ELEMENTARY �GAS LAWS: BOYLES’, GAY-LUSSAC’S, AND CHARLE’S LAWS

BARKING DOG, �KEITH HARING, 1990

IN THIS PRESENTATION…

• Gay-Lussac’s Law (pressure vs. temperature)
• Boyle’s Law (pressure vs. volume)
• Charles’s Law (volume vs. temperature)

BOYLE’S LAW: PRESSURE VS. VOLUME RELATIONSHIP

Given what we looked at in the past, are pressure and volume directly or inversely related?

BOYLE’S LAW: PRESSURE VS. VOLUME RELATIONSHIP

They are inversely related! As the bag of air was taken underwater, the pressure increased which decreased the volume of the bag of air.

BOYLE’S LAW: PRESSURE VS. VOLUME RELATIONSHIP

As one variable increases, the other one decreases.

BOYLE’S LAW: PRESSURE VS. VOLUME RELATIONSHIP

BOYLE’S LAW: PRESSURE VS. VOLUME RELATIONSHIP

If we rearrange the equation, we get

PV = k

This equation is true for any point on the line, so:

P₁V₁ = k

and

P₂V₂ = k

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BOYLE’S LAW: PRESSURE VS. VOLUME RELATIONSHIP

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Since both of the previous equations equal k, then the two equations equal each other:

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P₁V₁ = P₂V₂

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EXAMPLE 1

A weather balloon has a volume of 7589 L on the ground where the pressure is 0.98 atm. When the balloon is released, what will its volume be at 30,000 ft where the pressure is 0.29 atm?

To solve this, we will use the “GUESS” method of organization.

G: write down your Givens in the problem

U: write down your Unknown in the problem

E: write down the Equation you will use to solve the problem

S: Substitute the numbers in for the variables in the equation

S: Solve the problem for the unknown variable

EXAMPLE 1

A weather balloon has a volume of 7589 L on the ground where the pressure is 0.98 atm. When the balloon is released, what will its volume be at 30,000 ft where the pressure is 0.29 atm?

Givens: V₁ = 7589 L; P₁ = 0.98 atm; P₂ = 0.29 atm

Unknown: V₂

Equation: P₁V₁ = P₂V₂

Substitute: 0.98 atm x 7589 L = 0.29 atm x V₂

Solve: V₂ = 26,000 L (notice lower P, higher V)

The GUESS method is a useful organizational tool and you will use it to solve these gas law problems. It will save you from making many mistakes!

GAY-LUSSAC’S LAW: PRESSURE VS. TEMPERATURE RELATIONSHIP

Given what we looked at in the past, are pressure and temperature directly or inversely related?

GAY-LUSSAC’S LAW: PRESSURE VS. TEMPERATURE RELATIONSHIP

• Directly! As one variable increases, the other one increases also.

GAY-LUSSAC’S LAW: PRESSURE VS. TEMPERATURE RELATIONSHIP

• What is the equation of a line (direct relationship)?

GAY-LUSSAC’S LAW: PRESSURE VS. TEMPERATURE RELATIONSHIP

y = mx + b

Substituting the variables for y and x:

P = mT + b

At 0 temp (no kinetic energy) there is 0 pressure, so b = 0 and changing “m” to “k”, the symbol for a constant in science, we get:

P = kT

GAY-LUSSAC’S LAW: PRESSURE VS. TEMPERATURE RELATIONSHIP

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GAY-LUSSAC’S LAW: PRESSURE VS. TEMPERATURE RELATIONSHIP

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EXAMPLE 2

If a sample of a gas at 25^oC has a pressure of 19.4 psi, what pressure will the gas have if the temperature is decreased to -5.0^oC?

EXAMPLE 2

CHARLES’S LAW: VOLUME VS. TEMPERATURE RELATIONSHIP

Given what we looked at in the past, are volume and temperature directly or inversely related?

CHARLES’S LAW: VOLUME VS. TEMPERATURE RELATIONSHIP

They are directly related! When the crushed ping pong ball was heated, the gas inside expanded and pushed the dent out of the ping pong ball.

CHARLES’S LAW: VOLUME VS. TEMPERATURE RELATIONSHIP

Since the relationship is direct, the equation for Charles’s Law can be derived in the same manner as Gay-Lussac’s Law and will have a very similar form.

The useful equation of Charles’s Law is:

EXAMPLE 3

EXAMPLE 4: WHICH LAW TO USE?

Steam (gaseous water) in a pressure cooker initially has a pressure of 304 kPa at a temperature of 100.^oC. If the steam is heated to 150^oC in the pressure cooker, what will the new pressure be?

Givens: P₁ = 304 kPa; T₁ = 100.^oC (373 K); T₂ = 150^oC (424 K)

Unknown: P₂

Equation: How do we know what equation to use?

Look at the givens and unknown and decide which�equation includes all of those variables. In this case, it is�Gay-Lussac’s Law.

EXAMPLE 4: WHICH LAW TO USE?

NOW IT’S YOUR TURN!

• Your job is to perform the calculations for today’s assignment.
• You must use the GUESS method to show all of your work, as you solve these problems. No work, no credit. This applies to all calculations this year!
• Be careful with units and be sure to use only Kelvin for temperature values in your calculations!