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The Behavior ofGases
The kinetic theory of gases describes a gas ● as a large number of submicroscopic particles, ● all of which are in constant, rapid & random motion. ● The randomness arises from the particles' many
collisions with each other and with the walls of the container.
Factors Describing a Gas
1. Four Variables are used to describe a gas:
a. Pressure (P) in kilopascals(kPa),atmosphere(atm), milimeterMercury(mmHg), Pounds per Square Inch(psi)
b. Volume (V) in liters (L)c. Temperature (T) in Kelvin (K)d. Number of moles (n) – amount of
gas particles
1) PressurePressure of a gas = force per unit area that gas particles exert on the walls of their container. Pressure= Force
Area– # of Gas particles Pressure
– Ex: Inflating a ball adds more gas molecules which increases the pressure in the ball
2) Volume
Volume Pressure
Ex: piston in car engine, forces gas in cylinder to reduce in volume, creating more pressure.
3) TemperatureRemember…as temperature increases kinetic energy increases…temperature pressure
Ex: Heat up a propane tank, gas molecules will move faster and faster… and finally blow up
4. Amount of gas • Gas particles in a
container are in constant motion because of the negligible space between them.
• The amount of particles will influence the amount of pressure against each other & against the container.
Gas Laws
A.Boyle’s Law (Pressure vs. Volume)
1. Boyle’s Law = the pressure and volume of a gas are inversely proportional at a constant temperature.2.Pressure Volume3..Calculation: P1V1 = P2V2
4.DRAW!
Calculating Boyle’s Law1.Calculation:
P1V1 = P2V2 (P= pressure, V = volume)2.Ex: The volume of a scuba tank is 10.0 L. It contains 290 atm of gas pressure in it. What would be the volume of gas at 2.40 atm?
P1 = 290 atm P2 = 2.40 atmV1 = 10.0 L V2 = ?290 atm(10.0L) = 2.40atm(V2)
V2 = 1208 L
B.Charles’ Law(Temperature vs. Volume)
• 1.Charles’ Law = at constant pressure, the volume of a gas is directly proportional to temperature (K).2.Volume Temperature3.Ex: if you put a balloon in the freezer, it will shrink in size, take it out and it will expand!
4. Calculation: V1 = V2 T1 T2
5. DRAW!
Calculating Charles’ Law
1.Calculation:– V1 = V2 V = volume, T = temperature (K) T1 T22.Ex: A balloon is filled with 3.0 L of helium at 22°C and 760 mm Hg. It is then placed outdoors at 31°C, what will the new volume be? (convert °C to K first!) K= 273+31=304 K= 273+22=295
3.0 L = V2295 K 304K V2 = 3.1 L
C.Gay-Lussac’s Law(Temperature vs. Pressure)
1. Gay-Lussac’s Law = the pressure of a gas is directly proportional to the temperature, in Kelvin, at a constant volume.2.Pressure Temperature3.Calculation:
P1 = P2T1 T2
4. DRAW!
Calculating Gay-Lussac’s Law1.Calculation:
P1 = P2 P = pressure, T = temperature (K) T1 T22.Ex: If a can at a of pressure is 103 kPa at 25°C is thrown into a fire, what will the resulting pressure be at 928°C? K= 273+25= 298 103 kPa = _P2_
298 K 1201 K P2 = 415 kPa
D.) Combined Gas Law Combines the three gas laws: Boyle's Law, Charles' Law, and Gay-Lussac's Law. 1.Combined Gas Law: P1V1 = P2V2
T1 T22.Ex: A 2.7 L sample of nitrogen is at 121kPa and 288K. If the pressure increases to 202kPa and the temp. rises to 303K, what is the new volume?
121kPa(2.7L) = 202kPa(V2) 288K 303K
V2 = 1.7L (
STPStandard Temperature & PressureUsed when performing calculations on gases. • The standard temperature is
273 K (0°C or 32°F) &
• Standard pressure is 1 atm.
Converting from 0°C(Celcius) to K(Kelvin)
K= 273 + °CEx: Given temp. is 25°C.K=273+25= 298
(Stop here)
Gas Law OverviewGas Law Proportion Variable Constant Calculation Graph
Boyle
Charles
Gay-Lussac
Combined
Gas Law OverviewGas Law Proportion Variable Constant Formula Graph
Boyle Inverse Pressure, volume
Temp P1V1=P2V2
Charles Direct Volume, temp
Pressure V1 = V2 T1 T2
Gay-Lussac Direct Pressure, temp
Volume P1 = P2 T1 T2
Combined Pressure, temp,
volume
P1V1 = P2V2 T1 T2
Gas Law OverviewGas Law Proportion Variable Constant Formula
Boyle Inverse Pressure, volume
Temp P1V1=P2V2
Charles Direct Volume, temp
Pressure V1 = V2 T1 T2
Gay-Lussac Direct Pressure, temp
Volume P1 = P2T1 T2
Combined Pressure, temp,
volume
P1V1 = P2V2 T1 T2
Ideal Gases
E.Ideal Gas Law Calculation
• Ideal Gas Constant (R) = 8.31 L•kPa/K•mol• 1. Ideal Gas Law = PV = nRT; n = # of
moles2.Ex: You fill a rigid cylinder will a volume of 20.0L with N2 gas to a pressure of 2.00x104 kPa at 28°C. How many moles of N2 gas does the cylinder contain?2.00x104 kPa x 20.0L = n x 8.31 L•kPa/K•mol x 301K
n = 160 mol N2
Gas Molecules:Mixtures + Movements
Avogadro’s Hypothesis• Avogadro’s Hypothesis = equal volumes of gases
at the same temperature and pressure contain equal numbers of particles.
• Thus, at STP,1 mol = 6.02x1023 atoms, of any gas regardless of size, occupies a volume of 22.4 L
(Standard Temp is 0 0C. & Pressure is 1atm, 70mmHg,...)
At STP!!