In these lessons, we will learn and apply:

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

**Related Pages**

Solving Gas Law Problems

High School Chemistry

Chemistry Lessons

The following table gives the Gas Law Formulas. Scroll down the page for more examples and solutions
on how to use the Boyle’s Law, Charles’Law, Gay-Lussac’s Law, Combined Gas Law and Ideal Gas 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}.

A lesson on 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?

**Example:**

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

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}.

A lesson on 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?

**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 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.

**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:**

- 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?
- 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 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.

**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 rock 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?

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.

**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:**

- 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?
- 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)?

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