent.
Mark the location of the reaction product using a marking pencil or opaque tape.
Measure the length of the tube, and the distance from one cotton wad to the mark.

Handout Makeup

Name ___________________________ Class ________

Teacher__________________________

DoChem 080 Graham's Law of Diffusion

Watch the movie.

What would be the effect of clamping the tube in the vertical position?

Use this sample data to answer the questions.

Length of tube = 84.2 cm
Distance traveled by NH₃ = 51.3 cm
Distance traveled by HCl = 84.2 - 51.3 = 32.9 cm

Write a chemical equation for the reaction which took place.
Find the ratio of the experimental distance which the NH₃ molecules traveled to the distance which the HCl molecules traveled.
Compare this ratio to the ratio predicted from the molar masses.

Teachers Guide

Purpose

To demonstrate Graham's law by observing gaseous diffusion.

Materials

2 support stands
2 single-buret clamps
1 80-100 cm glass tube, 1.5-2.0 cm i.d.
2 stoppers or corks
2 cotton wads
meter stick
wax marking pencil
2 dropping pipets (eye droppers)
2 watch glass
2 tweezers
1 mL 6 M NH₃ (8 drops concentrated ammonia plus 12 drops water)
1 mL HCl (concentrated)
hair dryer

Lab Hints

Try this experiment, and compute data before going into class.
The tubes must be dry. Use a hair dryer to dry the tube between classes.

Time

Teacher preparation: 20 minutes

Demonstration: 10 minutes

Hazards

HCl and NH₃ are toxic by ingestion or inhalation, and corrosive to skin and eyes. They are irritating, especially to the eyes. They are also potentially fatal respiratory hazards.

Precautions

Dispense the chemicals in a hood. Have an eye wash accessible. Caution should be employed when saturating the cotton with the liquids. Do not inhale the vapors; provide adequate ventilation.

Disposal

Fill a 250-mL beaker with 200 mL of tap water. Remove one stopper; use tweezers to remove the cotton wad and immerse it into the water. Repeat this sequence for the second stopper. Place the cotton wads in a plastic bag and discard with ordinary trash. Flush the water down the sink. Rinse the tube with tap water.

Presentation?

Presentation Question:

What would be the effect of clamping the tube in the vertical position?
- The tube position should have no effect on the outcome. There may be a problem with liquids running, however, that will obscure the result. In this case, the cloud of salt will form nearer the bottom of the vertical tube than expected, no matter which end is up when the tube is clamped.

Sample Data

Length of tube = 84.2 cm
Distance traveled by NH₃ = 51.3 cm
Distance traveled by HCl = 84.2 - 51.3 = 32.9 cm

Closure?

Closure Questions:

Write a chemical equation for the reaction which took place.
Find the ratio of the experimental distance which the NH₃ molecules traveled to the distance which the HCl molecules traveled.
Compare this ratio to the ratio predicted from the molar masses.

Answers to Closure Questions:

NH₃ (g) + HCl(g) --> NH₄Cl(s)
Experimental ratio = 51.3 cm / 32.9 cm = 1.56
Predicted ratio = √ [(36.5 g/mol) / (17.0 g/mol)] = 1.47

% error = [ ( | Experimental - Accepted value | ) /
(Accepted value) ] x 100%
= [ (|1.56- 1.47|) / (1.47) ] x 100% = 6.1%

Application

The hydrochloric acid bottles left out in your lab, with time, become covered with a white powder. Suggest a possible composition for this powder. Why do the ammonia bottles become less covered than do the HCl bottles?

Background

Problems associated with this experiment are discussed by W. J. Deal in "Ideal Gas Laws," Journal of Chemical Education 52 (1975), 405-7.

Key Words

diffusion
diffusion rate
gaseous diffusion
Graham's law