Partial pressure and gas equilibria
In a nutshell
Partial pressure is the pressure each individual gas exerts out of the entire mixture of gases. The total pressure can be calculated by adding all of the partial pressures. Mole fractions can be used to calculate partial pressures. Kp is the equilibrium constant for a gaseous equilibrium.
Equations
word equation | symbol equation |
totalpressure=sumofpartialpressures | P=∑partialpressures |
molefractionofagas=totalnumberofmolesingasmixturenumberofmolesofgas | XA=ntotalnA |
partialpressureofagas=molefractionofagas×totalpressure | pA=XA×P |
gaseousequilibriumconstant=(reactantpartialpressure)reactantmolesratio(productpartialpressure)productmolesratio | Kp=p(reactants)mp(products)n |
Variable units
Quantity name | symbol | unit name | unit |
totalpressure | | atmosphereorpascals | atmorPa |
partialpressure | | atmosphereorpascals | atmorPa |
| | | |
molefraction | | nounits | nounits |
gaseousequilibriumconstant | | dependentonreaction | dependentonreaction |
Partial pressure
Partial pressure is the pressure each individual gas exerts out of the entire mixture of gases. The total pressure can be calculated by adding all of the partial pressures.
The partial pressure of an individual gas can be calculated if the total gas pressure and other partial pressures for the other gases are known.
totalpressure=sumofpartialpressures P=∑partialpressures
Example
1.50mol of the gas PI5 is heated, forming PI3 and I2. The partial pressure of I2 is 0.31atm in the equilibrium mixture. The total pressure of the gas mixture is 11atm. What is the partial pressure for PI5?
PI5(g)⇌PI3(g)+I2(g)
Write the equation for total partial pressure for the given equation:
P=p(PI5)+p(PI3)+p(I2)
Work out the partial pressure for PI3:
p(PI3)=p(I2)=0.31atm
Both have the same number of moles at equilibrium so their partial pressures will also be equal.
Insert known values into total pressure equation:
11=p(PI5)+0.31+0.31
Rearrange for p(PI5) and calculate:
p(PI5)=11−0.35−0.35=10.3atm
The partial pressure for PI5 is 10.3atm.
Mole fraction
The mole fraction is the fraction a gas out of the entire gas mixture.
molefractionofagas=totalnumberofmolesingasmixturenumberofmolesofgas XA=ntotalnA
This can be used to calculate the partial pressure of a gas.
partialpressureofagas=molefractionofagas×totalpressurepA=XA×P
Calculating the partial pressure of a gas by working out the mole fraction is described below.
Procedure
1. | Calculate the mole fraction of a gas using the equation:
XA=ntotalnA |
2. | Insert the value for the mole fraction and total pressure to calculate the partial pressure of the gas:
pA=XA×P |
Example
5.0mol of PBr5 was heated and decomposed to PBr3 and Br2. The moles of PBr3 is 1.1mol at equilibrium. The total pressure of the gas mixture is 10atm. What is the partial pressure of PBr5 at equilibrium? Round your answer to two significant figures.
PBr5(g)⇌PBr3(g)+Br2(g)
Work out the moles of Br2 at equilibrium:
Br2moles=PBr3moles=1.1mol
Their mole ratios are equal so their equilibrium moles will also be equal.
Work out the moles of PBr5 at equilibrium:
equilibriummolesofPBr5=initialmoles−molesreacted=5−1.1=3.9mol
Write the mole fraction equation:
XA=ntotalnA
Add all the moles together to calculate the total moles of gas in the gas mixture:
ntotal=3.9+1.1+1.1=6.1mol
Write the mole fraction equation for PBr5 and insert known values to calculate it:
XPBr5=ntotaln(PBr5)=6.1mol3.9mol=6139
Write the equation linking partial pressure and mole fraction:
pA=XA×P
Insert known values for PBr5:
p(PBr5)=XPBr5×P=(6139)×(10atm)=6.3934atm
Round to two significant figures:
p(PBr5)=6.4atm
The partial pressure of PBr5 is 6.4atm.
Equilibrium constant, Kp
Kp expression
The equilibrium constant, Kp, is an equilibrium constant for a gaseous equilibrium. The working out is the same as equilibrium constant, Kc. The only difference is that normal brackets are used instead of square brackets as pressure is being used instead of concentration.
This is the expression for Kp:
Kp=p(reactants)mp(products)n
n=numberofproductmoles
m=numberofreactantmoles
You will need to write expressions for Kp for any given reaction.
Procedure
1. | In the numerator, write the products separately in brackets after the letter p. |
2. | Write the number of moles each product has in the power form for each product. |
3. | In the denominator, write the reactants separately in brackets after the letter p. |
4. | Write the number of moles each reactant has in the power form for each reactant. |
Example
Write the expression for Kp for the production of nitrogen dioxide from nitrogen and oxygen.
Write the balanced equation:
N2(g)+2O2(g)⇌2NO2(g)
Write the Kp expression:
Kp=p(N2)p(O2)2p(NO2)2
Note: Normal brackets are used instead of square brackets.
Kp units
The units for the gaseous equilibrium constant, Kp, can vary depending on the reaction. You need to figure out the units every single time you calculate Kp.
procedure
1. | In the numerator, write the pressure units all to the power of the total product moles. |
2. | In the denominator, write the pressure units all to the power of the total reactant moles. |
3. | Simplify it fully. |
Example
What are the units for Kp for the given reaction? The unit for pressure is atm.
N2(g)+2O2(g)⇌2NO2(g)
Write the Kp expression:
Kp=p(N2)p(O2)2p(NO2)2
Insert the pressure units into the equation:
Kp=(atm)(atm)2(atm)2
Simplify fully:
Kp=(atm)(atm)2(atm)2=(atm)3(atm)2=atm1=atm−1
The units for Kp are atm−1.
Calculating Kp
The value of the gaseous equilibrium constant can be calculated with known partial pressures at equilibrium. Sometimes you have to calculate the partial pressures at equilibrium first.
procedure
1. | Write the balanced chemical equation. |
2. | If the partial pressure isn't given, calculate the partial pressure for each species. |
3. | Write down the Kp expression. |
4. | Insert partial pressure values into the Kp equation to calculate Kp. |
Example
Calculate the value of Kp when gaseous PBr5 dissociates into the gases, PBr3 and Br2 at 400K. The partial pressure for PBr5 is 2.6atm, for PBr3 is 2.0atm and for Br2 is 1.8atm.
Write the balanced equation:
PBr5(g)⇌PBr3(g)+Br2(g)
Write the Kp expression:
Kp=p(PBr5)p(PBr3)p(Br2)
Insert known partial pressure values to calculate Kp:
Kp=(2.6atm)(2.0atm)×(1.8atm)=1.38atm
The value of Kp is 1.38atm.
Finding partial pressure with a known Kp
When a value of Kp is given, you can use the equation to solve for an unknown partial pressure.
procedure
1. | Write the Kp expression. |
2. | Insert known values. |
3. | Rearrange and solve for unknown partial pressure. |
Kp and heterogeneous equilibrium
Heterogeneous equilibrium is when all the species aren't in the same physical state. Don't include non-gaseous species in the expression for Kp.
Example
Sulfur and oxygen react to form sulfur dioxide. The chemical equation is given below. Write the expression for Kp.
S(s)+O2(g)⇌SO2(g)
Write the Kp expression:
Kp=p(O2)p(SO2)
Sulfur isn't included because it's a solid.