# Mixtures and Partial Pressure of Gases with Examples

**Mixtures and Partial Pressure of Gases with Example**

If gases do not react with each other, they produce homogeneous mixture. Each gas in the container apply pressure. Now we learn concept related to this topic; partial pressure.

**Partial Pressure:**

Partial pressure of one of the gases in mixture placed in a closed container is equal to pressure of same gas only in same container at same temperature. Following picture summarizes what we try to say.

If temperature and volume of gas are kept constant, partial pressure of gas is directly proportional to number of particles of gas.

**Dalton’s Law of Partial Pressure:**

“Sum of partial pressures of the gases in the container gives us total pressure of mixture.” This statement is called Dalton’s law of partial pressure. Picture given above also examples of this law.

**P _{total} =P_{H2}+P_{CO2}**

Gases in same container has equal volumes and they share total pressure according to their number of moles.

If we write ideal gas law for total gas in the mixture and one of the gases and divide them to each other, we get partial pressure equation of one gas in the mixture.

P_{1}.V = n_{1}.R.T

¯¯¯¯ ¯¯¯¯¯¯

P_{total}.V=n_{total}.R.T

**P _{1}=(n_{1}/n_{total}).P_{total}**

(n_{1}/n_{total}) is called mole fraction of gas1

**P _{2}=(n2/n_{total}).P_{total}**

**P _{3}=(n_{3}/n_{total}).P_{total}**

**. . . . . . . . . . . . . . . .**

**Example:** In a closed container, there are 4 gram H_{2.} If we add 4 g He to this container, which ones of the following statements become true? (H=1, He=4)

**I.** Pressure of H_{2} is equal to initial pressure of it.

**II.** Kinetic energies of H_{2} and He particles are equal in mixture.

**III.** Partial pressure of H_{2} in mixture is double of He.

**Solution:**

**I.** We find partial pressure of H_{2}, using ideal gas law.

P_{H2}.V=n_{H2}.R.T

P_{H2}=n_{H2}.R.T/V

Since V, T and n_{H2} are constant, partial pressure of H_{2} does not change. I is true.

**II.** Since temperature of homogeneous mixture is same in container, kinetic energies of particles do not change and kinetic energy of H_{2} particles is equal to kinetic energy of He particles. II is true.

**III.** Molar mass of H_{2}=2.1=2

Mole of H_{2};

n_{H2}=4/2=2mol

Mole of He;

n_{He}=4/4=1mol

Partial pressure is directly proportional to number of moles; Thus partial pressure of H_{2} is double of partial pressure of He. III is true.

**Example:** Container contains 0,4mol CH_{4}, 0,1mol SO_{2}, and 0,3mol He. If partial pressure of He is 60cm Hg, which one of the following statement is false? (C=12, H=1, S=32, O=16)

**I.** Mixture contains 50 % CH_{4} by mole

**II.** Total pressure of container is 160 cm Hg

**III.** Density of SO_{2} is four times of density of CH_{4}

**IV.** Partial pressure of SO_{2} is 20 cm Hg.

**Solution:**

**I.** total moles of gases;

n_{total}=0,4+0,1+0,3=0,8mol

n_{CH4}=(0,4/0,8).100=50

I is true

**II.** Partial pressure of He is 60 cm Hg

P_{He}=(n_{He/}n_{total}).P_{total}

60=(0,3/0,8).Ptotal

P_{total}=160 cm Hg

II is true

**III.** Molar masses of SO_{2}=32+2.16=64 and CH_{4}=12+4.1=16

masses of m_{SO2}=n_{SO2}.Mm_{SO2}=0,1.64=6,4 g and m_{CH4}=n_{CH4}.Mm_{CH4}=0,4.16=6,4 g

Since they have equal volumes and masses, d=m/V

their densities are also equal, III is false.

**IV.** Partial pressure of SO_{2}

P_{SO2}=(n_{SO2}/n_{total}).P_{total}

P_{SO2}=(0,1/0,8).160

P_{SO2}=20 cm Hg IV. is true

**Pressure of Gases in Combined Containers**

Picture given below shows two container combined with tap A.

X and Y gases are put into containers I and II, they are do not react with each other. If we open the tap between containers, which quantities of total system change? We try to answer this question now.

We learned that, gases diffuse from high pressure to low pressure. In this system gas having higher pressure diffuse to other container until pressure balance.Since no reaction occurs initial and final number of moles of X and Y gases are equal. Total number of moles is equal to sum of n_{1} and n_{2}.

**Equation I. n _{total}=n_{1}+n_{2}**

If we write ideal gas law for each situation;

**n _{1}=(P_{1}.V_{1})/(R.T), n_{2}=(P_{2}.V_{2}/R.T), n_{total}=(P_{final}.V_{final}/.RT)**

we substitute these equations into equation I. and get;

We can write **V _{1}+V_{2}** into V

_{final}also.

**Example:** If we open the tap and make system balance, which ones of the following statements become true for this system?

**I.** Final pressure of Y is larger than initial pressure of Y

**II.** Partial pressures of X and Y becomes equal.

**III.** Total pressure becomes 2,4 atm

**Solution:**

**I.** Initial volume of gas Y is 6V, final volume of Y is 10 V. Since temperature, number of moles are constant, but volume of Y increases, its pressure decreases. I is false.

**II.** Partial pressures of gases are directly proportional to their number of moles. We find number of moles of gases and then we give relation betwen their partial pressures using ideal gas law.

**n=P.V/R.T**

n_{X}=Px.Vx/R.T=3.4V/RT=12V/RT

n_{Y}=P_{Y}.V_{Y}/R.T=2.6V/RT=12V/RT

Since number of moles of gases are equal their partial pressures become also equal.

**III.** P_{final}=(Px.Vx+Py.Vy)/(Vx+Vy)

P_{final}=(3.4V+2.6V)/(4V+6V)

P_{final}=24V/10V=2,4 atm

III is also true