Gas Laws Chapter 14 Opening thoughts… Have you ever: Seen a hot air balloon? Had a soda bottle...

Gas Laws

Chapter 14

Opening thoughts…

Have you ever:

Seen a hot air balloon?

Had a soda bottle spray all over you?

Baked (or eaten) a nice, fluffy cake?

These are all examples of gases at work!

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Properties of Gases

You can predict the behavior of gases based on the following properties:


Pressure

Volume

Amount (moles)

Temperature

Lets review each of these briefly…


PressureVolume

Amount (moles)

Temperature


Pressure

Pressure is defined as the force the gas exerts on a given area of the container in which it is contained. The SI unit for pressure is the Pascal, Pa.

• If you’ve ever inflated a tire, you’ve probably made a pressure measurement in pounds (force) per square inch (area).



Pressure

VolumeAmount (moles)

Temperature


Volume

Volume is the three-dimensional space inside the container holding the gas. The SI unit for volume is the cubic meter, m3. A more common and convenient unit is the liter, l.

Think of a 2-liter bottle of soda to get an idea of how big a liter is. (OK, how big two of them are…)



Pressure

Volume

Amount (moles)Temperature


Amount (moles)

Amount of substance is tricky. As we’ve already learned, the SI unit for amount of substance is the mole, mol. Since we can’t count molecules, we can convert measured mass (in kg) to the number of moles, n, using the molecular or formula weight of the gas.

By definition, one mole of a substance contains approximately 6.022 x 1023 particles of the substance. You can understand why we use mass and moles!



Pressure

Volume

Amount (moles)

Temperature


Temperature

Temperature is the measurement with which you’re probably most familiar (and the most complex to describe completely). For these lessons, we will be using temperature measurements in Kelvin, K.


The Kelvin scale starts at Absolute 0, which is -273.15°C. To convert Celsius to Kelvin, add 273.15.

How do they all relate?

Some relationships of gases may be easy to predict. Some are more subtle.Now that we understand the factors that affect the behavior of gases, we will study how those factors interact.


How do they all relate?

Some relationships of gases may be easy to predict. Some are more subtle.Now that we understand the factors that affect the behavior of gases, we will study how those factors interact.

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Let’s go!

Properties of GasesProperties of GasesGas properties can be modeled Gas properties can be modeled

using math. Model depends onusing math. Model depends on——

• V = volume of the gas (L)V = volume of the gas (L)• T = temperature (K)T = temperature (K)

– ALL temperatures in the ALL temperatures in the entire chapter MUST be in entire chapter MUST be in Kelvin!!! No Exceptions!Kelvin!!! No Exceptions!

• n = amount (moles)n = amount (moles)• P = pressureP = pressure

(atmospheres) (atmospheres)

Pressure and Volume: Boyle’s Law

How is the pressure applied to a gas related to its volume?

Piston

Gas molecules

Piston

Gas molecules

Boyle’s Law: P1V1 = P2V2

Volume is inversely proportional to applied pressure.

The Harder we Pushthe smaller the gas

volume gets!

Boyle’s Law: P1V1 = P2V2

340 kPa

Sample Problem 1: If the pressure of helium gas in a balloon has a volume of 4.0 L at 210 kPa, what will the pressure be at 2.5 L?

P1 V1 = P2 V2

Temperature and Volume: Charles’s Law

How is the volume of a gas related to its temperature?

gas molecules

moveable mass(constant pressure)

What happens if heat is applied to the gas?



gas molecules


Why did the volume change?

What happens to the average speed of the gas molecules?

.



gas molecules


The volume of a gas is directly proportional to its Temperature (temperature must be in Kelvin)

Charles’s Law: V1/T1 = V2/T2

V1 = V2

T1 T2

Sample Problem 2: A gas sample at 40 oC occupies a volume of 2.32 L. If the temperature is increased to 75 oC, what will be the final volume?

2.58 L

E. Gay-Lussac’s Law1. Volume held CONSTANT

2. Found direct relationshipbetween temperature & pressure

3. P1 = P2

T1 T2

http://www.marymount.k12.ny.us/marynet/06stwbwrk/06gas/1amcslussac/amcsgaylussac.html

http://www.marymount.k12.ny.us/marynet/06stwbwrk/06gas/1amcslussac/amcsgaylussac.html

P1 = P2

T1 T2

Sample Problem 3: The pressure of a gas in a tank is 3.2 atm at 22 oC. If the temperature rises to 60oC, what will be the pressure in the tank?

3.6 atm

A. The Combined Gas Law

1. Amount of Gas held CONSTANT

2. P1 V1 = P2 V2

T2T1

http://kids.earth.nasa.gov/archive/air_pressure/balloon.html

3. This law combines which 3 laws?

http://kids.earth.nasa.gov/archive/air_pressure/balloon.html

Combined Gas Law (Boyle and Charles):

T

VP

T

VP

2

22

1

11 T must be in Kelvin

Can be rearranged to:

P1V1T2 = P2V2T1

A combined gas law problem can be recognized by having two sets of conditions.

Note: if one set of parameters is unchanged that termwill cancel on each side.

Sample Problem 4: A gas at 110 kPa and 30 oC fills a container at 2.0 L. If the temperature rises to 80oC and the pressure increases to 440 kPa, what is the new volume? 0.58 L

A. The Ideal Gas Law1. Contains ALL variables2. P V = n R T3. Where

P = pressure (depends on R)

n = amount of gas (moles) R = ideal gas constant (depends on

pressure) T = temperature (Kelvin)

V = volume (liters)

R = ideal gas constant (depends onpressure)

Pressure R value

mm Hgtorr

62.4

kPa 8.314

atm 0.0821

Sample Problem 6: Calculate the volume of a gas at STP with 2.80 moles.

62.8 L

Sample Problem 7: Calculate the moles of a gas at STP with a volume of 238 L.

10.6 mol

Sample Problem 8: Calculate the number of moles of gas contained in a 3.0 L vessel at 27 oC with a pressure of 1.50 atm.

0.18 mol

B. Dalton’s Law of Partial Pressure1. Contains only pressure

3. Ptotal = P1 + P2 + P3 + . . .

2. Where pressure must be in the same units

4. Sample Problem 9: If the total pressure of a mixture of oxygen & nitrogen gases was 820 mmHg, how much pressure would nitrogen exert if oxygen had 580 mmHg? 240 mmHg

C. Graham’s Law of Effusion1. Contains rates & masses of gases2. Rate A = Mass B

Rate B Mass A

3. WhereRate is measured in m/s Mass is measured in grams

Sample Problem 8: If neon travels at 400. m/s, estimate the average speed of butane (C4H10) at the same temperature.

235 m/s

Sample Problem 9: Chlorine has a velocity of 0.0380 m/s. What is the average velocity of sulfur dioxide under the same conditions?

0.0400 m/s

Question 1

Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are:

a. Inversely proportional: if one goes up, the other comes down.

b. Directly proportional: if one goes up, the other goes up.c. Not related

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Question 1 is Correct!



Decreasing volume increases pressure. Increasing volume decreases pressure.

pressure

volume

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Try Question 1 again…




You selected b. While pressure and volume are related, it is not a direct proportion. Try again!

TRYAGAIN

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You selected c. Pressure and volume are related. Is the relationship inverse or direct?

TRYAGAIN

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Question 2

Based on Charles’ Law (V / T = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are:



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You selected a. While volume and temperature are related, it is not an inverse proportion. Try again!

TRYAGAIN

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b. Directly proportional: if one goes up, the other goes up.

Increasing temperature increases volume. Decreasing temperature decreases volume.

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volume

temperature





You selected c. Pressure and volume are related. Is the relationship inverse or direct?

TRYAGAIN

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Question 3

Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire?

a. Increase the force pressing on the outside of the tire.b. Increase the temperature of the gas (air) in the tire.c. Increase the amount (number of moles) of gas in the tire.

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TRYAGAIN

While increasing the load in the car might increase the force on the tires, it would prove to be a difficult way to adjust tire pressure. Try again!




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TRYAGAIN

Increasing the temperature of the air in the tire would definitely increase pressure. That is why manufacturers recommend checking air pressures when the tires are cold (before driving). But how would you increase temperature without damaging the tire? Is there a more practical solution?




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When you inflate a tire with a pump, you are adding air, or increasing the amount of air in the tire. This will often result in a slight increase in temperature because a tire is not a controlled environment. Such deviations and quirks will be discussed in class!

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Gas Laws Chapter 14 Opening thoughts… Have you ever: Seen a hot air balloon? Had a soda bottle...

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