Unit 3 - Part III - The Ideal Gas Law PV = nRT

Relating Mass to Numbers of Atoms• A mole (or mol) is the amount of a substance that

contains exactly 6.022 x 1023 atoms. • This is based on the number of atoms in exactly 12

grams of carbon-12.

For example -1 mole of Helium = 6.022 x 1023 atoms of Helium = 4 grams of Helium

• Avogadro’s number—6.022 1415 × 1023—is the number of particles in exactly one mole.

Mass = molar mass

• The mass of one mole of a substance is called the molar mass of that substance.

• Molar mass units = g/mol.• Atomic mass = molar mass

• Helium’s mass = 4.003 • Heliums molar mass = 4.003 g/mol

Gram/Mole Conversions• Chemists use molar mass as a conversion factor in

chemical calculations.• Since the molar mass of helium is 4.00 g/mol...• We can use this number to convert moles of Helium

to grams of Helium.

How many grams are in 4 moles of Helium?

How many moles are in 8 grams of Helium?

• All of the gas laws you have learned thus far can be combined into a single equation.

• The ideal gas law →

R = 0.082 - This is for

temperature in K.

The Ideal Gas Law

TK = Tc + 273.15

What is the pressure in atmospheres exerted by a 0.500 mol sample of nitrogen gas in a 10.0 L container at 298 K?

Keep in mind the following: n = moles V = liters (volume) Temperature = Kelvin P = atm (pressure)

Given: V of N2 = 10.0 L n of N2 = 0.500 mol

T of N2 = 298 KUnknown: P of N2 in atmSolution: Use the ideal gas law, which can be

rearranged to find the pressure, as follows.

The Ideal Gas Law

Substitute the given values into the equation:

The Ideal Gas Law, continued

• Recall that one mole of a substance contains a number of particles equal to 6.022 × 1023.

• The volume occupied by one mole of gas at STP is 22.414 10 L (rounded to 22.4 L).

• 1 mole = 22.4 L (at STP)

Molar Volume of a Gas Formula

• Knowing the volume of a gas, you can use the conversion factor 1 mol/22.4 L to find the moles (and therefore also mass) of a volume of gas at STP.

Molar Volume of a Gas, continued

Molar Volume of a Gas, continued• You can also use the molar volume of a gas to find

the volume, at STP, of a number of moles or a known mass of gas.

a. What volume does 0.0685 mol of gas occupy at STP?

b. What quantity of gas, in moles, is contained in 2.21 L at STP?

Given: 0.0685 mol of gas at STPUnknown: volume of gasSolution: Multiply the amount in moles by the conversion

factor.

Molar Volume of a Gas, continued

Given: 2.21 L of gas at STPUnknown: moles of gasSolution: Multiply the volume in liters by the conversion

factor.

Molar Volume of a Gas, continued

Ideal Gas Law and Density