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Thursday, October 22, 2009

Boyle's Law (Concept and Example)

If you trap a sample of air and measure its volume at different pressures (constant temperature), then you can determine a relation between volume and pressure. If you do this experiment, you will find that as the pressure of a gas sample increases, its volume decreases. In other words, the volume of a gas sample at constant temperature is inversely proportional to its pressure. The product of the pressure multiplied by the volume is a constant:
PV = k or V = k/P or P = k/V
where P is pressure, V is volume, k is a constant, and the temperature and quantity of gas are held constant. This relationship is called Boyle's Law, after Robert Boyle, who discovered it in 1660.

Worked Example Problem
The sections on the General Properties of Gases and Ideal Gas Law Problems may also be helpful when attempting to work Boyle's Law problems.
Problem
A sample of helium gas at 25°C is compressed from 200 cm3 to 0.240 cm3. Its pressure is now 3.00 cm Hg. What was the original pressure of the helium?
Solution
It's always a good idea to write down the values of all known variables, indicating whether the values are for initial or final states. Boyle's Law problems are essentially special cases of the Ideal Gas Law:
Initial:
P1 = ?; V1 = 200 cm3; n1 = n; T1 = T
Final: P2 = 3.00 cm Hg; V2 = 0.240 cm3; n2 = n; T2 = T
P1V1 = nRT (Ideal Gas Law)
P2V2 = nRT
so, P1V1 = P2V2
P1 = P2V2/V1
P1 = 3.00 cm Hg x 0.240 cm3/200 cm3
P1 = 3.60 x 10-3 cm Hg
Did you notice that the units for the pressure are in cm Hg? You may wish to convert this to a more common unit, such as millimeters of mercury, atmospheres, or pascals.
3.60 x 10-3 Hg x 10mm/1 cm = 3.60 x 10-2 mm Hg
3.60 x 10-3 Hg x 1 atm/76.0 cm Hg = 4.74 x 10-5 atm

How to Prepare Gases

Chemistry Lab Instructions

You can use common chemistry lab chemicals and equipment to prepare several gases. A conical flask, thistle funnel, delivery tube, pneumatic trough, and beehive are useful items to have on hand. Please make sure you are familiar with the use and functioning of the laboratory equipment you use, are aware of the characteristics of the substances (toxicity, flammability, explosivity, etc.), and take proper safety precautions. Use a ventilation hood (fume cupboard) and keep flammable gases away from heat or flame. I've tried to be as accurate as possible in my instructions, but you use them at your own risk. For convenience, I've listed the gases in alphabetical order. If you would like to add a procedure or have comments about any of these procedures, please feel free to e-mail me.


Gas Reagents Method Collection Reaction
Ammonia Gently heat a mixture of ammonium chloride and calcium hydroxide in water.
NH3 Ammonium chloride
Calcium hydroxide Upward displacement of air in a hood. Ca(OH)2 + 2NH4Cl --> 2NH3 + CaCl2 + 2H2O
Carbon Dioxide
CO2 Calcium carbonate (marble chips)
5 M Hydrochloric acid Add 5 M hydrochloric acid to 5 - 10 g marble chips. Upward displacement of air in a hood. 2HCl + CaCO3 --> CO2 + CaCl2 + H2O
Chlorine
Cl2 Potassium permanganate
Conc. Hydrochloric acid Add concentrated hydrochloric acid dropwise onto a small amount of potassium permanganate crystals (in flask). Upward displacement of air in a hood. 6HCl + 2KMnO4 + 2H+ --> 3Cl2 + 2MnO2 + 4H2O + 2K+
Hydrogen
H2 Zinc (granulated)
5 M Hydrochloric acid Add 5 M hydrochloric acid to 5 - 10 g granulated zinc pieces. Collect over water. 2HCl + Zn --> H2 + ZnCl2
Hydrogen Chloride
HCl Sodium chloride
Conc. Sulfuric acid Slowly add concentrated sulfuric acid to solid sodium chloride. Displacement of air in a hood. 2NaCl + H2SO4 --> Na2SO4 + 2HCl
Methane
CH4 Sodium acetate (anhydrous)
Soda lime Mix 1 part sodium acetate with 3 parts soda lime. Heat in a dry pyrex test tube or flask. Collect over water. CH3COONa + NaOH --> CH4 + Na2CO3
Nitrogen
N2 Ammonia
Calcium hypochlorite (bleaching powder) Shake 20 g calcium hypochlorite into 100 mL water for several minutes, then filter. Add 10 mL conc. ammonia and heat mixture. Use extreme caution! Chloramine and explosive nitrogen trichloride may be produced. Displacement of air.
2NH3 + 3CaOCl2 --> N2 + 3H2O + 3CaCl2
Nitrogen
N2 Air
Lighted Phosphorus (or heated Fe or Cu) Invert a bell jar over lighted phosphorus. Oxygen and phosphorus combine to form phosphorus pentoxide, which is absorbed by the water over which the bell jar stands (may be violent reaction), producing phosphoric acid and leaving the nitrogen behind. Removal of oxygen.
5 O2 + 4 P --> P4O10

Nitrogen Dioxide NO2 Copper (turnings)
10 M Nitric acid Add concentrated nitric acid to 5 - 10 g copper. Upward displacement of air in a hood.
Cu + 4HNO3 --> 2NO2 + Cu(NO3)2 + 2H2O
Nitrogen Monoxide
NO Copper (turnings)
5 M Nitric acid Add 5 M nitric acid to 5 - 10 g copper. Collect over water.
3Cu + 8HNO3 --> 2NO + 3Cu(NO3)2 + 4H2O
Nitrous Oxide
N2O Sodium nitrate
Ammonium sulfate Mix 10 g powdered sodium nitrate and 9 g ammonium sulfate. Heat well. Displacement of air.
NH4NO3 --> N2O + 2H2O
Oxygen
O2 6% Hydrogen peroxide
Manganese dioxide (catalyst) Add hydrogen peroxide to about 5 g of MnO2. Collect over water. 2H2O2 --> 2H2O + O2
Oxygen
O2 Potassium permanganate Heat solid KMnO4. Collect over water.
2KMnO4 --> K2MnO4 + MnO2 + O2
Sulfur Dioxide
SO2 Sodium sulfite (or sodium bisulfite)
2 M Hydrochloric acid Add dilute hydrochloric acid to 5 - 10 g sodium sulfite (or bisulfite). Upward displacement of air in a hood.
Na2SO3 + 2HCl --> SO2 + H2O + 2NaCl

Gases - General Properties of Gases

Gases: Examine the properties of real and ideal gases. Perform calculations using the Ideal Gas Law, Dalton's Law, Graham's Law, and Van der Waals Equation. Learn to prepare gases in the lab.

General Properties of Gases

All pure substances display similar behavior in the gas phase. At 0° C and 1 atmosphere of pressure, one mole of every gas occupies about 22.4 liters of volume. Molar volumes of solids and liquids, on the other hand, vary greatly from one substance to another. In a gas at 1 atmosphere, the molecules are approximately 10 diameters apart. Unlike liquids or solids, gases occupy their containers uniformly and completely. Because molecules in a gas are far apart, it is easier to compress a gas than it is to compress a liquid. In general, doubling the pressure of a gas reduces its volume to about half of its previous value. Doubling the mass of gas in a closed container doubles its pressure. Increasing the temperature of a gas enclosed in a container increases its pressure.
Because different gases act similarly, it is possible to write a single equation relating volume, pressure, temperature, and quantity of gas. This Ideal Gas Law and the related Boyle's Law, Law of Charles and Gay-Lussac, and Dalton's Law are central to understanding the more complex behavior of real gases.



Ideal Gas Law:
PV = nRT

Boyle's Law:
PV = k1

Law of Charles and Gay-Lussac:
V = k2T

Dalton's Law:
Ptot = Pa + Pb

where:
P is pressure, Ptot is total pressure, Pa and Pb are component pressures

Problem

2.50 g of XeF4 gas is placed into an evacuated 3.00 liter container at 80°C. What is the pressure in the container?

Solution

PV = nRT, where P is pressure, V is volume, n is number of moles, R is the gas constant, and T is temperature.

P=?
V = 3.00 liters
n = 2.50 g XeF4 x 1 mol/ 207.3 g XeF4 = 0.0121 mol
R = 0.0821 l·atm/(mol·K)
T = 273 + 80 = 353 K

Plugging in these values:

P = nRT/V

P = 00121 mol x 0.0821 l·atm/(mol·K) x 353 K / 3.00 liter

P = 0.117 atm

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