# 25 Gas Problems : Combined Gas Law and Mixtures of Gases

Introduction to the Ideal Gas Law
A balloon is floating around outside your window. The temperature outside is 31 , and the air pressure is 0.700 . Your neighbor, who released the balloon, tells you that he filled it with 3.60 of gas. What is the volume of gas inside this balloon?
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Part B
A 18.0 gas cylinder is filled with 7.00 of gas. The tank is stored at 13 . What is the pressure in the tank?
Express the pressure numerically in atmospheres.
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Part C
A 200 kiln is used for vitrifying ceramics. It is currently operating at 935 , and the pressure is 1.025 . How many moles of air molecules are within the confines of the kiln?
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Part D
A 12.0 gas cylinder has been filled with 7.80 of gas. You measure the pressure to be 4.60 . What is the temperature inside the tank?
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Mixture of Gases
A mixture of , , and has a total pressure of 2.80 .The partial pressure of is 0.200 , and the partial pressure of is 0.300 . What is the partial pressure of ?
Express the pressure numerically in atmospheres.
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Part B
A volume of 18.0 contains a mixture of 0.250 , 0.250 , and an unknown quantity of . The temperature of the mixture is 0 , and the total pressure is 1.00 . How many grams of helium are present in the gas mixture?
mass of =

Converting between Units of Pressure
Convert 1.20 of pressure to its equivalent in millimeters of mercury.
Express the pressure numerically in millimeters of mercury.
1.20 =

Part B
The pressure in car tires is often measured in pounds per square inch ( ), with the recommended pressure being in the range of 25 to 45 . Suppose a tire has a pressure of 43.5 . Convert 43.5 to its equivalent in atmospheres.
Express the pressure numerically in atmospheres.
43.5 =

Part C
High-pressure liquid chromatography (HPLC) is a method used in chemistry and biochemistry to purify chemical substances. The pressures used in this procedure range from around 500 kilopascals (500,000 ) to about 60,000 (60,000,000 ). It is often convenient to know the pressure in torr. If an HPLC procedure is running at a pressure of 3.35Ã-108 , what is its running pressure in torr?
Express the pressure numerically in torr.
3.35Ã-108 =

Pressure and Volume

A sample of ideal gas at room temperature occupies a volume of 21.0 at a pressure of 332 . If the pressure changes to 1660 , with no change in the temperature or moles of gas, what is the new volume, ?
Express the volume numerically in liters.
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Part B
If the volume of the original sample in Part A ( = 332 , = 21.0 ) changes to 62.0 , without a change in the temperature or moles of gas molecules, what is the new pressure, ?
Express the pressure numerically in torr.
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Temperature and Pressure
A sample of ideal gas is in a sealed container. The pressure of the gas is 135 , and the temperature is 26 . If the temperature changes to 92 with no change in volume or amount of gas, what is the new pressure, , of the gas inside the container?
Express the pressure numerically in torr.
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Part B
Using the same sample of gas ( = 135 , = 26 ), we wish to change the pressure to 1350 with no accompanying change in volume or amount of gas. What temperature , in Celsius, is needed to reach this pressure?
Express the temperature numerically in degrees Celsius.
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Temperature and Volume
A sample of gas in a balloon has an initial temperature of 26 and a volume of 1110 . If the temperature changes to 73 , and there is no change of pressure or amount of gas, what is the new volume, , of the gas?
Express the volume numerically in liters.
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Part B
What Celsius temperature, , is required to change the volume of the gas sample in Part A ( = 26 , = 1110 ) to a volume of 2220 ? Assume no change in pressure or the amount of gas in the balloon.
Express the temperature numerically in degrees Celsius.
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The Combined Gas Law
A very flexible helium-filled balloon is released from the ground into the air at 20. . The initial volume of the balloon is 5.00 , and the pressure is 760. . The balloon ascends to an altitude of 20 , where the pressure is 76.0 and the temperature is 50. . What is the new volume, , of the balloon in liters, assuming it doesn't break or leak?
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Part B
Consider 4.40 of a gas at 365 and 20. . If the container is compressed to 2.70 and the temperature is increased to 37 , what is the new pressure, , inside the container? Assume no change in the amount of gas inside the cylinder.
Express the pressure numerically in millimeters of mercury.
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Volume and Moles
A cylinder, with a piston pressing down with a constant pressure, is filled with 2.10 of a gas ( ), and its volume is 47.0 ( ). If 0.700 of gas leak out, and the pressure and temperature remain the same, what is the final volume of the gas inside the cylinder?
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Part B
A sample of gas in a cylinder as in the example in Part A has an initial volume of 46.0 , and you have determined that it contains 1.10 of gas. The next day you notice that some of the gas has leaked out. The pressure and temperature remain the same, but the volume has changed to 11.5 . How many moles of gas ( ) remain in the cylinder?
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Problem 7.2
Use the kinetic molecular theory of gases to explain each of the following
1. A container of non-stick cooking spray explodes when thrown into a fire
2. The air in a hot-air balloon is heated to make the balloon rise
Problem 7.22
Use the words inspiration and expiration to describe the part of the breathing cycle that occurs as a result of each of the following.
The diaphragm relaxes, moving up into the thoracic cavity.

Part B
The volume of the lungs expands.

Part C
The pressure within the lungs is greater than the atmosphere.

Problem 7.4
Identify the property of a gas that is measured in each of the following measurements.
425

pressure

amount of gas

volume

temperature

Part B
1.00

temperature

volume

pressure

amount of gas

Part C
10.0

amount of gas

pressure

volume

temperature

Part D
0.500 of He

temperature

amount of gas

volume

amount of gas and volume

Problem 7.6
Which of the following statement(s) describes the pressure of a gas?
A: The force of the gas particles on the walls of the container
B: The number of gas particles in a container
C: The volume of the container
D: 3.00
E: 750
Enter the letters of all the correct answers in alphabetical order. Do not use commas. For instance, if you think answers B and D are correct, enter BD.
Problem 7.80

How many liters of oxygen gas at STP are needed to react completely with 8.0 of magnesium?
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Problem 7.82
How many liters of gas can be produced at STP from 25.0 of ?
( ) + ( ) ( ) + ( )
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Problem 7.84
How many grams of water can be produced when 12.5 reacts at STP?
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Problem 7.90
What is the volume of the gas when measured at 22 and 675 ?
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Problem 7.92
How many liters of at STP are produced when 2.5Ã-1023 molecules react?
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Problem 7.42
A scuba diver 40 below the ocean surface inhales 85.0 of compressed air in a scuba tank at a pressure of 3.10 and a temperature of 9 .
What is the pressure of air in the lungs if the gas expands to 185.0 at a body temperature of 43 ?
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Introduction to the Ideal Gas Law

of gas. What is the volume of gas inside this balloon?

Part B

. What is the pressure in the tank?

Express the pressure numerically in atmospheres.

Part C

. How many moles of air molecules are within the confines of the kiln?

Part D

. What is the temperature inside the tank?

Mixture of Gases

?

Express the pressure numerically in atmospheres.

Part B

. How many grams of helium are present in the gas mixture?

Converting between Units of Pressure

of pressure to its equivalent in millimeters of mercury.

Express the pressure numerically in millimeters of mercury.

Part B

to its equivalent in atmospheres.

Express the pressure numerically in atmospheres.

Part C

, what is its running pressure in torr?

Express the pressure numerically in torr.

Pressure and Volume

?

Express the volume numerically in liters.

Part B

?

Express the pressure numerically in torr.

Temperature and Pressure

, of the gas inside the container?

Express the pressure numerically in torr.

Part B

, in Celsius, is needed to reach this pressure?

Express the temperature numerically in degrees Celsius.

Temperature and Volume

, of the gas?

Express the volume numerically in liters.

Part B

? Assume no change in pressure or the amount of gas in the balloon.

Express the temperature numerically in degrees Celsius.

The Combined Gas Law

, of the balloon in liters, assuming it doesn't break or leak?

Part B

, inside the container? Assume no change in the amount of gas inside
the cylinder.

Express the pressure numerically in millimeters of mercury.

Volume and Moles

of gas leak out, and the pressure and temperature remain the same,
what is the final volume of the gas inside the cylinder?

Part B

) remain in the cylinder?

Problem 7.2

Use the kinetic molecular theory of gases to explain each of the
following

A container of non-stick cooking spray explodes when thrown into a fire

The air in a hot-air balloon is heated to make the balloon rise

Problem 7.22

Use the words inspiration and expiration to describe the part of the
breathing cycle that occurs as a result of each of the following.

The diaphragm relaxes, moving up into the thoracic cavity.

Top of Form

Bottom of Form

Part B

The volume of the lungs expands.

Top of Form

Bottom of Form

Part C

The pressure within the lungs is greater than the atmosphere.

Top of Form

Bottom of Form

Problem 7.4

Identify the property of a gas that is measured in each of the following
measurements.

Top of Form

pressure

amount of gas

volume

temperature

Bottom of Form

Part B

Top of Form

temperature

volume

pressure

amount of gas

Bottom of Form

Part C

Top of Form

amount of gas

pressure

volume

temperature

Bottom of Form

Part D

of He

Top of Form

temperature

amount of gas

volume

amount of gas and volume

Bottom of Form

Problem 7.6

Which of the following statement(s) describes the pressure of a gas?

A: The force of the gas particles on the walls of the container

B: The number of gas particles in a container

C: The volume of the container

Enter the letters of all the correct answers in alphabetical order. Do
not use commas. For instance, if you think answers B and D are correct,
enter BD.

Problem 7.80

of magnesium?

Problem 7.82

?

)

Problem 7.84

reacts at STP?

Problem 7.90

?

Problem 7.92

react?

Problem 7.42

.

?