Chapter 14 Notes KEY

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GASES & GAS LAWS
RELATIONSHIPS BETWEEN PRESSURE, VOLUME & TEMPERATURE OF A GAS
Pressure and Temperature	
	Temp. (K)
	Pressure (atm)
	100
	0.5
	200
	1.0
	400
	1.5
	800
	2.0
Type of relationship?
Direct proportion
Equation
 P1 = P2
 T1 T2
Practice problem:
If a gas exerts a pressure of 2.5 atm at 100°C, what pressure would it exert at 200°C?
2.5 atm = P2
373 K 473 K
P2 = 3.2 atm
Volume and Temperature
	Temp. (K)
	Volume (L)
	100
	
	200
	
	400
	
	800
	
Type of relationship?
Direct proportion
Equation
 V1 = V2
 T1 T2
Practice problem:
If a gas occupies 10.0 L at 50°C, what volume will it occupy at 150°C?
10 L = V2
323 K 423 K
V2 = 13.1 atm
Volume and Pressure
	Pressure (atm)
	Volume (L)
	1200
	
	600
	
	300
	
	150
	
Type of relationship?
Inverse proportion
Equation
P1V1 = P2V2
Practice problem:
A gas occupies a volume of 7.5 L at 550 mmHg. What volume will it occupy at 850 mmHg?
7.5 L (550mmHg) = 850 L (V2)
4.85 L = V2
DEMONONSTRATIONS:
peep in vacuum tube
balloon in vacuum tube
Combined Gas Law:
Equation:
P1V1 = P2V2
 T1 T2
Practice Problem:
If a gas occupies 5.0 L at 1.25 atm and 75°C, what volume will it occupy at 0.5 atm and 125°C ?
1.25atm(5 L) = 0.5atm (V2)
 348 K 398 K
 14.3L = V2
PRACTICE PROBLEMS
1. A gas occupies 450mL at 23C. Determine its volume at 75C if the pressure remains constant.
Do you expect volume to go up or down?
Formula:
			__529 mL_____
2. A gas in an expandable container has a pressure of 1.2atm when the volume is 10.0L. Determine its volume if the pressure is reduced to 0.85atm and the temperature remains constant.
Do you expect volume to go up or down?
Formula:
			__14.1 L_______
3. A gas exerts a pressure of 106kPa in a sealed, rigid container at 25C. At what temperature will it exert a pressure of 149kPa?
Do you expect temperature to go up or down?
Formula:
			___419 K_______
4. A gas exerts a pressure of 1.2atm in a 525mL container. Find the pressure of the same gas in a 2.5L container.
Do you expect pressure to go up or down?
Formula:
			_0.25 atm_______
5. The temperature of a gas sample at standard pressure is 25°C. Find its pressure if it is heated to 98°C.
 Do you expect volume to go up or down?
Formula:
			1.2 atm
6. A gas occupies 240mL at 23°C and 650mmHg. It is transferred to a 375mL container at 30°C. Find the pressure in the new container.
Formula:
			_425.8mmHg_______
7. A gas occupies 525mL at 30°C and 1.2 atm. What volume will it occupy at STP?
Formula:
			__568 mL_____
RELATIONSHIP BETWEEN MOLES, VOLUME, TEMPERATURE AND PRESSURE OF GASES
moles and pressure – direct proportion
moles and volume – direct proportion
moles and temperature – inverse proportion
Ideal Gas Law: equal volumes of gas, at same temp and pressure, contain the same number of particles (moles)
Equation: PV = nRT
“R” – ideal gas constant 0.0821 atm L/mol K, 62.4 mmHg L/mol K, 8.31kPa L/mol K
Volume must be in L
Pressure must be in atm
Temperature must be in K
Moles if given grams, convert to moles using molar mass
Practice Problem:
Determine the volume of 0.54moles of hydrogen gas at 23ºC and 550 mmHg.
(0.72 atm) V = (0.54 moles) (0.0821) (296 K)
V = 18.2 L�
MOVEMENT OF GAS PARTICLES: MAXWELL-BOLTZMAN DISTRIBUTION
a. If both samples contain the same gas, which sample is at a higher temperature? B (higher speed = higher temp)
b. If both samples are at the same temperature, which gas has the higher molar mass? A (lower speed, lower temp)
PARTICLE SPEED AND MASS: GRAHAM’S LAW
Temperature is the average kinetic energy of particles in a sample. Kinetic energy is related to particle speed and mass. If two particles are at the same temperature, the lighter one will have the higher speed.
If a sample of hydrogen and a sample of nitrogen are each is a sealed 1.0L container at the same temperature and the same pressure:
	
 which sample contains more molecules? __same___________________
 which sample is heavier? N2
	c. which sample has the greater average kinetic energy? _same________
	d. in which sample are the particles moving faster? __H2___________
	
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DALTON’S LAW AND PARTIAL PRESSURE OF GASSES
DALTON’S LAW: the total pressure of a system is equal to the sum of the pressures of all the gases in the system
PT = P1 + P2 + Pn…
a. The container above contains 4.0moles of hydrogen, 3.0 moles of nitrogen and 2.0 moles of carbon dioxide. The total pressure of the container is 450mmHg.
Determine the partial pressure of each gas.
	PH2 = 4 moles H2	x 450 mmHg	=	200 mmHg
		9 moles total
	PN2 = 3 moles N2	x 450 mmHg	=	150 mmHg
		9 moles total
	PCO2= 2 moles CO2	x 450 mmHg	=	100 mmHg
		9 moles total
b. The pressure of nitrogen in the classroom is approximately 0.82atm. The pressure of oxygen in the room is approximately 0.20atm and the pressure of water vapor in the room is approximately 0.02atm.
	a. The total pressure in the room is 1.10atm. Assuming carbon dioxide is the only other gas present, find the pressure of carbon dioxide in the room.
		1.10 atm = 0.82 atm + 0.2 atm + 0.02 atm + PCO2
		0.06 atm = PCO2
	b. Find the number of moles of oxygen in the room if the room holds 8500 moles of air.
			0.02 atm O2	=	 x moles O2
			1.1 atm total		8500 moles total
				154.55 atm = moles O2
COLLECTING GASSES OVER WATER.
A gas is collected by water displacement in a 250mL flask at 30ºC and a barometric pressure of 95.00kPa. The vapor pressure of water at 30ºC is 31.82kPa.
Determine the pressure of the dry gas in the flask.
Patm = PH2O + Pgas
95.00 kPa = 31.82 kPa + Pgas
63.18 kPa = Pgas
HOMEWORK: MIXED GAS LAWS			Name: ________________________
SHOW ALL WORK FOR ALL PROBLEMS
1.0 atm = 760 mmHg = 101.3 kPa		And 		0C = 273 K
Change the following units:	
359 kPa = ___3.5______ atm				10C = _283_______ K
			
				
6.2 atm = _4712_______ mmHg				10K = _-263______ C
FOR EACH PROBLEM, WRITE OUT THE FORMUA YOU ARE USING. SHOW THE SUBSTITUTION AND BOX YOUR ANSWER!
1. The gas in a sealed can is at a pressure of 3.00 atm at 25C. A warning on the can tells the user not to store the can in a place where the temperature will exceed 52C. What would the gas pressure in the can be at 52C?
			P1	=	P2
			T1		T2
			 3 	=	 P2 
			298		325
			 3.27 atm = P2
2. A sample of hydrogen exerts a pressure of 0.329 atm at 47C. The gas is heated 77C at constant volume. What will its new pressure be?
			P1	=	P2
			T1		T2
			0.329 	=	 P2 
			 320		350
			 0.36 atm = P2
3. A sample of neon gas occupies a volume of 752 mL at 25C. What volume will the gas occupy at standard temperature if the pressure remains constant?
			V1	=	V2
			T1		T2
			 752 	=	 P2 
			 298		273
			 688.9 mL = V2
4. A sample of oxygen gas has a volume of 150 mL when its pressure is 440 mmHg. If the pressure is increased to standard pressure and the temperature remains constant, what will the new gas volume be?
			P1V1 = P2V2
			440 (150) = 760 (V2)
			86.6 mL = V2
5. Ralph had a helium balloon with a volume of 4.88 liters at 150 kPa of pressure. If the volume is changed to 3.15 liters, what would be the new pressure in atm?P1V1 = P2V2
			150 (4.88) = P2 (3.15)
			232.4 kPa= P2
232.4 kPa	1 atm		= 2.29 atm
		101.3 kPa
6. 5.36 liters of nitrogen gas are at -25C and 733 mm Hg. What would be the volume at 128C and 1.5atm?
			P1V1	=	P2V2
			 T1		 T2
			 5.36 (733) 	=	 1140 (V2) 
			 248			 401
			 5.57 L = V2
 COMBINED AND IDEAL PRACTICE PROBLEMS 
A gas has a pressure of 725mmHg in a 2.0L container at 33C. Determine its pressure in a 3.5L container at 100.0C.
P1V1	=	P2V2
			 T1		 T2
			 725mmHg (2.0 L) 	=	 P2 (3.5L) 
			 306K		 373K
			 505 mmHg= P2
A gas occupies 550mL at 98C and 890mmHg. Determine its volume at STP.
P1V1	=	P2V2
			 T1		 T2
			 550mL (890mmHg) 	=	 760 mmHg (V2) 
			 371K		 273 K
			 473.9mL= V2
Determine the temperature of a gas at 650mmHg in a 5.0L container if it occupies 875mL at 23C and 425mmHg.
P1V1	=	P2V2
			 T1		 T2
			 650 mmHg (5L) 	=	 425mmHg (0.875 L) 
			 T1		 296K
			 2586.9 K = T1
4. Determine the volume of 0.250moles of nitrogen gas at 33ºC and 655mmHg.
			PV = nRT
			0.86atm (V) = 0.25 moles (0.0821) (306K)
			V = 7.3 L
5. At what temperature will 0.75g of ammonia gas (NH3) occupy 750mL at a pressure of 105 kPa?
			PV = nRT
			105 kPa (0.75L) = 0.044 moles (8.31)(T)
			215.38 K = T
6. What mass of oxygen gas occupies 10.4L at 25°C and 1.5atm?
			PV = nRT
			1.5 atm (10.4 L) = n (0.0821) (298 K)
				0.63 moles = n
			0.63 moles	32 g O2 = 20.4 g O2
 1 mole	
IDEAL GAS LAW WORKSHEET 
) How many moles of a gas at 100°C does it take to fill a 1.00 L flask to a pressure of 1.50 atm? 
0.05 moles
2) A camping stove uses a 5.0 L propane tank that holds 3.0 kg of liquid C3H8. How large a container would be needed to hold the same amount of propane as a gas at 25°C and a pressure of 3.0 atm? 
556 L
3) What volume would be occupied by 100 g of oxygen gas at a pressure of 1.50 atm and a temperature of 25°C? 
50.97 L
4) On a warm day, an amusement park balloon is filled with 47.8 g of helium. The temperature is 33°C and the pressure in the balloon is 2.25 atm. Calculate the volume of the balloon. 
133.4 L
5) A ten-liter gas cylinder contains 380 g of nitrogen. What pressure, in kPa, is exerted by the nitrogen at 25°C? 
3360.4 kPa
6) A drum used to transport crude oil has a volume of 162 L. How many water molecules, as steam, are required to fill the drum at 1.00 atm and 100°C? (1 mole = 6.022 X 1023 molecules) 
3.18 x 1024 molecules H2O
7) How many moles of air are there in a 125 mL erlenmeyer flask if the pressure is 755 mm Hg and the temperature is 20°C? 
0.005 moles
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MIXED GAS LAW PROBLEMS, INCLUDING GRAHAM’S LAW AND DALTON’S LAW
1. A container holds 1 mole of nitrogen, 6 moles of methane and 5 moles of carbon dioxide. The total pressure in the container is 800mmHg. Find the pressure of each individual gas.
1 mole N2	x 800 mmHg	 6 moles CH4 x 800 mmHg	5 moles CO2 x 800 mmHg
12 moles			 12 moles				12 moles
	PN2 = _66.7 mmHg___	PCH4 = _400 mmHg____		PCO2 = _333.3 mmHg__
2. a) A student collects oxygen over water at 23°C. The atmospheric pressure is 755mmHg. The water vapor pressure at this temperature is 21.1mmHg. Find the pressure of the dry oxygen gas.
755 mmHg – 21.1 mmHg
											__733.9 mmHg___
***b. The student collected a total of 5.0moles of gas. Using your answer from part a, how many moles of oxygen did he collect?
733.9 mmHg = x moles
755 mmHg 5 moles
											__4.86 moles____
3. Find the temperature of a gas sample that contains 54g of oxygen in a 32L container at 1.2atm.
PV = nRT
(1.2 atm) (32 L) = (1.6875 moles)(0.0821 atm L/mol K)(T)
											_277.2 K________
4. A gas exerts a pressure of 88kPa in a 3.0L container. The container expands to 4.5L. Assuming the temperature remains constant, what is the new pressure of the gas?
88 kPa		=	 P
3.0 L			4.5 L
											__58.67 kPa_____
5. A gas occupies 250mL at 60°C and 425mmHg. Determine its volume at STP.
425 mmHg (250 mL)	=	760 mmHg (V)
 333 K		 273 K
											__114.6 mL____
6. A student has a 500mL flask filled with NO2 at 1.2atm and 25°C. He fills a second 500mL flask with O2 at 1.2atm and 25°C. 
 Which flask is heavier? ___ NO2___________________
 Which flask has more molecules? __same____________
 Which flask has the higher average kinetic energy? __same______________
In which flask are the molecules moving faster? ___ O2________________
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REVIEW WORKSHEET
1. A gas occupies a volume of 6.25 liters at 25.0C. What volume would it occupy at –25.0C?
5.2 L
2. If a gas occupies a volume of 3.75 liters and exerts a pressure of 925 mm Hg at 95.0C, what pressure would it exert at 75.0C and in a volume of 1.90 liters?
1,726.4 mmHg
3. What volume will 0.65 moles of xenon occupy at 895 mm Hg and 00.0C? 
12.3 L
4. If a gas occupies a volume of 125 ml at a pressure of 0.415 atm, what pressure will the gas exert in a 79.0 ml container? 
0.66atm
5. What mass of chlorine gas (F2) will occupy 1250 ml and exert a pressure of 2100 mm Hg at 100.0C?
4.18 g F2
6. What volume will 1.85 moles of xenon occupy at 1025 mm Hg and 100.0C? 
3.88 L
7. If a gas occupies a volume of 75.0 ml at a pressure of 3.45 atm, what volume will the gas occupy at 0.975 atm? 
265.4 mL
8. What mass of chlorine gas (Cl2) will occupy 2500 ml and exert a pressure of 625 mm Hg at 50.0C? 
5.6 g Cl2
9. A container holds 2.5moles of nitrogen and 5.5 moles of helium at STP. The total pressure of the container is 600mmHg. Find the pressure of the helium.
5.5 moles He	=	 PHe				PHe	= 412.5 mmHg
8 moles total		600 mmHg total
 Which gas is moving faster, the helium or the nitrogen?
Helium (it is ligher)
H2 N2
 H2 CO2 H2
 N2
CO2		H2	N2	 
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