The Ideal Gas Law and Mass

The ideal gas law can tell us the number of moles of a gas, given its volume, pressure and temperature. Once we know the number of moles, we can calculate the mass of a gas by multiplying the number of moles by molar mass.

Let’s do just that.

Sample Problem

How many grams of chlorine gas would occupy a volume of 35.5 L at a pressure of 100.0 kPa and a temperature of 100. ºC?

Wanted: ? grams Cl2

Given:

V = 35.5 L

P = 100.0 kPa

T = 100. ºC

Remember that, for all gas law problems, we need to convert degrees Celsius to Kelvin.

T373

Next, since Rydberg’s constant has the units L-atm-K-1-mol-1, pressure needs to be in the units atm.

Converting kPa to atm:

atm9872

Wanted: ? grams Cl2

Given:

V = 35.5 L

P = 100.0 kPa = 0.9872 atm

T = 100. ºC = 373.15 K

The Ideal Gas Law is:

ideal-gas-law

We want to solve for moles, n, and multiply moles by the molar mass of Cl2.

Rewriting the equation to solve for moles:

ideal-gas-law-n2

Plugging in our values for P, V and T:

ideal-gas-law-114

To determine the number of grams of chlorine gas, we multiply the number of moles by the molar mass of chlorine gas:

ideal-gas-law-808

The answer is 80.8 g Cl2.

Sample Problem

How many grams are in a sample of oxygen gas if the pressure is 1520 mm Hg, the volume is 8200 mL and the temperature is -73 ºC?

Wanted: ? g O2

Given:

P = 1520 mm Hg

V = 8200 mL

T = -73 ºC

We have a number of conversions to do before we can use the ideal gas law to calculate the number of moles of oxygen gas. Since the units of Rydberg’s constant are L-atm-K-1-mol-1, we need volume in Liters, pressure in atmospheres and temperature in Kelvin.

8200 mL is equal to 8.2 L (since there are 1000 mL in 1 L).

Converting 1520 mm Hg to atm, there are 760 mm Hg in 1 atm:

ideal-gas-law-2atm

Converting -73 ºC to K:

ideal-gas-law-200K

Wanted: ? g O2

Given:

P = 1520 mm Hg = 2.0 atm

V = 8200 mL = 8.2 L

T = -73 ºC = 200.15 K

The Ideal Gas Law is:

ideal-gas-law

To solve for moles, n:

ideal-gas-law-n2

Plugging in our values for P, V and T:

ideal-gas-law-1mol

To determine the number of grams of O2, we multiply the number of moles by oxygen’s molar mass.

ideal-gas-law-32g

There are 32 g O2.

Sample Problem

Dry ice is carbon dioxide in the solid state. 1.28 grams of dry ice are placed into a 5.00 L evacuated chamber that is maintained at 35.1 °C. What is the pressure in the chamber in kPa after all the dry ice has sublimed into CO2 gas?

Wanted: ? kPa

Given:

mass = 1.28 g CO2

V = 5.00 L

T = 35.1 °C

In this problem, we’re given mass in grams. We need to convert mass to moles, and then we can put that into the ideal gas law to calculate pressure.

To convert 1.28 g CO2 to moles, we need to divide by the molar mass of CO2.

ideal-gas-law-291mol

We also need to convert 35.1 °C to Kelvin:

ideal-gas-law-308K

Wanted: ? kPa

Given:

mass = 1.28 g CO2 = 0.0291 mol

V = 5.00 L

T = 35.1 °C = 308.25 K

The Ideal Gas Law is:

ideal-gas-law

To solve for pressure, we divide each side by V, and then, plugging in our values for n, V and T:

ideal-gas-law-147

The pressure of CO2 is 0.147 atm.

The problem asked for pressure in kPa, so we need to convert some units:

ideal-gas-law-149

The pressure of CO2 in kPa is 14.9 kPa.