A series of free High School Chemistry Video Lessons.

In this lesson, we will learn and apply

### Boyle's Law

Boyle's Law states that volume of a given amount of gas held at a
constant temperature varies inversely the with pressure. The
relationship between pressure and volume of Boyle's Law is expressed
in mathematical terms as P_{1}V_{1}= P_{2}V_{2}.

**An introduction to the relationship between pressure and volume, and
an explanation of how to solve gas problems with Boyle's Law**

Example:

At 1.70 atm, a sample of gas takes up 4.25L. If the pressure in the gas is increased to 2.40 atm, what will the new volume be?

**Understanding and applying Boyle's Law**

Example:

A sample of Ne gas occupies 0.220L at 0.86 atm. What will be its volume at 29.4kPa?

### Charles' Law

Charles' Law states that the volume of a given mass of a gas is
directly proportional to its Kelvin temperature at constant pressure.
In mathematical terms, the relationship between temperature and
volume is expressed as V_{1}/T_{1}=V_{2}/T_{2}.

**What is the relationship between volume and temperature of a gas and how to solve problems using Charles' Law?**

Example:

A balloon takes up 625L at 0°C. If it is heated to 80°C, what will its new volume be?**Understanding and applying Charles' Law**

Example:

A gas at 40.0°C occupies a volume of 2.32L. If the temperature is raised to 75.0°C, what will the new volume be if the pressure is constant?### Gay-Lussac's Law

Gay-Lussac's Law states that the pressure of a given mass of gas
varies directly with the Kelvin temperature when the volume remains
constant. Gay-Lussac's Law is expressed in a formula form as P_{1}/T_{1}
= P_{2}/T_{2}. When dealing with Gay-Lussac's Law,
the unit of the temperature should always be in Kelvin.

**Using Gay-Lussac's Law to understand the relationship between a gas' pressure and temperature**

Example:

If the pressure in a car tire is 1.88 atm at 25°C, what will be the pressure if the temperature warms to 37°C?**How to solve word problems that show how to use Gay-Lussac's Law?**

Examples:

1. The pressure in a sealed can of gas is 235kPA when it sits at room temperature (20°). If the can is warmed to 48°C, what will the new pressure inside the can be?

2. A car tire has a pressure of 2.38 atm at 15.2°C. If the pressure inside reached 4.08 atm, the tire will explode. How hot would the tire have to get for this to happen? Report the temperature in degrees Celsius.**Practice Problem to show how to use Gay-Lussac's Law**

Example:

In the morning, a paintball pressure tank is at 306 atm. The weather heats up over the course of the day, and by 3 PM, the outside temperature is roasting at 38.5°C, and the pressure inside the tank is 324 atm. What was the temperature (in degree Celsius) in the morning?

### Combined Gas Law

The Combined Gas Law combines Charles' Law, Boyle's Law and Gay
Lussac's Law. The Combined Gas Law states that a gas' (pressure × volume)/temperature = constant.

The combined law for gases.

Example:

A gas at 110kPa at 30.0°C fills a flexible container with an initial volume of 2.00L. If the temperature is raised to 80,0°C and the pressure increases to 440Kpa, what is the new volume?**How to solve problems with the Combined Gas Equation?**

Example:

A 40.0L balloon is filled with air at sea level (1.00 atm, 25.0°C). It is tied to a riavk and thrown in a cold body of water, and it sinks to the point where the temperature is 4.0°C and the pressure is 11.0 atm. What will its new volume be?### Ideal Gas Law

The Ideal Gas Law mathematically relates the pressure, volume,
amount and temperature of a gas with the equation:

pressure × volume = moles × ideal gas constant × temperature;

PV = nRT.

The Ideal Gas Law is ideal because it ignores interactions between the gas particles in order to simplify the equation. There is also a Real Gas Law which is much more complicated and produces a result which, under most circumstances, is almost identical to that predicted by the Ideal Gas Law.

**Understanding and applying the ideal gas law**

Example:

What is the pressure in atm of a 0.108 mol sample of the gas at a temperature of 20.0°C if its volume is 0.505L?**Sample problems for using the Ideal Gas Law, PV = nRT**

Examples:

1) 2.3 moles of Helium gas are at a pressure of 1.70 atm, and the temperature is 41°C. What is the volume of the gas?

2) At a certain temperature, 3.24 moles of CO_{2} gas at 2.15 atm take up a colume of 35.28L. What is this temperature (in Celsius)?

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

In this lesson, we will learn and apply

- Boyle's Law
- Charles' Law
- Gay-Lussac's Law
- Combined Gas Law
- Ideal Gas Law

Example:

At 1.70 atm, a sample of gas takes up 4.25L. If the pressure in the gas is increased to 2.40 atm, what will the new volume be?

Example:

A sample of Ne gas occupies 0.220L at 0.86 atm. What will be its volume at 29.4kPa?

Example:

A balloon takes up 625L at 0°C. If it is heated to 80°C, what will its new volume be?

Example:

A gas at 40.0°C occupies a volume of 2.32L. If the temperature is raised to 75.0°C, what will the new volume be if the pressure is constant?

Example:

If the pressure in a car tire is 1.88 atm at 25°C, what will be the pressure if the temperature warms to 37°C?

Examples:

1. The pressure in a sealed can of gas is 235kPA when it sits at room temperature (20°). If the can is warmed to 48°C, what will the new pressure inside the can be?

2. A car tire has a pressure of 2.38 atm at 15.2°C. If the pressure inside reached 4.08 atm, the tire will explode. How hot would the tire have to get for this to happen? Report the temperature in degrees Celsius.

Example:

In the morning, a paintball pressure tank is at 306 atm. The weather heats up over the course of the day, and by 3 PM, the outside temperature is roasting at 38.5°C, and the pressure inside the tank is 324 atm. What was the temperature (in degree Celsius) in the morning?

The combined law for gases.

Example:

A gas at 110kPa at 30.0°C fills a flexible container with an initial volume of 2.00L. If the temperature is raised to 80,0°C and the pressure increases to 440Kpa, what is the new volume?

Example:

A 40.0L balloon is filled with air at sea level (1.00 atm, 25.0°C). It is tied to a riavk and thrown in a cold body of water, and it sinks to the point where the temperature is 4.0°C and the pressure is 11.0 atm. What will its new volume be?

pressure × volume = moles × ideal gas constant × temperature;

PV = nRT.

The Ideal Gas Law is ideal because it ignores interactions between the gas particles in order to simplify the equation. There is also a Real Gas Law which is much more complicated and produces a result which, under most circumstances, is almost identical to that predicted by the Ideal Gas Law.

Example:

What is the pressure in atm of a 0.108 mol sample of the gas at a temperature of 20.0°C if its volume is 0.505L?

Examples:

1) 2.3 moles of Helium gas are at a pressure of 1.70 atm, and the temperature is 41°C. What is the volume of the gas?

2) At a certain temperature, 3.24 moles of CO

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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