Particles in a gas are far apart and move rapidly in a ______________________________ fashion.
"COOL FACTS" about ALL GASES (at the same temperature): If you have ONE MOLE of gas sample "A" and ONE MOLE of gas sample "B" these two gases will ______________________________ and have the ______________________________.
The key to the above statement is in regard to moles of a gas. A mole has 6.02 x 1023 particles (atoms or molecules) - ALWAYS compare gases to each other in terms of ______________________________ !!!
DESCRIBING GASES:
VOLUME: refers to the space matter occupies. Example; The volume of SOLID carbon dioxide is about 28 cm3. Yet, when CO2 is at room temperature ( 250C )the same number of carbon dioxide molecules occupy ______________________________ cm3 - a volume almost 1000 times greater.
For all gases, only a small fraction of the total volume of the gas is occupied by the molecules themselves - the rest is __________________________________.
When a gas is compressed, the same number of particles will occupy a different volume ______________________________.
A typical 44-liter tank of Helium is able to fill about 500 balloons (25cm in diameter) for a total volume of over 6500 liters!
TEMPERATURE: Temperature of a gas can be related to a box of Ping-Pong balls.
- Place a few Ping-Pong balls into a box. The box has a much larger volume than the Ping-Pong balls.
- Shaking the box ______________________________ results in the balls moving around slowly - this corresponds to a low temperature.
- Shaking the box ______________________________ results in a rapid motion of the balls - this corresponds to a high temperature.
PRESSURE: Pressure is equal to the force exerted over a given ______________________________.
FORCE vs. PRESSURE: Pressure is measured in Force per Area.
Example: a 100 pound woman with high heel shoes; Heel dimensions are:
a) 1 cm x 1 cm, b) 0.5 cm x 0.5 cm, c) 2 cm x 3 cm;
Find the pressure exerted by the different dimensions of each heel:
a) 1 cm x 1 cm: 
b) 0.5 cm x 0.5 cm: 
c) 2 cm x 3 cm: 
GAS PRESSURE:
Force is measured for a given unit of area.
Pressure is determined by the Number of ______________________________ by Molecules per Unit Area.
More collisions per given area = Higher (more) pressure
MEASURING GAS PRESSURE:
When working with gases, you need to know how much gas you have, but measuring the mass of a gas can be difficult.
Measuring the volume is much easier - if you know the ______________________________ and ______________________________ of a given quantity of a gas (which we will soon do...)
- Car Tires: Measured as Pounds per square inch
- Air Pressure is measured in millimeters of Mercury ( Hg ). 1 mm Hg = 1 torr.
S.I. Unit for Air Pressure is a Pascal (Pa). Since a Pascal is a very small unit of pressure we often use ______________________________ (kPa).
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| Pascal (Pa) | 1 kPa = 1000 Pa |
| Atmosphere (atm) | 1 kPa = 0.009869 atm |
| Torr | 1 kPa = 7.501 torr |
| Millimeters of Mercury (mm Hg) | 1 kPa = 7.501 mm Hg |
A True Vacuum: 0 kPa ( no gas molecules are present )
1 Atmosphere (atm) = 101.325 kPa [ Standard Pressure at Sea Level ]
Practice Problems:
1. When reading a classroom barometer, you find that the mercury has risen to a height of 72.9 cm. What is the value expressed in kilopascals and atmospheres?
a) 72.9 cm Hg = ? kPa
b) 533 mm Hg = ? atm
According to kinetic theory alone, it should be possible to lower the temperature at which all molecular motion should cease is known as Absolute Zero. Absolute Zero is equal to -273.150C (this value is usually rounded off to -2730C).
To make a temperature scale based on absolute zero, scientists have agreed on a system known as the Kelvin Scale.
The zero point of the Kelvin scale is Absolute Zero. The division, or degrees, are the same as those of the ___________________________ scale. Therefore,
Practice Problems:
2. Convert the temperature to the Celsius scale
a) 333 K
b) 173 K
3. Convert the temperature to the Kelvin scale
a) 1000C
b) 3760C
HOMEWORK PROBLEMS:
Convert the following Celsius temperatures to Kelvin temperatures:
1a. 230C
1b. -900C
1c. 250C
Convert the following Kelvin temperatures to Celsius temperatures:
1d. 86 K
1e. 191 K
1f. 894 K
1g. Change the pressure of 74.5 cm Hg into atmospheres.
1h. What is the pressure of 97.5 kPa in atmospheres.
1i. Convert 750. torr into atmospheres.
CLOSED-ENDED MANOMETER:
A device similar to a barometer can be used to measure the pressure of gases other than the atmosphere.
The U-Tube containing mercury is connected to a flask containing the gas in question.
Gas molecules moving within the flask rebound on the ______________________________ of the flask and the ______________________________ of the mercury - as the molecules push against the mercury, they exert a force that supports the column of mercury to a specific height.
The difference in height of the mercury in the two sides of the U-Tube can be used to find the gas pressure.
PARTIAL PRESSURE ( DALTON'S LAW OF PARTIAL PRESSURE ):
Because gases are widely ______________________________ under ordinary pressures. It is not unusual for ______________________________ to occupy the same volume.
However, as each gas is introduced into a fixed volume. The pressure must rise since more gas particles means more ______________________________ with the walls of the container.
It is logical to assume (and confirmed in the lab) that the number of gas particles is directly proportional to a part of the total pressure exerted by that gas.
Therefore, the individual pressure of each gas is called the ______________________________.
The fact that all of the "Partial Pressures" add up to the Total Pressure is known as Dalton's Law of Partial Pressures.
The method used to collect some gases without mixing the newly created gas with other gases - Water displacement.
EXAMPLE:
What is the pressure of hydrogen gas collected over water at 240C? The water levels inside and outside the collecting bottle are equal at the end of the experiment. The atmospheric pressure is 94.4 kPa. At this temperature, the vapor pressure of water is 3.0 kPa.
PRACTICE PROBLEMS:
1. You collect a sample of oxygen gas by the water-displacement method described in the example. If the atmospheric pressure is 99.4 kPa and the water-vapor pressure is 4.5 kPa, then what is the partial pressure of the oxygen gas. (answer: 94.9 kPa)
2. A mixture of 84.06 grams of nitrogen gas and 83.80 grams of krypton gas has a total pressure of 280. kPa. What is the partial pressure of each gas? ( answer: N2 = 210. kPa, Kr = 70.0 kPa )
HOMEWORK PROBLEMS:
2a. Due to gravity, does ( is it possible for ) a 50-kilogram woman exert more (or less) pressure on the ground than a 70-kilogram man? Explain.
2b. IS IT POSSIBLE for a 50-kilogram woman to exert greater pressure on the ground than a 70-kilogram man? Explain.
2c. A gas is put into a closed-end manometer. The mercury that separates the flask from the vacuum is found to be 165 mm higher on the side with the vacuum. a) What is the pressure of the gas in torr? b) what is the pressure of the gas in kiloPascals?
2d. A mixture of 20% hydrogen gas and 80% nitrogen gas, by volume, has a total pressure of 30 kPa. What is the partial pressure of each gas?
2e. A mixture of 28 grams of Nitrogen and 64 grams of Oxygen gas has a total pressure of 300.0 kPa. What is the partial pressure of each gas? (hint: WHENEVER, you "see" grams of a gas, automatically think: "I need MOLES !!!")
CHARLES'S LAW: THE TEMPERATURE-VOLUME RELATIONSHIP:
Jacques Charles is given credit for correctly describing a fundamental relationship between the volume of a gas and its temperature.
- Increase Temperature will ______________________________ the Volume.
- Decrease Temperature will ______________________________ the Volume.
The temperature MUST be expressed in the units of Kelvin when doing "GAS" calculations with temperature.
KELVIN SCALE: . . . . . K = 0C + 273
EXPRESSING A DIRECT PROPORTION:
When the pressure and amount (volume) of a gas are held constant, the volume of the gas is ______________________________ to its kelvin temperature.
For any sample of gas, a constant may be calculated for the V : T (Volume to Temperature) ratio. This constant can be used to find the volume of that particular sample at any other temperature.
This constant was used to ______________________________ the temperature of Absolute Zero (discussed during the last section.)
* * * Demo: "The Fountain !!!"
* * * Demo: "The Can Crush !!!"
After viewing the demonstrations... Try to explain the photos below - here is the background information:
I was told the interior of the tank car was washed out & cleaned with a steam-cleaner. Then all the outlet (pressure) valves were shut and the tank car was sealed. All the workers went home for the evening and when they returned, this is what they found. The shell on this tanker car is a half an inch thick (steel).
PRACTICE PROBLEMS:
6. A sample of gas occupies a volume of 100.0 cm3 at a temperature of 200.0 K. What volume would this gas occupy at a temperature of 150.0 K? The pressure and amount of gas do not change.
CLICK HERE TO VIEW A STEP BY STEP DEMONSTRATION FOR SOLVING FOR THIS QUESTION
7. If a sample of gas occupies a volume of 0.325 liters at a temperature of 30 0C, what temperature will the gas be if the volume changed to 200 mL? The pressure and amount of gas do not change.
HOMEWORK PROBLEMS:
3a. A sample of air with a volume of 2.25 liters is at a temperature of 298 K. If the temperature is increased to 373 K without changing the pressure, what is the new volume (in milliliters) for this sample of air?
3b. As the temperature of a sample of nitrogen gas increases from 273 K, the volume of the sample changes from 275 cm3 to 525 cm3. Assuming that the pressure does not change, what is the final temperature of this gas?
BOYLE'S LAW: THE PRESSURE-VOLUME RELATIONSHIP:
In 1660, Robert Boyle, a British scientist, performed an experiment that measured the volume of a gas as the pressure on the gas changed.
A calibrated syringe is filled with air, and the volume is read. A weight is placed on top of the plunger which increases the pressure on the air in the syringe. As the temperature is held constant, even more weight is added to the plunger, the volume is measured for several different pressures.
As in Charles's Law: volume increases with increasing temperature. In the case of pressure and volume ( Boyle's Law ), the relationship is an inverse proportionality: Volume ______________________________ with ______________________________ pressure.
Mathematically, an inverse proportionality may be expressed as: PV = constant (when temperature and moles are held constant)
Boyle's Law states: when the temperature and the number of moles of a sample of gas are held constant, its volume is inversely proportional to the pressure applied.
PRACTICE PROBLEMS:
8. A sample of gas has a volume of 100.0 cm3 when the pressure is at 150.0 kPa. What is the volume of this gas when the pressure is increased to 200.0 kPa? The temperature and amount of gas remain constant.
CLICK HERE TO VIEW A STEP BY STEP DEMONSTRATION FOR SOLVING FOR THIS QUESTION
9. A sample of gas has a volume of 330 milliliters when the pressure is 760 mm Hg, What is the final pressure (in atmospheres of pressure) when the volume is changed to 5.50 liters?
HOMEWORK PROBLEMS:
4a. If a sample of gas has a volume of 25 liters when the pressure is 100.0 kPa, what is its volume when the pressure falls to 75.0 kPa, providing that the temperature and amount of gas do not change?
4b. What pressure is required to reduce the volume of a sample of air from 1.00 liter to 0.250 liter? The original pressure on the sample is 98.0 kPa; the amount and temperature of the sample remain fixed.
AVOGADRO'S PRINCIPLE:
Avogadro recognized the importance of the Law of Combining Volumes, and wrote a paper that summarized Gay-Lussac's data - Equal volumes of gases (at the same temperature and pressure) contain equal numbers of particles - This is known as Avogadro's principle.
Therefore, if the number of particles increases (at the same temperature and pressure) the volume will increase.
| DALTON'S LAW | PT = P1 + P2 + P3 + . . . |
| CHARLES'S LAW |
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| BOYLE'S LAW |
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| AVOGADRO'S PRINCIPLE |
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PRACTICE PROBLEM:
10. A sample of hydrogen gas has a volume of 630.0 cm3 when the sample contains 3.00 moles of hydrogen. What is the volume of this gas ( in cm3 ) when the sample reduced the number of moles to 1.75? The temperature and pressure of the gas remain constant.
CLICK HERE TO VIEW A STEP BY STEP DEMONSTRATION FOR SOLVING FOR THIS QUESTION
HOMEWORK QUESTIONS: (these questions are NOT specific to just Avogadro's principle)
5a. How can the relationship between gas pressure and volume be described? Which law would you use?
5b. How can the relationship between gas temperature and volume be described? Which law would you use?
5c. If a sample of gas has a volume of 3.00 liters at a temperature of 52.30C, what will the volume be if the temperature of the gas system is lowered to -27.00C? Assume the pressure and number of moles are held constant.
5d. The pressure of a 5.71 liter sample of neon gas is 23.4 kPa. Calculate the new pressure when the volume becomes 3.40 liters. Assume that the temperature and amount of gas remain unchanged.
5e. A balloon has an initial volume for helium gas at 34.3 liters and an initial mass of 6.076 grams. Calculate the number of moles for helium gas remaining when the volume of the gas is changed to 575 milliliters.