7. Gases

The Ideal Gas Law

Ideal Gas Law | General Gas Equation | Chemistry

The Ideal Gas Law Example 1

Kinetic Molecular Theory and the Ideal Gas Laws

The reaction NO1g2 + NO21g2 ∆ N2O31g2 takes place in the atmosphere with Kc = 13 at 298 K. A gas mixture is prepared with 2.0 mol NO and 3.0 mol NO2 and an initial total pressure of 1.65 atm.
(b) What is the volume of the container?

A piece of dry ice (solid carbon dioxide) with a mass of 28.8 g sublimes
(converts from solid to gas) into a large balloon. Assuming
that all of the carbon dioxide ends up in the balloon, what is the
volume of the balloon at 22 °C and a pressure of 742 mmHg?

What is the temperature of 0.52 mol of gas at a pressure of 1.3 atm
and a volume of 11.8 L?

 This is the pressure assuming ideal behavior. 

 Correct calculation for real gas behavior. 

 Check the math in your calculation for sign errors. 

 You have calculated only the pressure correction term for intermolecular forces rather than the total pressure. 

 You have calculated only the pressure correction term for molecular volume rather than the total pressure. 

 Apply van der Waal's equation and the appropriate constants in Table 6.5. 

 Assuming that chlorine gas behaves as a real gas, what pressure would 1.000 mol would the gas exert in 22.41 L at 273.2 K? 

(b) The adult blue whale has a lung
capacity of 5.0 * 103 L. Calculate the mass of air (assume an
average molar mass of 28.98 g>mol) contained in an adult
blue whale’s lungs at 0.0 °C and 101.33 kPa, assuming the air
behaves ideally.

 Collisions are assumed to be elastic or energy is exchanged but not lost. 

 In an ideal gas, the volume of the gas particles is insignificant compared to the volume of the container. 

 The molecules of an ideal gas are considered to be point masses. 

 Molecules in an ideal gas do not interact with each other. 

 Molecules in an ideal gas have inelastic collisions. 

 Correct, the collisions are assumed to be elastic or energy is exchanged but not lost. 

 Review the basic postulates of kinetic molecular theory of gases. 

Which of the following statements about an ideal gas is false?

Be Lazy! Don't Memorize the Gas Laws!

(a) Calculate the number of molecules in a deep breath of
air whose volume is 2.25 L at body temperature, 37 °C, and
a pressure of 97.99 kPa. 

Complete the following table for an ideal gas:
P V n T
101.33 kPa ? L 3.333 mol 300 K

If 2.00 g of N2 gas has a volume of 0.40 L and a pressure of 6.0 atm, what is its Kelvin temperature?

The relative humidity of air equals the ratio of the par- tial pressure of water in the air to the equilibrium vapor pressure of water at the same temperature times 100%. If the relative humidity of the air is 58% and its temperature is 68 °F, how many molecules of water are present in a room measuring12ft * 10ft * 8ft?

Assume that you take a flask, evacuate it to remove all the air, and find its mass to be 478.1 g. You then fill the flask with argon to a pressure of 2.15 atm and reweigh it. What would the balance read in grams if the flask has a volume of 7.35 L and the temperature is 20.0 °C?

What volume is occupied by 12.5 g of argon gas at a pressure of
1.05 atm and a temperature of 322 K? Would the volume be different
if the sample were 12.5 g of helium (under identical
conditions)?

Ideal Gas Law

Many laboratory gases are sold in steel cylinders with a volume of 43.8 L. What is the mass in grams of argon inside a cylinder whose pressure is 17,180 kPa at 20 °C? (LO 10.4) 
(a) 1.83 * 107 g (b) 1.81 * 105 g
(c) 1.23 * 104 g (d) 122 g

(b) Carbon dioxide makes up approximately
0.04% of Earth’s atmosphere. If you collect a 2.0-L sample
from the atmosphere at sea level (101.33 kPa) on a warm day
127 °C2, how many CO2 molecules are in your sample?

The vapor pressure of CCl3F at 300 K is 856 torr. If 11.5 g of
CCl3F is enclosed in a 1.0-L container, will any liquid be present?
If so, what mass of liquid?

A typical high-pressure tire on a bicycle might have a volume of 365 mL and a pressure of 7.80 atm at 25 °C. Suppose the rider filled the tire with helium to minimize weight. What is the mass of the helium in the tire?

How many grams of carbon dioxide, CO2, are present in a 0.150 L flask recorded at 525 mmHg and 32 ºC?a) 1.77 gb) 0.93 gc) 0.66 gd) 0.18 ge) 0.052 g

(a) If the pressure exerted by ozone, O3, in the stratosphere is
304 Pa and the temperature is 250 K, how many ozone molecules
are in a liter?

 The temperature must be expressed in kelvins when using Charles&#8217;s law and the volume decreases if the temperature decreases. 

 The volume will be smaller at the lower temperature. 

 The temperature must be expressed in kelvins when using Charles&#8217;s law. 

Charles&#8217;s law states (V1/T1) = (V2/T2).

 A balloon is filled with 1.5 moles of helium at room temperature, 25&#x2103;, and has a volume of 2.4 L.  Calculate the volume of the balloon when it is placed into liquid nitrogen at &#x2212;196&#x2103;.  Assume that the pressure remains constant. 

A sealed flask contains 0.55 g of water at 28 °C. The vapor pressure 
of water at this temperature is 28.35 mmHg. What is the 
minimum volume of the flask in order that no liquid water be 
present in the flask?

Nickel carbonyl, Ni1CO24, is one of the most toxic substances
known. The present maximum allowable concentration
in laboratory air during an 8-hr workday is 1 ppb
(parts per billion) by volume, which means that there is one
mole of Ni1CO24 for every 109 moles of gas. Assume 24 C
and 101.3 kPa pressure. What mass of Ni1CO24 is allowable
in a laboratory room that is 3.5 m * 6.0 m * 2.5 m?

 For non-ideal behavior, the gas particles should be close together and moving slowly. 

 Consider STP conditions for an ideal gas and examine the postulates of kinetic molecular theory. 

 Under which of the following conditions is a gas least likely to be ideal? 

How many liters of HNO3 gas, measured at 28.0 ºC and 780 torr, are required to prepare 2.30 L of 4.15 M solution of nitric acid?

Air conditioners not only cool air, but dry it as well. A room in a
home measures 6.0 m * 10.0 m * 2.2 m. If the outdoor temperature
is 30 °C and the partial pressure of water in the air is
85% of the vapor pressure of water at this temperature, what
mass of water must be removed from the air each time the volume
of air in the room is cycled through the air conditioner?
(Assume that all of the water must be removed from the air.)
The vapor pressure for water at 30 °C is 31.8 torr.

The apparatus shown consists of three temperature-jacketed 1.000-L bulbs connected by stopcocks. Bulb A contains a mixture of H2O1g2, CO21g2, and N21g2 at 25 °C and a total pressure of 564 mm Hg. Bulb B is empty and is held at a temperature of -70 °C. Bulb C is also empty and is held at a temperature of -190 °C. The stopcocks are closed, and the volume of the lines connecting the bulbs is zero. CO2 sublimes at -78 °C, and N2 boils at -196 °C.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/2673e3fdd6f54e4a-1669404097243.jpg" alt="" />
(b) How many moles of H2O are in the system?

The reaction of sodium peroxide 1Na2O22 with CO2 is used in space vehicles to remove CO2 from the air and generate O2 for breathing:
2 Na2O21s2 + 2 CO21g2¡2 Na2CO31s2 + O21g2
(a) Assuming that air is breathed at an average rate of 4.50 L/min (25 °C; 735 mm Hg) and that the concentration of CO2 in expelled air is 3.4% by volume, how many grams of CO2 are produced in 24 h?

What volume is occupied by 0.118 mol of helium gas at a pressure
of 0.97 atm and a temperature of 305 K?

Olympic cyclists fill their tires with helium to make them lighter.
Calculate the mass of air in an air-filled tire and the mass of
helium in a helium-filled tire. Assume that the volume of the tire is 855 mL,
that it is filled to a total pressure of 125 psi, and that the temperature
is 25 °C. Also, assume an average molar mass for air of
28.8 g>mol. What is the mass difference between the two?

Natural gas is a mixture of hydrocarbons, primarily methane 1CH42 and ethane 1C2H62. A typical mixture might have Xmethane = 0.915 and Xethane = 0.085. Let’s assume that we have a 15.50 g sample of natural gas in a volume of 15.00 L at a temperature of 20.00 °C.
(b) What is the pressure of the sample in atmospheres?

At 273 K and 1 atm pressure, 1 mol of an ideal gas occupies 22.4 L. (Section 10.4) (b) Looking at Figure 18.1, we see that the temperature is lower at 85 km altitude than at 50 km. Does this mean that one mole of an ideal gas would occupy less volume at 85 km than at 50 km? Explain.

Ideal Versus Real Gases

An aerosol spray can with a volume of 125 mL contains 1.30 g
of propane gas (C3H8) as a propellant. (a) If the can is at 25 °C,
what is the pressure in the can? 

Carbon dioxide, which is recognized as the major contributor
to global warming as a “greenhouse gas,” is formed
when fossil fuels are combusted, as in electrical power
plants fueled by coal, oil, or natural gas. One potential way
to reduce the amount of CO2 added to the atmosphere is
to store it as a compressed gas in underground formations.
Consider a 1000-megawatt coal-fired power plant that produces
about 6 * 106 tons of CO2 per year. (a) Assuming
ideal-gas behavior, 101.3 kPa, and 27 C, calculate the volume
of CO2 produced by this power plant.

A scuba diver’s tank contains 2.50 kg of O2 compressed into
a volume of 11.0 L. (b) What volume would this oxygen occupy at
25 °C and 101.33 kPa?

If 15.0 g of CO2 gas has a volume of 0.30 L at 300 K, what is its pressure in millimeters of mercury?

In an experiment reported in the scientific literature, male
cockroaches were made to run at different speeds on a miniature
treadmill while their oxygen consumption was measured.
In 30 minutes the average cockroach (running at 0.08 km/h)
consumed 1.0 mL of O2 at 101.33 kPa pressure and 20 °C per
gram of insect mass. (a) How many moles of O2 would be consumed
in 1 day by a 6.3-g cockroach moving at this speed?

 Correct, as the volume expands the pressure will decrease. 

 To solve Boyle&#8217;s law, multiply the initial pressure by the ratio of the old volume to the new volume. 

 To solve Boyle&#8217; s law, multiply the initial pressure by the ratio of the old volume to the new volume. 

 As the volume expands, the pressure will decrease. 

Boyle&#8217;s law states that under conditions of constant temperature and moles, P1V1 = P2V2.

 A container with a movable piston contains 2.0 moles of argon gas.  When the volume of the container is 1.5 L, the pressure is 2.4 atm.  Calculate the pressure of the container when the piston is raised to give a volume of 2.5 L.  Assume the temperature remains constant. 

A 2.85-g sample of an unknown chlorofluorocarbon decomposes
and produces 564 mL of chlorine gas at a pressure of
752 mmHg and a temperature of 298 K. What is the percent
chlorine (by mass) in the unknown chlorofluorocarbon?

Olympic cyclists fill their tires with helium to make them lighter.
Calculate the mass of air in an air-filled tire and the mass of
helium in a helium-filled tire. Assume that the volume of the tire is 855 mL,
that it is filled to a total pressure of 125 psi, and that the temperature
is 25 °C. Also, assume an average molar mass for air of
28.8 g>mol. Calculate the mass of helium in a helium-filled tire.

A 50.0 g sample of solid CO2 (dry ice) is added at -100 °C to
an evacuated (all of the gas removed) container with a volume
of 5.0 L. If the container is sealed and then allowed to warm
to room temperature 125 °C2 so that the entire solid CO2 is
converted to a gas, what is the pressure inside the container?

When solid mercury(I) carbonate, Hg2CO3, is added to
nitric acid, HNO3, a reaction occurs to give mercury(II)
nitrate, Hg1NO322, water, and two gases A and B:
Hg2CO31s2 + HNO31aq2¡
Hg1NO3221aq2 + H2O1l 2 + A1g2 + B1g2
(a) When the gases are placed in a 500.0-mL bulb at 20 °C,
the pressure is 258 mm Hg. How many moles of gas
are present?

Dry ice (solid CO2) has occasionally been used as an “explosive” in mining. A hole is drilled, dry ice and a small amount of gunpowder are placed in the hole, a fuse is added, and the hole is plugged. When lit, the exploding gunpowder rapidly vaporizes the dry ice, building up an immense pressure. Assume that 500.0 g of dry ice is placed in a cavity with a volume of 0.800 L and the ignited gunpowder heats the CO2 to 700 K. What is the final pressure inside the hole?

A driver with a nearly empty fuel tank may say she is “running 
on fumes.” If a 15.0-gallon automobile gas tank had 
only gasoline vapor remaining in it, what is the farthest the 
vehicle could travel if it gets 20.0 miles per gallon on liquid 
gasoline? Assume the average molar mass of molecules in gasoline 
is 105 g/mol, the density of liquid gasoline is 0.75 g/mL, 
the pressure is 743 mm Hg, and the temperature is 25 °C.

As shown in Table 15.2, the equilibrium constant
for the reaction N21g2 + 3 H21g2 Δ 2 NH31g2 is
Kp = 4.34 * 10-3 at 300 C. Pure NH3 is placed in a 1.00-L
flask and allowed to reach equilibrium at this temperature.
There are 1.05 g NH3 in the equilibrium mixture.
(b) What was the initial mass of ammonia placed
in the vessel?

The Ideal Gas Law Example 2

What is the pressure in a 15.0-L cylinder filled with 32.7 g of
oxygen gas at a temperature of 302 K?

Real Gas and Ideal Gas

When 0.670 g argon is added to a 500 cm3 container with a sample of oxygen gas, the total pressure of the gases is found to be 1.52 atm at a temperature of 340 K. What is the mass of the oxygen gas in the bulb?

The radius of a xenon atom is 1.3 * 10 - 8 cm. A 100-mL flask is
filled with Xe at a pressure of 1.0 atm and a temperature of 273 K.
Calculate the fraction of the volume that is occupied by Xe
atoms. (Hint: The atoms are spheres.)

Air pollution in the Mexico City metropolitan area is among the worst in the world. The concentration of ozone in Mexico City has been measured at 441 ppb (0.441 ppm). Mexico City sits at an altitude of 7400 feet, which means its atmospheric pressure is only 0.67 atm. (b) How many ozone molecules are in 1.0 L of air in Mexico City? Assume T = 25 °C.

Olympic cyclists fill their tires with helium to make them lighter.
Calculate the mass of air in an air-filled tire and the mass of
helium in a helium-filled tire. Assume that the volume of the tire is 855 mL,
that it is filled to a total pressure of 125 psi, and that the temperature
is 25 °C. Also, assume an average molar mass for air of
28.8 g>mol. Calculate the mass of air in an air-filled tire.

A 334-mL cylinder for use in chemistry lectures contains
5.225 g of helium at 23 °C. How many grams of helium must
be released to reduce the pressure to 7.60 MPa assuming ideal
gas behavior?

An aerosol spray can with a volume of 125 mL contains 1.30 g
of propane gas (C3H8) as a propellant. (c) The can’s label says that exposure to temperatures above 50 °C may cause the can to burst.
What is the pressure in the can at this temperature?

The vapor pressure of water at 25 °C is 23.76 torr. If 1.25 g of
water is enclosed in a 1.5-L container, will any liquid be present?
If so, what mass of liquid?

How to Use the Ideal Gas Law in Two Easy Steps

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[BOOK CHEM] Clutch Version

Partial Pressure

Partial Pressure (PGas) is the pressure exerted by an individual gas within a container.

Velocity Distributions

Velocity Distributions represent probability distributions for a gas when examining their molar mass and temperature.

Mole Fraction

Mole Fraction (X) represents the mole component by total moles.&nbsp;

Mole Fraction -

The Ideal Gas Law Derivations

The&nbsp;Ideal Gas Law Derivations are a convenient way to solve gas calculations involving 2 sets of the same variables.&nbsp;

Root Mean Square Speed

Root Mean Square Speed&nbsp;allows for the determination of the velocity of 1 type of gas molecule.

The Ideal Gas Law: Density

Under certain conditions of pressure and temperature, the Ideal Gas Law can determine the density&nbsp;of a gas.&nbsp;

Effusion

Effusion is the escaping of gas molecules or atoms through a pinhole.&nbsp;

Kinetic Energy of Gases

Kinetic Energy is the energy an object possesses due to its motion.

Gas Stoichiometry

Gas Stoichiometry involves chemical reactions that contain gases.

The Ideal Gas Law formula relates the behavior of gases under varying conditions of pressure, volume, moles and temperature.

Chemistry Gas Laws: Combined Gas Law

The Combined Gas Law&nbsp;is created from “combining” Boyle’s Law, Charles’ Law, and Gay–Lussac’s Law.

Pressure Units

Pressure is the force that is exerted within a given volume of space.&nbsp;

Kinetic Molecular Theory

A gas is seen as a collection of molecules or individual atoms that are in constant motion. The Kinetic-Molecular Theory tries to use data of real gases to predict how an ideal gas would behave if they existed.&nbsp;&nbsp;

Standard Temperature and Pressure

In order to accurately study the effect that changes in pressure, temperature and moles have on volume, chemists will often run their experiments under Standard Temperature and Pressure.&nbsp;

The Ideal Gas Law Applications

The Ideal Gas Law Applications establish both the direct and inverse relationships between the Ideal Gas Law variables.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann Distribution is a probability distribution curve that describes the speed of a gas at a specific temperature.

Chemistry Gas Laws

Chemistry Gas Laws&nbsp;are laws that relate together the pressure, volume and temperature of a gas.

The Ideal Gas Law: Molar Mass

The Ideal Gas Law can be further extended to find the molar mass of a gas.&nbsp;

Van der Waals Equation

The&nbsp;Van der Waals Equation is used when dealing with real, non-ideal gases.&nbsp;