STATES OF MATTER 
properties of gases and liquids (fluids) and solids
22.
Dalton's Law of Partial Pressures and calculations and use in solving gaseous
equilibrium expression problems
Helpful for UK
advanced level chemistry students aged ~1618, IB courses and US grades 1112 K12 honors.
22. Dalton's law of partial pressures
and calculations

Dalton's Law of partial
pressures states that at constant temperature the total pressure exerted by a
mixture of gases in a definite volume is equal to the sum of the individual
pressures which each gas would exert if it alone occupied the same total
volume.

For a mixture of gases
1, 2, 3 ...

P_{tot} = p_{1} + p_{2} + p_{3}
etc.

where p_{1}, p_{2} etc. represent the partial pressures.

The partial pressure ratio
is the same as the % by volume ratio and the same as the mole ratio of gases
in the mixture.

This means for a component
gas z, the partial pressure is expressed as:

p_{z}
= P_{tot}
x %z/100

for % of volume
of gases or in terms of moles of gases:

p_{z}
= P_{tot} x mol z/total
mol

p_{z}=
P_{tot} x mol fraction z

Examples of partial pressure calculations

Ex. Q4d.1

In the
manufacture of ammonia a mixture of nitrogen : hydrogen in a 1 : 3 ratio is
passed over an iron/iron oxide catalyst at high temperature and high pressure.

What are the partial pressures of nitrogen and hydrogen if the total pressure
of the gases is 200 atm prior to reaction? So P_{tot} = 200 atm.

The 1 : 3, N_{2}
:H_{2} ratio means that nitrogen forms ^{1}/_{4} of
the mixture, therefore

p_{N2} = ^{1}/_{4} x
200 = 50 atm and

p_{H2} = p_{tot}
– p_{N2} =
150 atm (or from ^{3}/_{4} x 200)

Ex. Q4d.2

Methanol can be
synthesised by combining carbon monoxide and hydrogen in a 1 : 2 ratio.

In an experimental reactor
experiment, 300^{o}C at a total pressure of 400kPa, the final
equilibrium gaseous mixture contained 10% carbon monoxide.

(a) Calculate the % of
hydrogen gas and % methanol vapour in the final mixture.

Whatever hydrogen is left,
its % must be double that of carbon monoxide since they were both mixed and
react in a 1 : 2 ratio, so there will 20% hydrogen left in the equilibrium
mixture.

Therefore there will be
100 – 10 – 20 = 70% methanol vapour in the final mixture.

(b) Calculate the partial
pressures of the three gases in the mixture.

p_{CO} = 0.1 x 400 = 40 kPa

p_{H2} = 0.2 x 400 = 80 kPa

p_{CH3OH} = 0.7 x 400 =
280 kPa

(useful to check 40 + 80 + 280 =
400)

(c) From the
partial pressure data in (b) calculate the value of
the equilibrium constant, K_{p}, under these reaction conditions
(use Pa pressure units).

–
Learning objectives
for Dalton's Law of partial pressures
Be able to quote and use
in calculations Dalton's Law of partial pressures.
Know how to calculate
partial pressures from the % of gases in a mixture.
Know how to calculate
partial pressures from the complete ratio of gases in a mixture.
Know how to calculate
partial pressures from the molar composition of gases in a mixture.
Know how to calculate
partial pressures and use them to solve gaseous equilibrium problems,
either given the
equilibrium constant K_{p} and known partial pressures apart
from one unknown,
or given all the
partial pressures to calculate the equilibrium constant K_{p}.
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