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Gases Lecture III

- The Ideal Gas Law and Daltons Law of Partial

Pressures

The Ideal Gas Law

Is there a relationship between the following

variables?

pressure

volume

YES

number of moles

temperature

they all have an affect on one another

the ideal gas law allows us to quantify this

relationship by providing us an equation to

evaluate the effects of one variable on another

In equation form, the ideal gas law looks like

this

PVnRT

P is pressure in atmospheres

V is volume in liters

n is the number of moles of all gases present

T is the temperature in Kelvin

R is the ideal gas constant

- R 0.0821 atm x L/mol x K

Heres a problem using this equation

What pressure, in atmospheres, is exerted by

0.450 mol of nitrogen gas in a 6.10 L container

at standard temperature?

1. Identify the variables

n0.450 mol V6.10 L T273 K R 0.0821 atm x

L/mol x K

2. Rearrange the equation

PVnRT

PnRT/V

3. Solve the problem

P(0.450 mol)(0.0821)(273 K)/(6.10 L)

P1.65 atm

My lungs hold 6.30 L of air at normal body

temperature (37 oC) and standard pressure.

Assuming that air is made up of 20.9 oxygen, how

many oxygen molecules are in my lungs after I

take a breath?

1. Identify the variables

V6.30 L T310 K P1.00 atm R0.0821 atm x L/mol

x K

2. Solve the equation

PVnRT

nPV/RT

3. Solve the equation

n(1.00 atm)(6.30 L)/(0.0821 atm x L/mol x K)(310

K)

n0.2475 mol

4. Apply the percentage

- n is the number of molecules of any gas, so each

gas contributes the same to the total volume and

pressure, regardless of molar mass

moles of oxygen0.2475 mol x 20.9

moles of oxygen0.05173 mol

5. Convert to molecules

0.05173 mol

X

6.022 x 1023 molecules

1 mol

3.12 x 1022 molecules

Daltons Law of Partial Pressures

- partial pressure is defined as the pressure of

each individual gas in a mixture

- remember ideal gases all behave the same way

- Daltons law of partial pressures states that the

total pressure of a mixture of gases is equal to

the sum of the partial pressures of the gases in

the mixture

In an equation, it looks like this. . .

PtotalP1P2P3. . .

barometer

Poxygen0.12 atm

bulb with gas

Pnitrogen0.12 atm

Ptotal0.24 atm

What does the pressure of a gas depend on?

Primarily the number of moles of gas present

The greater the number of moles of a particular

gas present in a sample, the greater that gas

contributes to the total pressure of the sample

- if a gas makes up 3/5 of a sample, it accounts

for 3/5 of the total pressure - if a gas makes up 64 of a sample, it accounts

for 64 of the total pressure

the percentages and fractions refer to the number

of moles, not the mass

IMPORTANT

lets try an example

A 4.8 g sample of gas containing only nitrogen

and oxygen contains 3.1 g of O2. The gas is

sealed in a container and exerts a pressure of

940 mm Hg. What is the partial pressure of each

gas in the container?

1. Find the number of moles of each gas

molmass(g)/molar mass

mol O2(3.1 g)/(32.00g/mol)

0.09688 mol O2

mol N2(1.7 g)/(28.02g/mol)

0.06067 mol N2

2. Determine the mole fraction of each gas

mole fractionmoles of individual gas

total moles of gas

total moles of gas 0.09688 mol O2 0.06067 mol N2

0.15755 mol

mole fraction O20.09688 mol/0.15755 mol

0.6149

mole fraction N20.06067 mol/0.15755 mol

0.3851

3. Multiply total pressure by the mole fraction

to determine partial pressure of each gas

Poxygen940 mm Hg x 0.6149

578 mm Hg

Pnitrogen940 mm Hg x 0.3851

362 mm Hg

check 578 mm Hg 362 mm Hg 940 mm Hg

- When chemists want to collect a gas, they often

do it with a technique known as water

displacement - the reaction you are about to see makes hydrogen

gas

H2O is present due to slight evaporation

reaction vessel

What factor could increase the amount of

evaporated H2O?

temperature

the greater the temperature, the greater the

number of water molecules present above the water

What will this do to the partial pressure of H2O?

Increased temperature will increase the partial

pressure of H2O

this can be observed in chart 8 in the appendix

of your book

The gas inside the water displacement chamber is

at equilibrium with the gas outside the chamber

in other words, the gas inside is at the same

pressure as the gas outside (Patm)

the atmospheric pressure is the same as the total

pressure inside the chamber

PatmPgasPwater

Helium gas is collected over water at 25 oC.

What is the partial pressure of the helium if the

atmospheric pressure outside the water collection

bottle is 765 mm Hg?

1. Find the pressure of water at that temperature

2. Rearrange the equation

PatmPgasPwater

PgasPatm-Pwater

3. Solve the equation

Pgas765 mm Hg 23.8 mm Hg

741.2 mm Hg

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