The Ideal Gas Law

Section 11.3

Standard Molar Volume of a Gas

• Assume the gas is an ideal gas• Standard molar volume of a gas: the

volume occupied by one mole of a gas at STP, the value is 22.4 L

• Knowing the volume of gas at STP, you can find the number of mol by dividing by 22.4 L

Continued

• Knowing the mol of the gas, you can multiply by 22.4 L to find the volume of the gas (at STP)

• At STP, what is the volume of 7.08 mol of nitrogen gas?

• 159 L N2

Another Problem

• A sample of hydrogen gas occupies 14.1 L at STP. How many moles of the gas are present?

• 0.629 mol H2

The Ideal Gas Law

• Ideal gas law: the mathematical relationship among pressure, volume, temperature, and the number of moles of a gas

• If “R” is a constant and “n” is the number of moles:

• PV = nRT

The Ideal Gas Constant

• The constant “R” is the ideal gas constant• The value and units of “R” vary according

to the units used for P and V• If P is in kPa, and V is in L, then R = 8.314• Temperature has to be K

Problem• A tank of hydrogen gas has a volume of

22.9 L and holds 14.0 mol of the gas at 12°C. What is the pressure of the gas in kPa?

• Given: • V = 22.9 L• n = 14.0 mol• T = 12 + 273 = 285 K• R = 8.314• P = ?

Solution

• PV = nRT

• P = 1448.596507• P = 1450 kPa

Another Formula

• You can use the ideal gas law to find the molar mass of a substance

• M = molar mass• m = mass of the substance• R, T, P, and V represent the regular stuff

Problem

• What is the molar mass of a gas which has a mass of 20.24 g and a volume of 8.13 L at 20.0 °C and 99.2 kPa?

• = 61.1 g/mol

Problems• Calculate the volume that a 0.323-mol

sample of a gas will occupy at 265 K and a pressure of 91.2 kPa.

• 7.80 L• What is the pressure in kPa of a 0.108-mol

sample of helium gas at a temperature of 20.0°C if its volume is 0.505 L?

• 521 kPa

Another Problem

• Determine the kelvin temperature required for 0.0470 mol of gas to fill a balloon to 1.20 L under 100.0 kPa

• 307 K