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## Group Activity: Gas Laws

### Boyle’s Law (1662)

At a given constant temperature and number of moles of gas, the pressure and volume of a gas are inversely proportional. That is, the higher the pressure, the smaller the volume; the lower the pressure, the larger the volume. This relationship can be expressed in the equation:
```P · V = constant
```
To find out how one of the quantities changes when you change the other, use the following equation:
```P1 · V1 = P2 · V2
```

1) An inflated balloon has a volume of 0.55 L at sea level (1 atm) and is allowed to rise to a height of 6.5 km, where the pressure is about 0.40 atm. Assuming that the temperature remains constant, what is the final volume of the balloon? Convert your answer to cubic meters (1 m3 = 1000 L). (Source: Chemistry, Raymond Chang)

2) A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. Calculate the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL. Convert your answer to atm (1 atm = 760 mmHg). (Source: Chemistry, Raymond Chang)

3) At 46°C a sample of ammonia gas exerts a pressure of 5.3 atm. What is the pressure when the volume of the gas is reduced to one-tenth (0.10) of the original value at the same temperature? Convert your answer to kPa (1 atm = 101.325 kPa) (Source: Chemistry, Raymond Chang)

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### Charles’s Law (1787)

At a given constant pressure and number of moles of gas, the volume and temperature of a gas are directly proportional. In other words, the more you raise the temperature, the larger the volume of gas. Temperature must be expressed in kelvins, not degrees Celsius (x°C = x + 273 K). This relationship can be expressed in the equation:
```V
— = constant
T
```
To find out how one of the quantities changes when you change the other, use the following equation:
```V1    V2
—  =  —
T1    T2
```

1) A 452 mL sample of fluorine gas is heated from 22°C to 187°C at constant pressure. What is its final volume in liters? (Source: Chemistry, Raymond Chang)

2) A sample of carbon monoxide gas occupies 3.20 L at 125°C. Calculate the temperature at which the gas will occupy 1.54 L if the pressure remains constant. Be sure to express your answer in kelvins. (Source: Chemistry, Raymond Chang)

3) Under constant pressure conditions 9.6 L of hydrogen gas initially at 88°C is cooled to -15°C. What is its volume after the cooling is complete? (Source: Chemistry, Raymond Chang)

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At a given constant temperature and constant pressure, the volume and mass (i.e., the number of moles, n) of a gas are directly proportional. This relationship can be expressed in the equation:
```V
— = constant
n
```
To find out how volume changes when you change the number of moles, use the following equation:
```V1    V2
—  =  —
n1    n2
```
Note: you cannot change the number of moles just by changing the volume! For that you have to add or subtract gas particles.

1) One mole of an ideal gas has a volume of 22.4 L at 1 atm and 273K. (This set of conditions is known as STP: Standard Temperature and Pressure). What is the volume of 0.50 mol of gas? Of 0.01 mol of gas?

### Combined Gas Laws

The combined gas law brings all these relationships together into one simple equation.
```PV = nRT
```
The only complicating factor is the introduction of the gas constant (R = 0.0821 L·atm/K·mol or R = 8.314 L·kPa/K·mol). This constant can be derived from the ideal gas law as follows:
```PV
——  =  R
nT
```
You can see now how the units of R work with pressure and volume in the numerator and moles and temperature in the denominator. This same expression can be used to follow changes in volume, pressure, and temperature by realizing that no matter how you change these three variables, they will always equal R. Assuming that there is no change in the number of moles, use the following expression to take all three variables into account during changes:
```P1V1      P2V2
————  =  ————
T1        T2
```

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1) A man filled his tires with air to a pressure of 32 lb/in2 when the temperature outside was -10°C. What pressure (in units of atm) of air is in the tire once the weather finally warms up to a more comfortable 20°C? (Hint: solve the equation for P). (Source: Chemistry, Raymond Chang)

2) Sulfur hexafluoride (SF6) is a colorless, odorless, very unreactive gas. It is sometimes used in double-pane windows as a filler gas because of its insulative properties. Calculate the pressure (in atm) exerted by 1.82 moles of the gas in a steel vessel of volume 5.43 L at 69.5°C. (Hint: solve the equation for P). (Source: Chemistry, Raymond Chang)

3) Calculate the volume (in liters) occupied by 2.12 moles of nitric oxide (NO) at 6.54 atm and 76°C. (Hint: solve the equation for V). (Source: Chemistry, Raymond Chang)

4) An average pair of human lungs contains about 3.5 L of air after inhalation and about 3.0 L after exhalation. Assuming that air in your lungs is at 37°C (body temp.) and 1.0 atm, determine the number of moles in a typical breath. (Hint: solve the equation for n). (Source: PLTL Unit 5, USM Chemistry Department)

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5) Using your answer from the previous question, find the number of moles of oxygen usually inhaled in a single breath. Oxygen is 20.948% by volume of air. (Hint: use Avogadro’s Law to help answer this question).

6) A gas is known to be one of the following nitrogen oxides: NO, NO2, N2O4, or N2O. It has a density of 1.96 g/L. If you have a 1.00 L sample at 273K, what is its identity? (Source: PLTL Unit 5, USM Chemistry Department)

### Stoichiometry with Gases

Stoichiometry is as important for gases as it is for solids, liquids and solutions. To solve problems with gases you do exactly what you did for reactants in other states of matter: convert to moles! You can use a variety of ways to find the number of moles, depending on the information you are given. Given grams, finding moles is easy. Given a volume, temperature and pressure, finding moles means using n = PV/RT. Given a density and a volume, find the mass and from there you can find the number of moles. Remember to convert to the units required by the problem once you have performed your calculation.

1) Aqueous lithium hydroxide solution is used to purify air in spacecraft and submarines because it absorbs carbon dioxide according to the equation:

2LiOH(aq) + CO2(g) → LiCO2(aq) + H2O(l)

The pressure of carbon dioxide in a cabin having a volume of 2.4 × 105 L is 7.9 × 10-3 atm at 312 K. A solution of lithium hydroxide (LiOH) of negligible volume is introduced into the cabin. Eventually the pressure of CO2 is reduced to 1.2 × 10-4 atm. How many grams of lithium carbonate are formed in this process? (Source: Chemistry, Raymond Chang)

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2) Consider the following description of an automobile air bag:
“In a frontal impact of sufficient severity, the air bag sensing system on the vehicle will detect that the vehicle is suddenly stopping as a result of a crash. The sensing system completes an electrical circuit, triggering a chemical reaction of the sodium azide sealed in the inflators. the reaction produces nitrogen gas, which inflates the air bag." (Source: 1995 Saturn Owner's Manual, p. 33)

The reaction is: 2NaN3(s) → 2Na(s) + 3N2(g)

How many grams of sodium azide are needed to produce 40.0 L of nitrogen to fill an air bag at a pressure of 1.30 atm and a temperature of 28.0°C? (Source: PLTL Unit 5, USM Chemistry Department)