The Empirical Gas Laws

Unit 10Chapter 13

Boyle’s Law Published in 1662 by Robert Boyle,

it states that for a fixed amount of a gas at a fixed temperature, the pressure of the gas is inversely proportional to the volume of the gas.

P ∝ V-1

Generalizing this, we get

1 1 2 2PV P V

Boyle-ing your Brain

A gas occupies 17.4 liters at 0.862 atm. What is the pressure if the volume becomes 15.0 L?

P1 = 0.862 atm V1 = 17.4 L P2 = ? V2 = 15.0 L (0.862 atm)(17.4 L) = P2(15.0 L) P2 = 1.000 atm

Charles’s Law Published in 1802 by Joseph Gay-Lussac

based off of work from the 1780’s by Jacques Charles, it states that for a fixed amount of a gas at a fixed pressure, the volume of the gas is directly proportional to the temperature of the gas.

V ∝ T Generalizing this, we get

(since there is a sign inversion at 0 °C, always use Kelvin)

1 2

1 2

V V

T T

Giving Your Brain a Charlie Horse

The temperature of a 4.00 L sample of gas is changed from 10.0 °C to 20.0 °C. What will the volume of this gas be at the new temperature?

V1 = 4.00 L T1 = 10.0°C + 273 = 283 K

V2 = ? T2 = 20.0°C + 273 = 293 K

V2 = 4.14 L

2V4.00L

283K 293K

Pressure/Temperature Law Published in 1702 by Guillaume Amontons

but made famous by Gay-Lussac (in the same paper from 1802), it states that for a fixed amount of a gas at a fixed volume, the pressure of the gas is directly proportional to the temperature of the gas.

P ∝ T Generalizing this, we get

(remember to always use Kelvin)

1 2

1 2

P P

T T

Feeling the Pressure

If a gas in a closed container is pressurized from 15.0 atm to 16.5 atm and its original temperature was 23.7 °C, what would the final temperature of the gas be?

P1 = 15.0 atm T1 = 296.7 K P2 = 16.5 atm T2 = ?

T2 = 326.4 K = 53.4°C

2

15.0atm 16.5atm

296.7K T

The Combined Gas Law

Combining Boyle’s, Charles’s, and the Pressure/Temperature Law, assuming a fixed amount of gas, we get:

(Always use Kelvin!)

1 1 2 2

1 2

PV P V

T T

I’ll Have the Combo-Meal

A gas has a volume of 800.0 mL at -23.00 °C and 300.0 torr. What would the volume of the gas be if it were heated to 289.5 °C and the pressure doubled?

P1 = 300.0 torr V1 = 800.0 mL T1 = 250.00 K

P2 = 600.0 torr V2 = ? T2 = 562.5 K

V2 = 900.0mL

2(600.0torr)V(300.0torr)(800.0mL)

250.0K 562.5K

Avogadro’s Law Published in 1811 by Amedeo

Avogadro, it states that for a gas with a fixed pressure and temperature, the volume of the gas is directly proportional to the number of particles of the gas – we now use moles.

V ∝ n Generalizing this, we get

1 2

1 2

V V

n n

Attack of the Mole A container with a volume of 18.7 L contains

0.379 mol nitrogen. How many moles of fluorine must be added to

increase the volume to 43.4 L? V1 = 18.7 L n1 = 0.379 mol N2

V2 = 43.4 L n2 = ?

n2 = 0.880 mol

nF2 = 0.880 – 0.379 = 0.501 mol F2

2

18.7L 43.4L

0.379mol n

Ideal Gas Law (pt 1)

Published in 1834 by Émile Clapeyron based off of Boyle’s Law and Charles’s Law, it states that for an ideal gas, the pressure-volume product is directly proportional to the mole-temperature product.

PV ∝ nT 

Ideal Gas Law (pt 2)

The proportionality constant is the same for all gases!

It is called the Ideal (or Universal) Gas Constant with symbol R.

Adding R, we get

PV nRT

What’s the Pirate Movie Rated?

R has many possible values. The 3 most common ones: If P is in atm, R = 0.08205746 atm·L /

mol·K in kPa, R = 8.314472 kPa·L / mol·K in mmHg, R = 62.36367 mmHg·L /

mol·K (same for torr)

An Ideal Test

What volume will 1.15 moles of H2 occupy at 20.0ºC and 801.8 mmHg?

P = 801.8 mmHg V = ? n = 1.15 mol T = 293.0 K P V = n R T (801.8)V = (1.15)(62.36)(293.0) V = 26.20628835 = 26.2 L

Universally Yours

At what temperature will 10.967 g of oxygen occupy 0.683 L at 1,266.4 kPa?

P = 1,266.4 kPa V = 0.683 L n = ? T = ? n = 10.967 g O2 / 32.00 g/mol = 0.3427 mol

O2

P V = n R T (1,266.4)(0.683) = (0.3427)(8.314)T T = 303.5760326 = 303.6 K

T = 30.6°C

Ideal Gases

Ideal gases are assumed to consist of: 1. Randomly moving point particles

(no size/volume) that are 2. Infinitely compressible and 3. Have no intermolecular attractions (i.e. will not stick to other atoms/molecules)

But Seriously, Folks

There is no such thing as an ideal gas! 1. Real gases are not point particles.

They have a volume And they are usually at least two atoms

bonded together (except the noble gases)

Deviation from Ideal

2. Real gases are not infinitely compressible and

3. Individual molecules show at least a small amount of attraction to other molecules This is how we are able to liquefy &

solidify gases.

Losing “R” Religion

Approaching the Ideal

Gases exhibit ideal behavior at low pressures and high temperatures (big volumes).

The closest thing to an ideal gas is helium.