Chemistry Gas Laws: Combined Gas Law: Videos & Practice Problems

Understanding the relationships between pressure, volume, and temperature is crucial in the study of gases. The combined gas law integrates Boyle's Law, Charles's Law, and Gay-Lussac's Law to establish a direct relationship between these variables. Boyle's Law indicates that pressure and volume are inversely proportional, while Charles's Law shows that volume is directly proportional to temperature. Similarly, Gay-Lussac's Law states that pressure is directly proportional to temperature. The combined gas law formula,

$\frac{PV}{T}=\mathrm{constant}$

allows us to predict how changes in one variable affect the others under different conditions, using the equation

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

when comparing two different sets of conditions. This law is fundamental in predicting the behavior of gases under varying pressures, volumes, and temperatures, which is essential in fields such as chemistry and physics.

Combined Gas Law

Now we have the combined gas law. The combined gas law was created from combining Boyle's law, Charles Law, and Gay Lusak's Law. We're going to say it highlights the relationship between the variables of pressure, volume and temperature. Remember, Boyle's law says that pressure is inversely proportional to volume. Charles losses that volume is directly proportional to temperature and gain loose X losses. That pressure is directly proportional to temperature.

If we take a look down here we can figure out how the combined gas law was derived. So it comes from combining Boyle's law, Trolls law and Gelu Sack's law. If we look we have pressure and volume as numerators. So volume here numerator, pressure here numerator. So they share those variables in common with one another. So that would be PV as numerators.

Charles Law and Galusak's law have as their denominators temperature, so that comes down here. O here we'd say that the combined gas law is PVT = k. So k here would be a constant. This here would represent our combined gas law and if we're dealing with two sets of pressures, volumes and temperature, then it can go further and say P1V1T1 = P2V2T2. So this is how the combined gas law can be derived from these earlier chemistry gas laws.

Combined Gas Law Example

Here in this example question, it says a sample of gas initially has a volume of 900 milliliters at 520 Kelvin and 1.85 atmospheres. What is the pressure of the gas if the volume decreases to 330 milliliters while the temperature increases to 770 Kelvin?

All right. So in this question, they're giving me a volume. We're going to say it's V₁ because later on they give me a second new volume V₂. They give me a temperature T₁ and then later give me a second temperature T₂. They give me this pressure in atmosphere. So this is P₁ because later they ask me what is the new pressure. So they're asking us to find P₂.

Now we have our ideal gas law PV = nRT. If you have watched my videos on ideal law derivations, you know that we can manipulate the ideal gas law in order to get our combined gas law. Now, if you haven't watched those videos, I highly suggest you go back and take a look. So look under ideal gas Derivation videos.

Now here we're talking about two pressures. We're talking about two volumes. We're talking about two temperatures. Moles aren't being discussed because they're being held constant. R is a constant. We divide out the T so that everything is on the left side, and we see that since we're dealing with two different values for these variables, it becomes

P 1 V 1 T 1 = P 2 V 2 T 2

So here we just showed how we derived the combined gas law.

All right, so now we're going to plug in the values that we have. Our pressure is 1.85 atmospheres initially. Our volume, when we change the milliliters to liters, it gives us 0.900 liters. Remember, temperature must always be in kelvins when doing calculations. It's already in Kelvin so we don't have to worry about that.

Equals. We don't know what P₂ is. V₂ is 0.330 liters and then temperature 2 is 770 Kelvin. We're just looking to isolate our P₂ so you can cross multiply these and then you can cross multiply these so that you can isolate P₂. So if I come over here, I'm going to see that

P 2 = P 1 × 0.330   liters × 520   Kelvin = 1.85   atmospheres × 0.900   liters × 770   Kelvin

So divide out the volume and the temperature that we have here on both sides here. So we divide them both to both sides. By that we'll have isolated at the end our P₂, so liters cancel out, Kelvin's cancel out and we'll see here that P₂ = 7.47 atmospheres. We can see that by changing our volume and changing our temperature, it's caused this change in our pressure too, which comes out again to 7.47 atmospheres.

A 4.30 L gas has a pressure of 7.0 atm when the temperature is 60.0 ºC. What will be the temperature of the gas mixture if the volume and pressure are decreased to 2.45 L and 403.0 kPa respectively?

• A. 110 K
• B. 181 K
• C. 206 K
• D. 310 K
• E. 381 K

Answer: (A)

A sealed container with a movable piston contains a gas with a pressure of 1380 torr, a volume of 820 mL and a temperature of 31°C. What would the volume be if the new pressure is now 2.83 atm, while the temperature decreased to 25°C?

• A. 0.0253 L
• B. 0.167 L
• C. 0.326 L
• D. 0.516 L
• E. 1.46 L

Answer: (D)

Here’s what students ask on this topic:

What is the combined gas law?

The combined gas law is a fundamental principle in chemistry that combines three gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law. This law relates the pressure, volume, and temperature of a fixed amount of gas. The combined gas law is expressed mathematically as:

$\frac{P_1\times V_1}{T_1}=\frac{P_2\times V_2}{T_2}$

Here, P1 and P2 are the initial and final pressures of the gas, V1 and V2 are the initial and final volumes of the gas, and T1 and T2 are the initial and final temperatures of the gas in Kelvin. This law assumes that the amount of gas and the number of molecules (n) are constant.

When using the combined gas law, it's important to remember that temperature must always be in Kelvin for the law to be applied correctly. The combined gas law is useful for predicting the behavior of a gas when it undergoes changes in pressure, volume, and temperature.

How can the combined gas law be solved?

The combined gas law is a relation between the pressure, volume, and temperature of a fixed amount of gas. It combines the principles of Boyle's law, Charles's law, and Gay-Lussac's law. The combined gas law formula is:

$\frac{P_1\cdot V_1}{T_1}=\frac{P_2\cdot V_2}{T_2}$

Here's how to solve a problem using the combined gas law:

1. Make sure all your units are consistent. Pressure (P) should be in atmospheres, volume (V) in liters, and temperature (T) in Kelvin. If they're not, convert them before proceeding.
2. Identify the known values (P1, V1, T1) for the initial state of the gas and the known values (P2, V2, T2) for the final state of the gas. One of these six values will be your unknown that you're solving for.
3. Rearrange the formula to solve for the unknown variable. For example, if you're solving for P2, the formula becomes:

$P_2=\frac{P_1\cdot V_1}{T_1}\cdot \frac{T_2}{V_2}$

4. Plug in the known values and calculate the answer.

Remember to keep track of significant figures based on the precision of the given values, and always check your final units to ensure they make sense for the variable you're solving for.

What is the formula for the combined gas law?

The combined gas law is a formula that combines the three individual gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law. It shows the relationship between the pressure, volume, and temperature of a fixed amount of gas. The formula for the combined gas law is:

$\frac{P_1\times V_1}{T_1}=\frac{P_2\times V_2}{T_2}$

In this formula:

• P1 and P2 are the initial and final pressures of the gas, respectively.
• V1 and V2 are the initial and final volumes of the gas, respectively.
• T1 and T2 are the initial and final temperatures of the gas, measured in Kelvin.

To use the combined gas law, you need to make sure that the temperatures are in Kelvin and that the pressure and volume units are consistent between the initial and final states. This law is useful when you need to predict the behavior of a gas when more than one property (pressure, volume, or temperature) is changing.