Key Gas Laws in Electrical Chemistry

Today I want to give you the formulas and equations that you need to know if you're currently studying the gas laws in electrical chemistry. Now this is going to be a fast-paced video so I'm going to give you a lot of formulas in a short time. Let's begin. The first one you need to know is the definition of pressure. Pressure is force divided by area. Now in physics the standard unit of pressure is the Pascal's. And the standard unit of force in physics is Newtons, and area is square meters. So 1 Pascal is 1 Newton per square meter. So that's the standard unit of pressure. But now in chemistry, pressure is going to be in units of atm typically. You need to know that 1 atm is equal to 101,300 plus dals, which is 101.3 kilopascals. Now one atm is also equal to 764 which is also equal to 760 millimeters of mercury and this is also equal to 14.7 psi pounds per square inch. In chemistry typically you'll be using these three conversion factors. The other ones are less common, but you could still use them in certain problems. Now the first formula we're going to talk about is the ideal gas law. EV is equal to MRT. In this equation, R is the gas constant, which is 0.08206, and the units are liters times ATM. per mole per Kelvin. So the units of R tell you the units that you need to use in this formula. So in order for this formula to work, the pressure has to be in atm, the volume has to be in liters, n is the number of moles, and t is the temperature, as you can see in Kelvin. If you need to calculate the Kelvin temperature, you can use this formula if you know the Celsius temperature. It's the Celsius temperature plus 273.15. If you're given the Fahrenheit temperature, you can calculate the Celsius temperature using this formula. Now, there's another value for R as well. R also equals 8.3145 joules per mole or Kelvin. Now with the ideal gas law equation, 95% of the time, or even more, you'll be using this value for R. Now I want you to understand, if you use the second value for R, the units will be different. So if you want to use that one, you need to use basically the physics units for pressure, which will be in pascals. For volume, instead of using liters, you need to use cubic meters. The temperature will still be in Kelvin and will still be in moles. So that's the difference between the two R values. So if you're going to use this R value, make sure the pressure is in atm and the volume is in liters. If you're using the second R value, make sure the pressure is in pascals and the volume is cubic meters. Now going back to this equation, if we were to solve for R, we would get... PV over NT. And if we write it twice, but with a different subscript, this will give us a variant of the combined gas law. So let's start with this. P1V1 over N1T1 equals P2V2 over N2T2. To get the combined gas law equation, the moles have to be the same. So if the moles are held constant, you can get rid of N, and you'll get this formula. P1 V1 over T1 is equal to P2 V2 over T2. So that is the combined gas law. In order for this equation to work, pressure has to be in the same units. So if P1 is in atm, E2 has to be an ATM. If p1 is in torr, v2 has to be in torr. If p1 is in millimeters of mercury, p2 has to be in millimeters of mercury. The same is true for the volume. If v1 is in liters, v2 has to be in liters. If v1 is in milliliters, v2 has to be in milliliters. You could use both units, but they have to match. The temperature has to be in Kelvin. For this to work, You can't use Celsius or Fahrenheit, even if they match for temperature. Pressure and volume, you can use different units, but they have to match. For temperature, it has to be in Kelvin only. So that's the first equation that we can get from this equation. Now, the next equation is going to be Boyle's Law. If we hold the moles and the temperature constant, we're left with what we have on top. which is P1 V1 is equal to P2 V2. So that's Boyle's law. His law describes the relationship between volume and pressure, which is an inverse relationship. As you increase the volume, the pressure decreases. Now let's move on to Charles law. For Charles law, we're going to hold the pressure and the moles constant. So we're left with V1 over T1 is equal to V2 over T2. So his law describes the relationship between the volume of a gas. and the temperature. As you increase the temperature, the volume of the gas is going to increase. It's going to expand. And so that relationship is associated with Charles'Law. Next up, we have Gay-Lussac's Law, which shows the relationship between pressure and temperature. So hold in volume and moles constant, we get P1 over T1 is equal to P2 over T2. So that's Gay-Lussac's law. If we were to plot graph for this place in temperature on the x-axis pressure on the y-axis This too shows a direct relationship Between the two much in the same way as Charles law as the temperature goes up pressure goes up So imagine having a gas in a rigid container If you heat up the gas the pressure on the inside is going to build now the next one has to do with Avogadro's law. For this one we're going to hold the pressure and the temperature constant. So we get a relationship between volume and moles. So we get V1 over N1 is equal to V2 over N2. So if we were to plot the number of moles on the x-axis and the volume on the y-axis, as we increase the moles, the volume is going to increase. So in other words, the more moles of gas that you have, the greater the volume that that gas will occupy. So imagine blowing more air inside a balloon. The balloon is going to expand. Now, let's go back to this formula. PV is equal to nRT, the ideal gas law equation. We know that the moles is equal to the mass divided by the molar mass, or the molecular weight of the gas. So what I'm going to do is I'm going to replace n with m over mw. And then multiplying both sides by the molar mass, we get this equation. So the pressure times the volume times the molar mass or the molecular weight of the gas is equal to the mass of the gas times R times T. So this formula is very useful. if you need to calculate the molar mass of a gas. I mean, you could use a combination of these two formulas, but if you want to write this down in your list, it'll be helpful if you need to calculate the mass or the molar mass of a gas. Now, starting from that formula, I'm going to divide both sides by V. So I get pressure times the molar mass is equal to M over V times RT. m over v mass divided by volume is density so we get this and then divide them both sides by rt we get the formula that will help us to calculate the density of a gas which is this the density of a gas is equal to the pressure times the molar mass of the gas divided by rt So if you know the molar mass of the gas, you can calculate the density of that gas. If you need to determine the identity of the gas, you could use the density, calculate the molar mass, and with the molar mass, that can help you identify what kind of gas you have. So make sure you add these two formulas to your list. Now, you need to be familiar with the term STP. STP stands for standard temperature and pressure. At STP the standard temperature is 270 degrees, I mean let me say that again, I said it too fast, 273 degrees Kelvin which is the same as 0 degrees Celsius. The standard pressure is 1 ATM or 760 Torr. Now another fact that you want to keep in mind is that at STP, one mole of gas occupies a volume of 22.4 liters. So this is very useful when dealing with gas stoichiometry problems at STP. You can convert from moles to liters easily. And I do have some practice problems in the description section that explains how to do that. So feel free to take a look at that when you get a chance. Now the next thing we need to talk about is Dalton's law of partial pressures. The total pressure inside a container is the sum of the individual partial pressures exerted by each gas. So imagine if you have a container with the gases nitrogen, oxygen, and carbon dioxide. The total pressure will be the sum of the partial pressures of each of these gases. So in this container, nitrogen will exert a certain amount of pressure on that container. Oxygen will exert a certain amount of pressure, and the same thing is true for carbon dioxide. So each substance will exert their own partial pressure on that container. And when you add it up, you get the total. pressure exerted by all of the gases in that container. Now the partial pressure of substance A is equal to the mole fraction of that substance times the total pressure. And the mole fraction is basically the moles of that substance divided by the total moles. Mole fraction is also equal to the partial pressure of that substance divided by the total pressure. Now the sum of all the mole fractions for all the substances inside a container is going to add up to one. So those are some other formulas you want to add to your list. The next thing you need to know is that the average kinetic energy of a gas is directly proportional to temperature. Now for this formula, you want to use 8.3145 joules per mole per Kelvin for the value of R. When you do so, the kinetic energy will be in joules, and the temperature has to be in Kelvin. So this equation helps us to see the relationship between the average kinetic energy of a gas with the temperature. So if you increase the temperature of a sample of gas, the average kinetic energy will increase. The next formula you need to be familiar with is the root mean square velocity of a gas. And that's going to be equal to the square root of 3RT over the molecular weight of that gas. For this formula 2, R is going to be 8.3145 joules per mole per Kelvin. When you use that particular value of R, the velocity that you get is going to be in meters per second. Now, the molecular weight... It's not going to be grams per mole. It's going to be kilograms per mole in order for this formula to work. So for instance, O2, when you use a periodic table, it has a molar mass of 32 grams per mole. Converting grams to kilograms, you need to divide by 1,000. So that's going to be 0.032 kilograms per mole. The next thing we're going to talk about is Graham's Law of Effusion. The basic concept of effusion, imagine if you have a container. My drawing is not perfect, but we'll make do with it. Let's say there's a hole in this container, and you want to find out the rate at which nitrogen gas escapes this hole. As it leaves that hole, this is related to the concept of effusion. It effuses out of that container. Now, the rate of effusion is inversely related to the square root of the molecular weight of the gas. So you'll see this formula associated with Graham's Law of Effusion. R2 over R1 is equal to the square root of MW1 over MW2. So if you know the rate of effusion of one gas and you know its molecular weight, you could find the rate of effusion of another gas if you know its molecular weight. So as the molecular weight of a gas increases, the rate of effusion decreases. And it makes sense because heavy gases, they tend to move a lot slower. Lighter gases move faster. This equation is based on this formula. As you can see, if you look at the relationship between velocity and molecular weight, they're inversely related. The molecular weight is on the bottom of the fraction, and it's inside of the square root, much in the same way as we see this formula is. So the more mass that a gas particle has, the slower it's going to be when moving. So that's the basic idea behind Graham's Law of Effusion. Now you might see some problems that may ask you how long it's going to take for a certain gas to effuse. So they'll introduce elements like time instead of rate. We need to know that time is inversely related to rate. In other words, a gas particle that can move faster is going to take a shorter time to effuse out of that container. A gas particle that's heavier and moves slower is going to take a longer time to effuse. So the rate of effusion is inversely related with time. So knowing that, R2 over R1 is going to equal T1 over T2. So time and rate, they're inversely related, but time and molecular weight, they're somewhat related. So those are the formulas you could use when dealing with Graham's Law of Effusion. And I do have practice problems on this topic, so if you want to see how to use this formula, feel free to check out the links in the description section below. I have a ton of videos on the Gauss laws that, you know, you can really see how you can put these equations to use. So feel free to take a look at that when you get a chance. And thanks for watching.

The first one you need to know is the definition of pressure. Pressure is force divided by area. Now in physics the standard unit of pressure is the Pascal's. And the standard unit of force in physics is Newtons, and area is square meters. So 1 Pascal is 1 Newton per square meter.

So that's the standard unit of pressure. But now in chemistry, pressure is going to be in units of atm typically. You need to know that 1 atm is equal to 101,300 plus dals, which is 101.3 kilopascals. Now one atm is also equal to 764 which is also equal to 760 millimeters of mercury and this is also equal to 14.7 psi pounds per square inch.

In chemistry typically you'll be using these three conversion factors. The other ones are less common, but you could still use them in certain problems. Now the first formula we're going to talk about is the ideal gas law. EV is equal to MRT.

In this equation, R is the gas constant, which is 0.08206, and the units are liters times ATM. per mole per Kelvin. So the units of R tell you the units that you need to use in this formula. So in order for this formula to work, the pressure has to be in atm, the volume has to be in liters, n is the number of moles, and t is the temperature, as you can see in Kelvin.

If you need to calculate the Kelvin temperature, you can use this formula if you know the Celsius temperature. It's the Celsius temperature plus 273.15. If you're given the Fahrenheit temperature, you can calculate the Celsius temperature using this formula. Now, there's another value for R as well.

R also equals 8.3145 joules per mole or Kelvin. Now with the ideal gas law equation, 95% of the time, or even more, you'll be using this value for R. Now I want you to understand, if you use the second value for R, the units will be different. So if you want to use that one, you need to use basically the physics units for pressure, which will be in pascals. For volume, instead of using liters, you need to use cubic meters.

The temperature will still be in Kelvin and will still be in moles. So that's the difference between the two R values. So if you're going to use this R value, make sure the pressure is in atm and the volume is in liters. If you're using the second R value, make sure the pressure is in pascals and the volume is cubic meters.

Now going back to this equation, if we were to solve for R, we would get... PV over NT. And if we write it twice, but with a different subscript, this will give us a variant of the combined gas law.

So let's start with this. P1V1 over N1T1 equals P2V2 over N2T2. To get the combined gas law equation, the moles have to be the same.

So if the moles are held constant, you can get rid of N, and you'll get this formula. P1 V1 over T1 is equal to P2 V2 over T2. So that is the combined gas law. In order for this equation to work, pressure has to be in the same units. So if P1 is in atm, E2 has to be an ATM.

If p1 is in torr, v2 has to be in torr. If p1 is in millimeters of mercury, p2 has to be in millimeters of mercury. The same is true for the volume.

If v1 is in liters, v2 has to be in liters. If v1 is in milliliters, v2 has to be in milliliters. You could use both units, but they have to match.

The temperature has to be in Kelvin. For this to work, You can't use Celsius or Fahrenheit, even if they match for temperature. Pressure and volume, you can use different units, but they have to match.

For temperature, it has to be in Kelvin only. So that's the first equation that we can get from this equation. Now, the next equation is going to be Boyle's Law.

If we hold the moles and the temperature constant, we're left with what we have on top. which is P1 V1 is equal to P2 V2. So that's Boyle's law. His law describes the relationship between volume and pressure, which is an inverse relationship.

As you increase the volume, the pressure decreases. Now let's move on to Charles law. For Charles law, we're going to hold the pressure and the moles constant.

So we're left with V1 over T1 is equal to V2 over T2. So his law describes the relationship between the volume of a gas. and the temperature. As you increase the temperature, the volume of the gas is going to increase. It's going to expand.

And so that relationship is associated with Charles'Law. Next up, we have Gay-Lussac's Law, which shows the relationship between pressure and temperature. So hold in volume and moles constant, we get P1 over T1 is equal to P2 over T2. So that's Gay-Lussac's law.

If we were to plot graph for this place in temperature on the x-axis pressure on the y-axis This too shows a direct relationship Between the two much in the same way as Charles law as the temperature goes up pressure goes up So imagine having a gas in a rigid container If you heat up the gas the pressure on the inside is going to build now the next one has to do with Avogadro's law. For this one we're going to hold the pressure and the temperature constant. So we get a relationship between volume and moles. So we get V1 over N1 is equal to V2 over N2. So if we were to plot the number of moles on the x-axis and the volume on the y-axis, as we increase the moles, the volume is going to increase.

So in other words, the more moles of gas that you have, the greater the volume that that gas will occupy. So imagine blowing more air inside a balloon. The balloon is going to expand.

Now, let's go back to this formula. PV is equal to nRT, the ideal gas law equation. We know that the moles is equal to the mass divided by the molar mass, or the molecular weight of the gas.

So what I'm going to do is I'm going to replace n with m over mw. And then multiplying both sides by the molar mass, we get this equation. So the pressure times the volume times the molar mass or the molecular weight of the gas is equal to the mass of the gas times R times T.

So this formula is very useful. if you need to calculate the molar mass of a gas. I mean, you could use a combination of these two formulas, but if you want to write this down in your list, it'll be helpful if you need to calculate the mass or the molar mass of a gas.

Now, starting from that formula, I'm going to divide both sides by V. So I get pressure times the molar mass is equal to M over V times RT. m over v mass divided by volume is density so we get this and then divide them both sides by rt we get the formula that will help us to calculate the density of a gas which is this the density of a gas is equal to the pressure times the molar mass of the gas divided by rt So if you know the molar mass of the gas, you can calculate the density of that gas. If you need to determine the identity of the gas, you could use the density, calculate the molar mass, and with the molar mass, that can help you identify what kind of gas you have. So make sure you add these two formulas to your list.

Now, you need to be familiar with the term STP. STP stands for standard temperature and pressure. At STP the standard temperature is 270 degrees, I mean let me say that again, I said it too fast, 273 degrees Kelvin which is the same as 0 degrees Celsius. The standard pressure is 1 ATM or 760 Torr. Now another fact that you want to keep in mind is that at STP, one mole of gas occupies a volume of 22.4 liters.

So this is very useful when dealing with gas stoichiometry problems at STP. You can convert from moles to liters easily. And I do have some practice problems in the description section that explains how to do that.

So feel free to take a look at that when you get a chance. Now the next thing we need to talk about is Dalton's law of partial pressures. The total pressure inside a container is the sum of the individual partial pressures exerted by each gas.

So imagine if you have a container with the gases nitrogen, oxygen, and carbon dioxide. The total pressure will be the sum of the partial pressures of each of these gases. So in this container, nitrogen will exert a certain amount of pressure on that container.

Oxygen will exert a certain amount of pressure, and the same thing is true for carbon dioxide. So each substance will exert their own partial pressure on that container. And when you add it up, you get the total.

pressure exerted by all of the gases in that container. Now the partial pressure of substance A is equal to the mole fraction of that substance times the total pressure. And the mole fraction is basically the moles of that substance divided by the total moles. Mole fraction is also equal to the partial pressure of that substance divided by the total pressure. Now the sum of all the mole fractions for all the substances inside a container is going to add up to one.

So those are some other formulas you want to add to your list. The next thing you need to know is that the average kinetic energy of a gas is directly proportional to temperature. Now for this formula, you want to use 8.3145 joules per mole per Kelvin for the value of R.

When you do so, the kinetic energy will be in joules, and the temperature has to be in Kelvin. So this equation helps us to see the relationship between the average kinetic energy of a gas with the temperature. So if you increase the temperature of a sample of gas, the average kinetic energy will increase. The next formula you need to be familiar with is the root mean square velocity of a gas.

And that's going to be equal to the square root of 3RT over the molecular weight of that gas. For this formula 2, R is going to be 8.3145 joules per mole per Kelvin. When you use that particular value of R, the velocity that you get is going to be in meters per second.

Now, the molecular weight... It's not going to be grams per mole. It's going to be kilograms per mole in order for this formula to work. So for instance, O2, when you use a periodic table, it has a molar mass of 32 grams per mole.

Converting grams to kilograms, you need to divide by 1,000. So that's going to be 0.032 kilograms per mole. The next thing we're going to talk about is Graham's Law of Effusion.

The basic concept of effusion, imagine if you have a container. My drawing is not perfect, but we'll make do with it. Let's say there's a hole in this container, and you want to find out the rate at which nitrogen gas escapes this hole.

As it leaves that hole, this is related to the concept of effusion. It effuses out of that container. Now, the rate of effusion is inversely related to the square root of the molecular weight of the gas.

So you'll see this formula associated with Graham's Law of Effusion. R2 over R1 is equal to the square root of MW1 over MW2. So if you know the rate of effusion of one gas and you know its molecular weight, you could find the rate of effusion of another gas if you know its molecular weight.

So as the molecular weight of a gas increases, the rate of effusion decreases. And it makes sense because heavy gases, they tend to move a lot slower. Lighter gases move faster.

This equation is based on this formula. As you can see, if you look at the relationship between velocity and molecular weight, they're inversely related. The molecular weight is on the bottom of the fraction, and it's inside of the square root, much in the same way as we see this formula is.

So the more mass that a gas particle has, the slower it's going to be when moving. So that's the basic idea behind Graham's Law of Effusion. Now you might see some problems that may ask you how long it's going to take for a certain gas to effuse. So they'll introduce elements like time instead of rate. We need to know that time is inversely related to rate.

In other words, a gas particle that can move faster is going to take a shorter time to effuse out of that container. A gas particle that's heavier and moves slower is going to take a longer time to effuse. So the rate of effusion is inversely related with time.

So knowing that, R2 over R1 is going to equal T1 over T2. So time and rate, they're inversely related, but time and molecular weight, they're somewhat related. So those are the formulas you could use when dealing with Graham's Law of Effusion.

And I do have practice problems on this topic, so if you want to see how to use this formula, feel free to check out the links in the description section below. I have a ton of videos on the Gauss laws that, you know, you can really see how you can put these equations to use. So feel free to take a look at that when you get a chance.

And thanks for watching.

Transcript for:Key Gas Laws in Electrical Chemistry

Transcript for:
Key Gas Laws in Electrical Chemistry