1. Home
  2. Chemistry
  3. Gases
  4. Stoichiometry of gaseous substances

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

<< Chapter < Page
  Chemistry     Page 3 / 13
Chapter >> Page >

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

Got questions? Get instant answers now!

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!

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 4

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Chemistry' conversation and receive update notifications?

Ask