GS_Gas Laws Calculations Lesson

Gas Laws Calculations

Each of the gas laws can be made into mathematical equations. To do this, let's first recall the relationships for each of these laws.

Law

Relationship

Boyle's

P is inversly proportional to V

Charles'

T is directly proportional to V

Gay-Lussac's

T is directly proportional to P

Watch the following video - whose law does it illustrate?

  • Whose law does it illustrate? 
    • Answer: Charles' Law

gif of weights being added (pressure) causing pressure to increase

This animation gives you a way to visualize the relationship between volume and pressure changes in a gas when the amount (number of particles) and temperature are held constant.

 The trapped air is rather like a spring, exerting a force upward. The downward force is compression by the sea of atmosphere above it. Boyle called this effect 'the spring of the air' and even published his results in a pamphlet with that title back in 1662! The difference between the heights of the mercury columns shows the pressure change. The volume is shown as the length of the air column in a tube of known radius.

Boyle's Law: for a fixed amount of an ideal gas kept at a fixed temperature, the pressure and volume are inversely proportional: when one doubles, the other is reduced by half when the amount and temperature are both unchanging.

BOYLE'S LAW PV=k When a gas is changes conditions, this relationship is expressed as: P₁V₁=P₂V₂

Just like Boyle's law, Charles' law is a proportion. It can be converted into an equation as shown below. We will use k' this time, instead of k, to emphasize that this is a different constant than used in the Boyle's law equation.

CHARLES'LAW V=TK' or V/T =k' When a gas changes conditions, this relationship is expressed as: 2 V₁/Τ₁ =V ₂/T₂

Example Problem: Use Charles' Law to answer the following. A sample of gas has a volume of 852 mL at 25°C. What Celsius temperature is necessary for the gas to have a volume of 945 mL? Start by making a list of your data. Label the initial conditions as 1 and the new conditions as 2. V₁ = 852 mL V2=945 mL T₁= 25°C T2= ? Next, look at your units to see if anything needs to be converted. In gas calculations, temperature must be expressed in Kelvin. Make a habit of always converting your temperature to Kelvin at the beginning of any gas problem. V₁ = 852 mL V2= 945 mL T₁= 25°C + 273 298 K T₂= ? Now, simply plug the values in to Charles' Law equation. T₁/V₁= T₂/V₂ 852K/298K= 945mL/T₂ (852K)(T2)=(298K)(945mL) T₂ =331K 331-273 =58°C

Finally, Gay-Lussac's Law can be converted into an equation as shown below (using k' ' as the constant).

GAY-LUSSAC'S LAW P=Tk" or P /T =k" When a gas changes conditions, this relationship is expressed as: P₁/T₁= P₂/ T₂

Watch the following video for an example of a problem involving Gay-Lussac's Law. This particular example has some common twists, so make sure to watch it and follow along!

Combined Gas Law

The  combined gas law takes into account all of the gas laws above. Notice that the amount of gas is not part of the equation because it is not varied in the combined gas law.

LaTeX: \frac{P_1V_1}{T_1}=kP1V1T1=k

The combined gas law is most commonly used to compare two different sets of conditions.

COMBINED GAS LAW (P₁V₁)/T₁=(P₂V₂)/ T₂

If you look closely at the equation above, you should see that this is the only equation you need to memorize on this page.   This is because each of the individual gas laws is actually shown in the combined law.   In Boyle's Law, temperature remains constant. So, if you take temperature out of the equation above, you have Boyle's Law.   If you take pressure out of the equation above, you have Charles' Law.   If you take volume out of the equation above, you have Gay-Lussac's Law.  

Example Problem: What is the final pressure of a sample of oxygen with a volume of 975 m³ at 740 torr and 23.0°C if it is heated to 58.0°C and has a final volume of 1275 m³? Start by making a list of your data. Don't forget to convert temperature to Kelvin. Initial Gas Measurements P₁ = 740 torr V₁ = 975 m³ T₁ = 23.0°C + 273 = 296 K Final Gas Measurements P₂ = ? V₂=1275 m³ T₂ = 58.0°C + 273 = 331 K Now, simply plug the values into the Combined Law equation. P₁V₁ / T₁ = P₂V₂ / T₂ (740torr)(975m³) / 296K = P₂(1275m³)/331K (740torr)(975m³)(331K) = P(1275m³)(296K) P₂ =633torr

Remember to work on the module practice problems as you complete each section of content.

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