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9.3 Stoichiometry of gaseous substances, mixtures, and reactions  (Page 3/13)

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The pressure of a mixture of gases: dalton’s law

Unless they chemically react with each other, the individual gases in a mixture of gases do not affect each other’s pressure. Each individual gas in a mixture exerts the same pressure that it would exert if it were present alone in the container ( [link] ). The pressure exerted by each individual gas in a mixture is called its partial pressure    . This observation is summarized by Dalton’s law of partial pressures    : The total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the component gases :

P T o t a l = P A + P B + P C + ... = Σ i P i

In the equation P Total is the total pressure of a mixture of gases, P A is the partial pressure of gas A; P B is the partial pressure of gas B; P C is the partial pressure of gas C; and so on.

This figure includes images of four gas-filled cylinders or tanks. Each has a valve at the top. The interior of the first cylinder is shaded blue. This region contains 5 small blue circles that are evenly distributed. The label “300 k P a” is on the cylinder. The second cylinder is shaded lavender. This region contains 8 small purple circles that are evenly distributed. The label “600 k P a” is on the cylinder. To the right of these cylinders is a third cylinder. Its interior is shaded pale yellow. This region contains 12 small yellow circles that are evenly distributed. The label “450 k P a” is on this region of the cylinder. An arrow labeled “Total pressure combined” appears to the right of these three cylinders. This arrow points to a fourth cylinder. The interior of this cylinder is shaded a pale green. It contains evenly distributed small circles in the following quantities and colors; 5 blue, 8 purple, and 12 yellow. This cylinder is labeled “1350 k P a.”
If equal-volume cylinders containing gas A at a pressure of 300 kPa, gas B at a pressure of 600 kPa, and gas C at a pressure of 450 kPa are all combined in the same-size cylinder, the total pressure of the mixture is 1350 kPa.

The partial pressure of gas A is related to the total pressure of the gas mixture via its mole fraction ( X )    , a unit of concentration defined as the number of moles of a component of a solution divided by the total number of moles of all components:

P A = X A × P T o t a l where X A = n A n T o t a l

where P A , X A , and n A are the partial pressure, mole fraction, and number of moles of gas A, respectively, and n Total is the number of moles of all components in the mixture.

The pressure of a mixture of gases

A 10.0-L vessel contains 2.50 × 10 −3 mol of H 2 , 1.00 × 10 −3 mol of He, and 3.00 × 10 −4 mol of Ne at 35 °C.

(a) What are the partial pressures of each of the gases?

(b) What is the total pressure in atmospheres?

Solution

The gases behave independently, so the partial pressure of each gas can be determined from the ideal gas equation, using P = n R T V :

P H 2 = ( 2.50 × 10 −3 mol ) ( 0.08206 L atm mol −1 K −1 ) ( 308 K ) 10.0 L = 6.32 × 10 −3 atm
P He = ( 1.00 × 10 −3 mol ) ( 0.08206 L atm mol −1 K −1 ) ( 308 K ) 10.0 L = 2.53 × 10 −3 atm
P Ne = ( 3.00 × 10 −4 mol ) ( 0.08206 L atm mol −1 K −1 ) ( 308 K ) 10.0 L = 7.58 × 10 −4 atm

The total pressure is given by the sum of the partial pressures:

P T = P H 2 + P He + P Ne = ( 0.00632 + 0.00253 + 0.00076 ) atm = 9.61 × 10 −3 atm

Check your learning

A 5.73-L flask at 25 °C contains 0.0388 mol of N 2 , 0.147 mol of CO, and 0.0803 mol of H 2 . What is the total pressure in the flask in atmospheres?

Answer:

1.137 atm

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Here is another example of this concept, but dealing with mole fraction calculations.

The pressure of a mixture of gases

A gas mixture used for anesthesia contains 2.83 mol oxygen, O 2 , and 8.41 mol nitrous oxide, N 2 O. The total pressure of the mixture is 192 kPa.

(a) What are the mole fractions of O 2 and N 2 O?

(b) What are the partial pressures of O 2 and N 2 O?

Solution

The mole fraction is given by X A = n A n T o t a l and the partial pressure is P A = X A × P Total .

For O 2 ,

X O 2 = n O 2 n T o t a l = 2.83 mol ( 2.83 + 8.41 ) mol = 0.252

and P O 2 = X O 2 × P T o t a l = 0.252 × 192 kPa = 48.4 kPa

For N 2 O,

X N 2 = n N 2 n Total = 8.41 mol ( 2.83 + 8.41 ) mol = 0.748

and

P N 2 = X N 2 × P Total = 0.748 × 192 kPa = 143.6 kPa

Check your learning

What is the pressure of a mixture of 0.200 g of H 2 , 1.00 g of N 2 , and 0.820 g of Ar in a container with a volume of 2.00 L at 20 °C?

Answer:

1.87 atm

Got questions? Get instant answers now!

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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