The Ideal Gas Law

Ideal Gas Real GasMade of small particles that have mass

Same

Mostly Empty Space SameLow density SameParticles are in constant motion

Same

No attractive or repulsive forces between particles

Small attractive or repulsive forces between particles

Particles have no volume Particles have small volumeCollision are elastic (lose no KE)

Collision are NOT elastic (lose KE)

P1 x V1 = P2 x V2

= Rn1 x T1 n1 x T2

Standard Temperature and Pressure

The conditions 0 0C and 1 atm are called standard temperature and pressure (STP).

PV = nRT

R = PV

nT=

(1 atm)(22.414L)

(1 mol)(273.15 K)

R = 0.082057 L • atm / (mol • K)

Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.

What is the volume (in liters) occupied by 49.8 g of HCl at STP?

PV = nRT

V = nRT

P

T = 0 0C = 273.15 K

P = 1 atm

n = 49.8 g x 1 mol HCl

36.45 g HCl= 1.37 mol

V =1 atm

1.37 mol x 0.0821 x 273. 15 KL•atmmol•K

V = 30.6 L

GIVEN:P = ? atmn = 0.412 molT = 16°C = 289 KV = 3.25 LR = 0.0821Latm/molK

WORK:PV = nRT

P(3.25)=(0.412)(0.0821)(289) L mol Latm/molK K

P = 3.01 atm

Calculate the pressure in atmospheres of 0.412 mol of He at 16°C & occupying 3.25 L.

GIVEN:V = ?n = 85 gT = 25°C = 298 KP = 104.5 kPaR = 8.315 dm3kPa/molK

Find the volume of 85 g of O2 at 25°C and 104.5 kPa.

= 2.7 mol

WORK:85 g 1 mol = 2.7 mol 32.00 g

PV = nRT(104.5)V=(2.7) (8.315) (298) kPa mol dm3kPa/molK K

V = 64 dm3

Example

A gas sample occupies a volume of 0.685 L at 38°C and 0.775 atm. What will be the temperature of the sample if it occupies 0.125 L at 1.25 atm?

Example

A sample of nitrogen gas in a 2.00 L container has a pressure of 1800.6 mmHg at 25°C. What would be the pressure on the sample in a 1.00 L container at 125°C?

Example

The gas pressure in an aerosol can is 1.5 atm at 25 oC. Assuming that the gas inside obeys the ideal-gas equation, what would the pressure be if the can were heated to 450 oC?

What volume does 48.0 g of methane, CH4, occupy at 140. oC under a pressure of 1280 torr?

A 250. mL flask contains a mixture of nitrogen, oxygen, and helium at a temperature of 27 oC and a pressure of 0.850 atm. How many moles of gas are present?

What pressure in kilopascals is exerted by 0.480 g of carbon dioxide in a 1.00 L flask at 100 oC?

What is the volume of a 15.0-g sample of neon gas at 130.0 kPa and 39°C?

At what temperature will 2.85 moles of hydrogen gas occupy a volume of 0.58 L at 1.00 atm?