5 Steps to a 5 AP Chemistry

We could work this into the combined gas law, but more commonly the amount of

gas is related to the other physical properties through another relationship that Avogadro

developed:

1 mol of any gas occupies 22.4 L at STP

[Standard Temperature and Pressure of 0°C (273 K) and 1 atm]

The combined gas law and Avogadro’s relationship can then be combined into the ideal

gas equation, which incorporates the pressure, volume, temperature, and amount relation-

ships of a gas.

Ideal Gas Equation

The ideal gas equationhas the mathematical form of PV=nRT, where:

P=pressure of the gas in atm, torr, mm Hg, Pa, etc.

V=volume of the gas in L, mL, etc.

n=number of moles of gas

R=ideal gas constant: 0.0821 L·atm/K·mol

T=Kelvin temperature

This is the value for Rif the volume is expressed in liters, the pressure in atmospheres,

and the temperature in kelvin (naturally). You could calculate another ideal gas constant

based on different units of pressure and volume, but the simplest thing to do is to use the

0.0821 and convert the given volume to liters and the pressure to atm. And remember that

you must express the temperature in kelvin.

Let’s see how we might use the ideal gas equation. Suppose you want to know what

volume 20.0 g of hydrogen gas would occupy at 27°C and 0.950 atm. You have the pres-

sure in atm, you can get the temperature in kelvin (27°C + 273 =300. K), but you will

need to convert the grams of hydrogen gas to moles of hydrogen gas before you can use the

ideal gas equation. Also, remember that hydrogen gas is diatomic, H 2.

First you’ll convert the 20.0 g to moles:

(20.0 g/l) ×(1 mol H 2 /2.016 g) =9.921 mol H 2

(We’re not worried about significant figures at this point, since this is an intermediate

calculation.)

Now you can solve the ideal gas equation for the unknown quantity, the volume.

PV=nRT

V=nRT/P

Finally, plug in the numerical values for the different known quantities:

V =(9.921 mol)(0.0821 L atm/K mol) (300. K)/0.950 atm

V=257 L

Is the answer reasonable? You have almost 10 mol of gas. It would occupy about 224 L

at STP (10 mol ×22.4 L/mol) by Avogadro’s relationship. The pressure is slightly less than

standard pressure of 1 atm, which would tend to increase the volume (Boyle’s law), and

temperature is greater than standard temperature of 0°C, which would also increase the

volume (Charles’s law). So you might expect a volume greater than 224 L, and that is

exactly what you found.

Remember, the final thing you do when working any type of chemistry problem is

answer the question: Is the answer reasonable?

Gases  109

KEY IDEA

KEY IDEA