# Gas Laws

In these lessons, we will learn and apply:

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

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

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 P1V1= P2V2.

#### An Introduction To The Relationship Between Pressure And Volume

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?

#### 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 V1/T1=V2/T2.

#### What Is The Relationship Between Volume And Temperature Of A Gas

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?

#### 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 P1/T1 = P2/T2. 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.

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 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?

### 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 CO2 gas at 2.15 atm take up a colume of 35.28L. What is this temperature (in Celsius)?

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