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Lesson Transcript

Instructor:
*Nissa Garcia*

Nissa has a masters degree in chemistry and has taught high school science and college level chemistry.

While studying chemistry, you may have learned about the different gas laws, including Boyle's law, Charles' law, and Gay-Lussac's law. What happens if we combine all these laws together? We come up with a whole new gas law: the combined gas law, which we'll take a look at in this lesson.

The **combined gas law** makes use of the relationships shared by pressure, volume, and temperature: the variables found in other gas laws, such as Boyle's law, Charles' law and Gay-Lussac's law. Let's review the basic principles of these three laws.

Imagine you are a diver, and you begin your dive with lungs full of air. As you go deeper under water, the pressure you experience in your lungs increases. When this happens, the air inside your lungs gets squished, so the volume decreases. This is an example of **Boyle's law** in action, which states that the higher the pressure (*P*), the lower the volume (*V*), as shown in this image. Here, *k* is any constant number.

Have you ever tried putting a balloon in the refrigerator and notice that it shrinks? As the temperature of the refrigerated balloon decreases, the volume of the gas inside the balloon also decreases. When you take the balloon out of the refrigerator, it reverts to its original size, so the opposite is also true; when the temperature increases, the volume also increases. The shrinking balloon serves as a demonstration of **Charles' law**, which states that the higher the temperature (*T*), the higher the volume (*V*).

Imagine yourself driving down a road, which can cause the temperature to increase within your tires. As a result, the air inside the tires expands, and the pressure increases. This is an example of **Gay-Lussac's law**, which shows the relationship between pressure (*P*) and temperature (*T*) when the volume remains constant; as the temperature increases, the pressure also increases.

When we put Boyle's law, Charles' law, and Gay-Lussac's law together, we come up with the **combined gas law**, which shows that:

- Pressure is inversely proportional to volume, or higher volume equals lower pressure.
- Pressure is directly proportional to temperature, or higher temperature equals higher pressure.
- Volume is directly proportional to temperature, or higher temperature equals higher volume.

Let's take a look at the formula for the combined gas law. Here, *PV* / *T* = *k* shows how pressure, volume and temperature relate to each other, where *k* is a constant number.

The formula for the combined gas law can be adjusted to compare two sets of conditions in one substance. In the equation, the figures for pressure (*P*), volume (*V*), and temperature (*T*) with subscripts of one represent the initial condition, and those with the subscripts of two represent the final condition.

P`1`V`1` / T`1` = P`2`V`2` / T`2`

It is important to note that the temperature should always be in Kelvin, so if the given units are in Celsius, then those should be converted to Kelvin by adding 273. We will demonstrate how this is done in the next section.

How do we use the combined gas law? Let's go over a few sample problems.

Example One: 450 mL of a gas occupies a container that has a temperature of 28°C and a pressure of 788 mmHg. What is the temperature if the volume is reduced to 50 mL at 760 mmHg? As the unit of measurement is in Celsius, remember to convert it to Kelvin.

Here, we see that the pressure decreased by a little and the volume decreased by a lot. As temperature and pressure are directly proportional to teach other, the final temperature also decreased in comparison to the initial temperature.

Example Two: A mixture of gases occupies a container and has a volume of 654 mL at 6°C and 65.3 kPa. The temperature and pressure change to 4°C and 108.7 kPa. What volume does the gas occupy now?

In this case, we see that the pressure increased, and the temperature decreased slightly. The final volume also decreased compared to the initial volume because pressure is inversely proportional to volume.

Example Three: A gas with a volume of 2.5 L is in a container at 64°C and 700 mmHg. When subjected to a temperature of -33°C and a pressure of 900 mmHg, what is the new volume of the gas?

In this example, we see that the pressure increased and the temperature decreased when comparing the initial and final conditions. The final volume also decreased in comparison to the initial volume because pressure is inversely proportional to volume and because volume is directly proportional to temperature.

Let's review. The **combined gas law** is the combination of Boyle's law, Charles' law and Gay-Lussac's law and shows the relationship shared by pressure, temperature and volume. By combining the formulas, the combined gas law proves that as pressure increases, temperature increases and volume decreases. It also proves that as volume increases, temperature increases. The formula for combined gas laws for a substance with two sets of conditions is this:

P`1`V`1` / T`1` = P`2`V`2` / T`2`

When using this formula, it is important to remember that the unit of temperature should always be in Kelvin. In cases when the given temperature is in Celsius, we need to convert it to Kelvin by adding 273 to the temperature in Celsius.

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Physical Science: Help and Review19 chapters | 244 lessons

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