Ideal Gas Law - AP Chemistry
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What is the final pressure of a gas initially has a pressure of 10 atm at 50 L if the volume s now 25 L?
What is the final pressure of a gas initially has a pressure of 10 atm at 50 L if the volume s now 25 L?
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Use P1V1 = P2V2
P1 = 10atm; V1 = 50L
P2 = X; V2 = 25L
(10atm)(50L) = (x)(25L)
500 = 25x
x = 20
Use P1V1 = P2V2
P1 = 10atm; V1 = 50L
P2 = X; V2 = 25L
(10atm)(50L) = (x)(25L)
500 = 25x
x = 20
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How many moles of Oxygen gas are present at a volume of 10 L at 1 atm and 25o C? (MW Oxygen gas = 32 g/mol)
How many moles of Oxygen gas are present at a volume of 10 L at 1 atm and 25o C? (MW Oxygen gas = 32 g/mol)
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use PV = nRT
n = PV/ RT
P = 1 atm; V = 10 L; R = 0.0821 Latm/molK; T = 298 K (MUST switch temperature to K)
n = moles of gas
n = (1atm)(10L)/(0.0821Latm/molK)(298K)
n= 0.41 mol
use PV = nRT
n = PV/ RT
P = 1 atm; V = 10 L; R = 0.0821 Latm/molK; T = 298 K (MUST switch temperature to K)
n = moles of gas
n = (1atm)(10L)/(0.0821Latm/molK)(298K)
n= 0.41 mol
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An ideal gas takes up 60L at 2 atm. If the gas is compressed to 30L, what will the new pressure be?
An ideal gas takes up 60L at 2 atm. If the gas is compressed to 30L, what will the new pressure be?
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Ideal gas law (modified)
P1V1 = P2V2
P1 = 2 atm; V1 = 60L; P2 = ?; V2 = 30L
(2)(60) = (X)(30)
P2 = 4 atm
Ideal gas law (modified)
P1V1 = P2V2
P1 = 2 atm; V1 = 60L; P2 = ?; V2 = 30L
(2)(60) = (X)(30)
P2 = 4 atm
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Each of the following compounds are contained in a closed container with a volume of 100mL. Which of the following will exert the most pressure?
Each of the following compounds are contained in a closed container with a volume of 100mL. Which of the following will exert the most pressure?
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The pressure exerted is dependent on molar concentration only (not mass). As the containers are all the same volume, the container with the most moles will exert the most pressure. 60g of 44g/mole CO2 gives 1.4mol, 50g of O2 gives 1.4mol, 46g N2 gives 1.6mol, and 54g F2 gives 1.4mol, 40g H2 gives 40mol.
The pressure exerted is dependent on molar concentration only (not mass). As the containers are all the same volume, the container with the most moles will exert the most pressure. 60g of 44g/mole CO2 gives 1.4mol, 50g of O2 gives 1.4mol, 46g N2 gives 1.6mol, and 54g F2 gives 1.4mol, 40g H2 gives 40mol.
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A mixture of three gases in a balloon is able to generate 2 atm of pressure. The identies and amounts of each gas are as follows. 2 moles of O2, 3 moles of N2, 5 moles of H2.
What is the partial pressure of Oxygen gas?
A mixture of three gases in a balloon is able to generate 2 atm of pressure. The identies and amounts of each gas are as follows. 2 moles of O2, 3 moles of N2, 5 moles of H2.
What is the partial pressure of Oxygen gas?
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Partial pressure is the amount of pressure that is the result of one gas. This is calculated by mutiplying the mole fraction of the gas by the overall pressure. The mole fraction is calculated as the moles of the compound of interest divided by the total amount of moles present. 2 moles O2/ 2 moles O2 + 3 moles N2 + 5 moles H2 = 2/10 = mole fraction of O2. 2/10 multiplied by the total pressure gives us the answer as 0.4 atm.
Partial pressure is the amount of pressure that is the result of one gas. This is calculated by mutiplying the mole fraction of the gas by the overall pressure. The mole fraction is calculated as the moles of the compound of interest divided by the total amount of moles present. 2 moles O2/ 2 moles O2 + 3 moles N2 + 5 moles H2 = 2/10 = mole fraction of O2. 2/10 multiplied by the total pressure gives us the answer as 0.4 atm.
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Match each gas law definition to the correct name of the person who is credited with discovering it: (a) The total pressure of a mixture of gases is equal to the sum of the pressures of each of the individual gases in the container. (b) The volume of a fixed amount of gas varies inversely with the pressure at constant temperature. (c) The temperature and volume of a gas at constant pressure are directly proportional. (d) The volume of two different gases at the same temperature and pressure is the same, and each sample contains the same number of gas molecules.
Match each gas law definition to the correct name of the person who is credited with discovering it: (a) The total pressure of a mixture of gases is equal to the sum of the pressures of each of the individual gases in the container. (b) The volume of a fixed amount of gas varies inversely with the pressure at constant temperature. (c) The temperature and volume of a gas at constant pressure are directly proportional. (d) The volume of two different gases at the same temperature and pressure is the same, and each sample contains the same number of gas molecules.
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Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is equal to the sum of the pressures of each of the individual gases in the container. Boyle's Law states that the volume of a fixed amount of gas varies inversely with the pressure at constant temperature. Charles's Law states that the temperature and volume of a gas at constant pressure are directly proportional. Avogadro's Law can also be expressed by saying that one mole of any gas at standard temperature and pressure occupies 22.4L.
Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is equal to the sum of the pressures of each of the individual gases in the container. Boyle's Law states that the volume of a fixed amount of gas varies inversely with the pressure at constant temperature. Charles's Law states that the temperature and volume of a gas at constant pressure are directly proportional. Avogadro's Law can also be expressed by saying that one mole of any gas at standard temperature and pressure occupies 22.4L.
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How many moles will a gas that is behaving ideally be if it takes up 2L at 4atm at 37o C?
How many moles will a gas that is behaving ideally be if it takes up 2L at 4atm at 37o C?
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Use PV = nRT
n = PV/RT
= (2L)(4atm) / (0.0821 Latm/molK)(310 K) <-- must change T into K
= 8/25.451
= 0.314 mol
Use PV = nRT
n = PV/RT
= (2L)(4atm) / (0.0821 Latm/molK)(310 K) <-- must change T into K
= 8/25.451
= 0.314 mol
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If the pressure of a sample of one mole of an ideal gas is increased from 2atm to 3atm at a constant volume, and the initial temperature was 20˚C, what is the final temperature of the sample?
If the pressure of a sample of one mole of an ideal gas is increased from 2atm to 3atm at a constant volume, and the initial temperature was 20˚C, what is the final temperature of the sample?
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Because the mass and volume of the sample of the ideal gas are kept constant, a change in pressure causes only a direct change in the temperature. This can be derived from the following ideal gas equation:
.
Because the mass and volume of the sample of the ideal gas are kept constant, a change in pressure causes only a direct change in the temperature. This can be derived from the following ideal gas equation:
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A 2mol sample of an ideal gas with a volume of 3L and temperature of 298K experiences a decrease in pressure of 4atm. If the mass and temperature remain constant, what is the final volume?
A 2mol sample of an ideal gas with a volume of 3L and temperature of 298K experiences a decrease in pressure of 4atm. If the mass and temperature remain constant, what is the final volume?
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First, one must find the initial pressure by plugging the initial conditions into the ideal gas equation.
Decreasing this by 4 atm leads to a final pressure of 12.31atm, which one can plug into the ideal gas equation to find the final volume.
Because only the pressure and volume change, one can also use Boyle's law after finding the initial and final pressure values.
First, one must find the initial pressure by plugging the initial conditions into the ideal gas equation.
Decreasing this by 4 atm leads to a final pressure of 12.31atm, which one can plug into the ideal gas equation to find the final volume.
Because only the pressure and volume change, one can also use Boyle's law after finding the initial and final pressure values.
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If a container holds 1mol of hydrogen, 2.5mol of helium, and 2mol of oxygen at a total pressure of 4atm, what is the partial pressure of the oxygen gas?
If a container holds 1mol of hydrogen, 2.5mol of helium, and 2mol of oxygen at a total pressure of 4atm, what is the partial pressure of the oxygen gas?
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According to Dalton's law of partial pressures, when two or more gases are in one container without chemical interaction, each behaves independently of the others. The partial pressure of oxygen can, therefore, be found by multiplying the molar fraction of oxygen in the container by the total pressure of the three gases.
According to Dalton's law of partial pressures, when two or more gases are in one container without chemical interaction, each behaves independently of the others. The partial pressure of oxygen can, therefore, be found by multiplying the molar fraction of oxygen in the container by the total pressure of the three gases.
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A glass container holds a mixture of two gases. Gas A exerts a pressure of 5atm on the container.
If there are twice as many moles of gas A as there are moles of gas B in the container, what is the total pressure in the container?
A glass container holds a mixture of two gases. Gas A exerts a pressure of 5atm on the container.
If there are twice as many moles of gas A as there are moles of gas B in the container, what is the total pressure in the container?
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This is an equation which requires us to find the partial pressures of each gas in the container. The equation for partial pressure is 
where 
is the molar fraction of one of the gases. Since there are twice as many moles of gas A as there are gas B, we know that gas A accounts for 2/3 of the moles in the container.
This is an equation which requires us to find the partial pressures of each gas in the container. The equation for partial pressure is
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Ammonia is created according to the balanced equation below.
The reaction is allowed to take place in a rigid container. Eight moles of hydrogen gas are mixed with two moles of nitrogen gas. The initial pressure exerted on the container is 5atm.
Assuming the reaction runs to completion, what will the pressure exerted on the vessel be after the reaction takes place?
Ammonia is created according to the balanced equation below.
The reaction is allowed to take place in a rigid container. Eight moles of hydrogen gas are mixed with two moles of nitrogen gas. The initial pressure exerted on the container is 5atm.
Assuming the reaction runs to completion, what will the pressure exerted on the vessel be after the reaction takes place?
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Since the total pressure is dependent on the number of moles in the container, we can use the ratio of moles before and after the reaction to determine the final pressure in the container. There are initially ten moles of gas in the container, eight moles of hydrogen and two moles of nitrogen.
The next step is to determine how many moles of ammonia are created in the reaction, and if there is any excess reactant left over after the reaction. Since there is a 1:3 ratio for hydrogen gas to nitrogen gas, only six of the moles of hydrogen gas will be used in order to react will all two moles of the nitrogen gas.
This leaves two moles of excess hydrogen gas. Using stoichiometry and the molar ratios, we determine that four moles of ammonia are created in the reaction that comsumes two moles of nitrogen.
Four moles of ammonia, plus the two remaining moles of hydrogen gas, results in six moles of total gas after the reaction has run to completion.
Six moles is 60% of the inital moles in the container, so the final pressure will be 60% of the initial pressure. We can solve using the ideal gas law.
Since the total pressure is dependent on the number of moles in the container, we can use the ratio of moles before and after the reaction to determine the final pressure in the container. There are initially ten moles of gas in the container, eight moles of hydrogen and two moles of nitrogen.
The next step is to determine how many moles of ammonia are created in the reaction, and if there is any excess reactant left over after the reaction. Since there is a 1:3 ratio for hydrogen gas to nitrogen gas, only six of the moles of hydrogen gas will be used in order to react will all two moles of the nitrogen gas.
This leaves two moles of excess hydrogen gas. Using stoichiometry and the molar ratios, we determine that four moles of ammonia are created in the reaction that comsumes two moles of nitrogen.
Four moles of ammonia, plus the two remaining moles of hydrogen gas, results in six moles of total gas after the reaction has run to completion.
Six moles is 60% of the inital moles in the container, so the final pressure will be 60% of the initial pressure. We can solve using the ideal gas law.
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A sample of ideal gas is heated in a 2L vessel at a temperature of 320 Kelvin. The pressure in the vessel is 2.5atm. What is the new pressure in the vessel if the volume is halved and the temperature is reduced to 250 Kelvin?
A sample of ideal gas is heated in a 2L vessel at a temperature of 320 Kelvin. The pressure in the vessel is 2.5atm. What is the new pressure in the vessel if the volume is halved and the temperature is reduced to 250 Kelvin?
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Since the gas is ideal, we can use a variation of the ideal gas law in order to find the unknown final pressure.
Since we know that the number of moles is constant between both vessels (and R is a constant as well), we can simply compare the three factors being manipulated between the two vessels: pressure, volume, and temperature. Using a combination of Boyle's law and Charles's law, we can compare the two vessels to one another using the following equation.
Use the given values to solve for the final pressure.
Since the gas is ideal, we can use a variation of the ideal gas law in order to find the unknown final pressure.
Since we know that the number of moles is constant between both vessels (and R is a constant as well), we can simply compare the three factors being manipulated between the two vessels: pressure, volume, and temperature. Using a combination of Boyle's law and Charles's law, we can compare the two vessels to one another using the following equation.
Use the given values to solve for the final pressure.
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A sample of chlorine gas fills a vessel at a temperature of 
. The vessel has a volume of 3L and experiences a pressure of 3atm. What is the mass of the chlorine gas in the vessel?
A sample of chlorine gas fills a vessel at a temperature of
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This problem requires us to substitute the moles of gas in the ideal gas law to mass over molar mass.
We can then isolate for the mass of chlorine gas in the vessel.
Chlorine is diatomic, so its molecular weight will be twice the atomic mass.
The temperature must be expressed in Kelvin.
Using these values, we can solve for the mass of chlorine gas in the vessel.
This problem requires us to substitute the moles of gas in the ideal gas law to mass over molar mass.
We can then isolate for the mass of chlorine gas in the vessel.
Chlorine is diatomic, so its molecular weight will be twice the atomic mass.
The temperature must be expressed in Kelvin.
Using these values, we can solve for the mass of chlorine gas in the vessel.
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A mixture of gases is present in a container. The total pressure on the container is 12atm. Six moles of one of the gases accounts for nine atmospheres of pressure. What is the molar fraction of the remaining gases in the container?
A mixture of gases is present in a container. The total pressure on the container is 12atm. Six moles of one of the gases accounts for nine atmospheres of pressure. What is the molar fraction of the remaining gases in the container?
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There are a couple of things to consider in this problem. First, the problem asks for the molar fraction of the remaining gases in the mixture. As a result, we do not need to know how many different gases are in the mixture, since they all have the same effect on the pressure in the container. Second, the number of moles that one gas accounts for is not relevant since the question is asking to find the molar fraction for the remaining gases. Knowing this, we can find the molar fraction for the described gas, and then subtract it from the total in order to find the remaining molar fraction. The equation for partial pressure is written as 
.
Since we know how much pressure one gas accounts for, we can solve for the molar fraction of that particular gas.
In other words, the known gas accounts for 75% of the gas molecules in the container. This means that the remaining gases must account for 25% of the gas molecules in the container.
So, the molar fraction for the remaining gases is 0.25.
There are a couple of things to consider in this problem. First, the problem asks for the molar fraction of the remaining gases in the mixture. As a result, we do not need to know how many different gases are in the mixture, since they all have the same effect on the pressure in the container. Second, the number of moles that one gas accounts for is not relevant since the question is asking to find the molar fraction for the remaining gases. Knowing this, we can find the molar fraction for the described gas, and then subtract it from the total in order to find the remaining molar fraction. The equation for partial pressure is written as
Since we know how much pressure one gas accounts for, we can solve for the molar fraction of that particular gas.
In other words, the known gas accounts for 75% of the gas molecules in the container. This means that the remaining gases must account for 25% of the gas molecules in the container.
So, the molar fraction for the remaining gases is 0.25.
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How many moles of carbon dioxide occupy a space of 16 liters at a pressure of 760torr and a temperature of 250K?
How many moles of carbon dioxide occupy a space of 16 liters at a pressure of 760torr and a temperature of 250K?
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We can calculate the number of moles using the ideal gas law:
Units always have to be in SI units: atm, liters, kelvin, etc. For this question, we have SI units for everything except for the pressure, which is given in torr, rather than atm.
Now that we have the proper units, we can use our given values for pressure, temperature, and volume to find the moles of gas present.
We can calculate the number of moles using the ideal gas law:
Units always have to be in SI units: atm, liters, kelvin, etc. For this question, we have SI units for everything except for the pressure, which is given in torr, rather than atm.
Now that we have the proper units, we can use our given values for pressure, temperature, and volume to find the moles of gas present.
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An ideal gas is initially at the following conditions:
The gas is then isothermally compressed to 15 atm.
What is the volume of the gas after compression? Round to the nearest liter.
An ideal gas is initially at the following conditions:
The gas is then isothermally compressed to 15 atm.
What is the volume of the gas after compression? Round to the nearest liter.
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The system is isothermal, which means the temperature is constant.
The system is isothermal, which means the temperature is constant.
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A sealed container containing 15L of oxygen gas, 
, with a pressure of 3atm at 
. How many grams of oxygen gas is present in the container? Assume ideal behavior of the gas.
A sealed container containing 15L of oxygen gas,
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is pressure, 
volume, 
moles, 
gas constant, 
temperature. Rearrange the equation, plug in the appropriate values and solve.
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A sealed container containing 7L of an unknown gas, with a pressure of 6atm at 
. The amount of gas in the container is 68.8g. What is the molecular weight of the unknown gas present in the container? Assume ideal behavior of the gas.
A sealed container containing 7L of an unknown gas, with a pressure of 6atm at
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is pressure, volume, moles, gas constant, temperature. Rearrange the equation, plug in the appropriate values and solve.
Since we start with 68.8g of the unknown gas, and we have 1.81mol, we can find the molecular weight.
Since we start with 68.8g of the unknown gas, and we have 1.81mol, we can find the molecular weight.
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A sealed container containing 4L of an unknown gas, with a pressure of 3atm at 
. The amount of gas in the container is 1.82g. What is the molecular weight of the unknown gas present in the container? Assume ideal behavior of the gas.
A sealed container containing 4L of an unknown gas, with a pressure of 3atm at
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is pressure, volume, moles, gas constant, temperature. Rearrange the equation, plug in the appropriate values and solve.
Since we know we have 1.82g of the unknown gas, and we have 0.5mol, we can find the molecular weight by dividing grams by moles.
Since we know we have 1.82g of the unknown gas, and we have 0.5mol, we can find the molecular weight by dividing grams by moles.
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