The Ideal Gas law

Bringing It All Together

IntroductionWhen we use the combined gas law

we allow P, V, and T to vary.

we keep the amount of gas constant.

If we vary the amount of gas as well as the pressure, volume, and temperature

we will use the Ideal Gas Law

IntroductionWhen we use the phrase “Ideal Gas Law,”

we are talking about an ideal gas

we are not talking about a real gas

An ideal gas obeys all of the assumptions of the kinetic theory of gases -

small particles • no attraction

moving rapidly • perfectly elastic

IntroductionUnder most common circumstances, real gases act like ideal gases.

Only under conditions of -

low temperature

or

high pressure

will real gases deviate from ideality.

ApplicationApplying the kinetic theory, as we add an amount of gas to a container of gas, we are introducing additional particles to collide with the walls of the container.

Pressure goes up to keep V & T const.

Volume goes up to keep P & T const.

Temperature goes down to keep P & V const.

ApplicationThis means that the amount (number of mols) of material varies -

directly with pressure and volume

inversely with temperature

We will use the equation -

PV = nRT

P is pressure, V is volume, n is mols of gas, T is temperature, and R is the gas constant.

ApplicationPV = nRT

P: measured in atm, kPa, or mm Hg

V: measured in L

n: measured in mol

T: measured in K

R: a constant whose value depends on the units of P, V, n, and T

ApplicationPV = nRT

If P is measured in atm:

R = 0.0821 atm-L/mol-K

If P is measured in kPa:

R = 8.31 kPa-L/mol-K

If P is measured in mm Hg:

R = 62.4 mm Hg-L/mol-K

ApplicationPV = nRT

Remember:

The value of R is dependent on the units of pressure.

Always use the correct value of R.

All appropriate values for R will be given to you for any test or quiz.

Example 1What is the pressure, in atm, of 0.125 mols of helium in a 4.00 L container at a temperature of 153°C (430 K)?

P = ? atmV = 4.00 Ln = 0.125 molR = 0.0821 atm-L/mol-KT = 430 K

PV = nRT ➔ P = = atmnRT (0.125)(0.0821)(430)

V (4.00)

P = 1.10321875 atm = 1.10 atm

Example 2What is the volume of 2.50 mols of oxygen at a pressure of 85.0 kPa and a temperature of 42.0°C (315 K)?

P = 85.0 kPaV = ? Ln = 2.50 molR = 8.31 kPa-L/mol-KT = 315 K

PV = nRT ➔ V = = LnRT (2.50)(8.31)(315)

P (85.0)

V = 76.98970588 L = 77.0 L

Example 3How many mols of nitrogen is contained in a volume of 22.4 L at a pressure of 760 mm Hg and a temperature of 0°C (273 K)?

P = 760 mm HgV = 22.4 Ln = ? molR = 63.4 mm Hg-L/mol-KT = 273 K

PV = nRT ➔ n = = molPV (760)(22.4)

RT (62.4)(273)

n = 0.999342538 mol = 1.00 mol

Example 4What is the temperature of 1.60 mols of neon contained in a volume of 15.0 L at a pressure of 1.20 atm?

P = 1.20 atmV = 15.0 Ln = 1.60 molR = 0.0821 atm-L/mol-KT = ? K

PV = nRT ➔ T = = KPV (1.20)(15.0)

nR (1.60)(0.0821)

T = 137.0280146 K = 137 K

We can also combine this with other equations to give us even more detailed information

Example 5What mass of Argon (M = 40.0 g/mol) is in a volume of 565 L at a pressure of 1,640 mm Hg and a temperature of 127°C (400 K)?

P = 1,640 mm HgV = 565 Ln = ? molR = 63.4 mm Hg-L/mol-KT = 400 K

PV = nRT

➔ n = = molPV (1,640)(565)

RT (62.4)(400)

n = 37.1 mol

m = nM = (37.1)(40.0) g

m = 1,480 g

SummaryWhen we use the phrase “Ideal Gas Law,”

we are talking about an ideal gas

we are not talking about a real gas

An ideal gas obeys all of the assumptions of the kinetic theory of gases -

small particles • no attraction

moving rapidly • perfectly elastic

SummaryWe will use the equation -

PV = nRT

P is pressure, V is volume, n is mols of gas, T is temperature, and R is the gas constant.

The value of R is dependent on the units of pressure.

Always use the correct value of R.

All appropriate values for R will be given to you for any test or quiz.