gas laws

Gas Laws.notebook
May 05, 2014
Gas Laws
• At constant temperature, all gases behave the same when compressed
• As increasing pressure is applied to a gas in a closed container, the volume of the gas decreases
.
• The product of pressure and volume is always constant
P V = k
P1V1 = P2V2
Why does
the plunger
bounce back?
Use the terms:
­particles
­collisions
­Walls of
container
­plunger
The gas in a balloon has a volume of 7.5 L at 100 kPa. The balloon is released into the atmosphere, and the gas in it expands to a volume of 11 L. Assuming a constant temperature, what is the pressure on the balloon at the new volume?
•
•
•
•
List what you know
Write the formula
Solve for the variable you need
Plug 'n chug
= 70 kPa
70 kPa
P1V1 = P2V2
1 atm = 101.325 kpa
= Standard Pressure
(at sea level)
Graph
• Jacques Charles discovered that the volume of a gas is directly proportional to its temperature (Kelvin scale)
• At constant pressure, the volume of a gas divided by its absolute temperature is constant.
V
T
= k V
k =
T
V1 V2
=
T 1 T2
Why does the
plunger go up as
the temperature
increases?
_T,_KE,_V, _Collisions, _Pressure
1
Gas Laws.notebook
May 05, 2014
A sample of gas occupies 24 m3 at 175.0 K. What volume would the gas occupy at 400.0 K?
•
•
•
•
List what you know
Write the formula
Solve for the variable you need
Plug 'n chug
55m3
Answer
water
freezes
K
o
C
o
1. A syringe has a sample of gas with a volume of 3.95 mL
at a pressure of 1.00 atm. What is the pressure of the gas
in the syringe if the volume is changed to 2.53 mL?
F
Write a formula that will convert oC to K
? K ? = ? oC ?
o
C + 273 = K
Answer
1.56 atm
2. A partially inflated weather balloon has a volume of 1.50 x 103 L at 98.8 kPa of pressure. What is the volume of the balloon when
= 3,360 L
it is released to a height where the pressure is 44.1 kPa?
3
3.36 x 10 L
3. A sample of gas has a volume of 852 mL at 198 K. What volume does the gas occupy at 293 K?
1260mL
4. A sample of gas has a volume of 234.9 L at a temperature of 23oC. Do p.440#1­2 What temperature is necessary to have a volume of 200.0 L?
252 K or ­21oC
Do p. 436#1­4. Show work
Do p.440#1­2
1. A syringe has a sample of gas with a volume of 3.95 mL
at a pressure of 1.00 atm. What is the pressure of the gas
in the syringe if the volume is changed to 2.53 mL?
•
•
•
•
2. A partially inflated weather balloon has a volume of 1.50 x 103 L at 98.8 kPa of pressure. What is the volume of the balloon when
it is released to a height where the pressure is 44.1 kPa?
List what you know
Write the formula
Solve for the variable you need
Plug 'n chug
3. A sample of gas has a volume of 852 mL at 198 K. What volume does the gas occupy at 293 K?
A sample of gas has a volume of 234.9 L at a temperature of 23oC. What temperature is necessary to have a volume of 200.0 L?
252 K or ­21oC
o
C + 273 = K
2
Gas Laws.notebook
May 05, 2014
Uncle Larry tells his nephews to never throw paint cans into the fire. "Why?" they ask. "I'll show you." Uncle Larry builds a bonfire. "Get ready to run," he warns.
• Gay­Lussac discovered that the pressure of a gas is directly proportional to its temperature (Kelvin scale)
• At constant volume, the pressure of a gas divided by its absolute temperature is constant. P
T
= k
P
k =
T
P1 P2
=
T 1 T2
The can is rated to 9.00 atm before bursting. The temperature inside the can reaches 414oC after being in the fire for 17 sec. The temperature before being thrown recklessly was 72 oC., with a pressure of 7.00 atm. Will it burst? Show work.
PV
T
Peter
H/W: p. 449 #
Tom
Uncle Larry tells his nephews to never throw paint cans into the fire. "Why?" they ask. "I'll show you." Uncle Larry builds a bonfire. "Get ready to run," he warns.
p. 449 # I­4
The can is rated to 9.00 atm before bursting. The temperature inside the can reaches 414oC after being in the fire for 17 sec. The temperature before being thrown recklessly was 72 oC., with a pressure of 7.00 atm. Will it burst? Show work.
Boyle's Law + Charles' Law + Gay­Lussac's Law = Combined Gas Law
P1V1 P2V2
=
T2
T1
P V
T
H/W: p
3
Gas Laws.notebook
May 05, 2014
A weather balloon containing helium with a volume of 410.0 L rises in the atmosphere and is cooled from 27oC to ­27oC. The pressure on the gas is reduced from 110.0 kPa to 25.0 kPa. What is the volume of the gas at the lower temperature and pressure?
H/W:
p.436#1­4
p.440#1
p.449#1­4
1 atm = 101,325 Pa = 101.325 kPa
1 atm = 760 mm Hg
A weather balloon containing helium with a volume of 350.0 L rises in the atmosphere and is cooled from 24oC to ­31oC, and increases in size to 989 L. The pressure on the gas changes from 115.0 kPa to what new pressure?
STP
= STANDARD TEMPERATURE
AND PRESSURE
273K
P
STP
= STANDARD TEMPERATURE
AND PRESSURE
1 atm = 101,325 Pa = 101.325 kPa
1 atm = 760 mm Hg
4
Gas Laws.notebook
May 05, 2014
1. A gas has a volume of 18.5 L at 85.5 kPa and 296 K. What is the volume of the gas at STP?
1 atm = 101,325 Pa = 101.325 kPa
1 atm = 760 mm Hg
2. A balloon full of helium gas has a volume of 132 L at 99.7 kPa and 30oC. What temperature is required for the balloon to have a volume of 176 L at a pressure of 77.6 kPa?
3. A plastic bag is inflated to a volume of 3.89 L at 1.095 atm and 23oC. If the volume drops to 3.05 L at a temperature of ­4oC, what is the new pressure?
STP
= STANDARD TEMPERATURE
AND PRESSURE
273K
1. A gas has a volume of 18.5 L at 85.5 kPa and 296 K. What is the volume of the gas at STP?
3. A plastic bag is inflated to a volume of 3.89 L at 1.095 atm and 23oC. If the volume drops to 3.05 L at a temperature of ­4oC. What is the new pressure?
2. A balloon full of helium gas has a volume of 132 L at 99.7 kPa and 30oC. What temperature is required for the balloon to have a volume of 176 L at a pressure of 77.6 kPa?
p.449#4
A sample of carbon dioxide gas occupies 45m3 at 750 K and 500. kPa. What is the volume of this gas at STP?
V
5
Gas Laws.notebook
May 05, 2014
A sample of carbon dioxide with a mass of 0.250 g is placed in a 350.0 ml container at 400.0 K. What is the pressure exerted Where:
n = number of moles
by the gas?
R = (8.314 L x kPa) / (mol x K)
To solve for P, V, T, or the number of moles:
P V= n R T
R = (0.0821 L x atm) / (mol x K)
1 atm = 101.325 kPa
Where:
n = number of moles
R = (8.314 L x kPa) / (mol x K)
R = (0.0821 L x atm) / (mol x K)
1 atm = 101.325 kPa
­Intro Gas La
Does he look like a pvnrt?
H/W Tues.
p.436 pp#1­4; p.440#1­2; 449#1­4
Wed.
p.451#5­9
Thurs.
p.462 #27,29,30,44,46
1) How many moles of a gas are in a balloon that has a volume of 15.9 L at a pressure of 149 kPa and a temperature of 28oC?
4/10/14
27) A flexible container with 2.0 L of methyl bromide has
an internal pressure of 506.6 kPa at 25oC. What is the
volume of methyl bromide at standard pressure if the
temperature remains constant?
2) What mass of ammonia, NH3, is required to fill a 14.88 L bottle to a pressure of 199 kPa at 25oC?
4/22/13
Where:
n = number of moles
R = (8.314 L x kPa) / (mol x K)
R = (0.0821 L x atm) / (mol x K)
1 atm = 101.325 kPa
29) A child receives a balloon filled with 2.30 L of helium from a vendor at an amusement park, where the temperature is 311 K. What will the volume of the balloon be when the child brings the balloon home to an air­
conditioned house at 295K?
6
Gas Laws.notebook
May 05, 2014
Hydrogen peroxide (H2O2) decomposes to water and oxygen (O2) gas. H2O2(l) H2O(l) + O2(g)
4/11/14
• Write the balanced equation for the reaction.
• After hydrogen peroxide reacts with a catalyst, 36.7 mL of oxygen gas are collected in a room at 22° C and 1.01 atm. Calculate the number of moles of gas that were produced.
• Calculate the mass of the hydrogen peroxide that must have reacted.
A 283.3­g sample of X2(g) has a volume of 30 L at 3.2 atm and 27 °C. What is element X? PV = nRT
PV = n =
RT = moles X2 Hydrogen peroxide (H2O2) decomposes to water and oxygen (O2) gas. H2O2(l) H2O(l) + O2(g)
4/11/14
• Write the balanced equation for the reaction.
• After hydrogen peroxide reacts with a catalyst, 36.7 mL of oxygen gas are collected in a room at 22° C and 1.01 atm. Calculate the number of moles of gas that were produced.
• Calculate the mass of the hydrogen peroxide that must have reacted.
29) A child receives a balloon filled with 2.30 L of helium from a vendor at an amusement park, where the temperature is 311 K. What will the volume of the balloon be when the child brings the balloon home to an air­
conditioned house at 295K?
283.3g X2 = ? mol X2 X = ? g = ? mol X Check the periodic table...
What mass of ammonia, NH3, is required to fill a 14.88 L bottle to a pressure of 199 kPa at 25oC?
H/W ­Intro Gas Laws w/s
­p.451 #5­9
A) A sample of gas has a volume of 852 mL at 189 K. What volume does the gas occupy at 293 K?
2
V = 1320 mL or 1.32 L
n = 0.947 mol
T2 = 252 K, or ­2
B) How many moles of gas are in a balloon that has a volume of 15.9L at a pressure of 149kPa and a temperature of 28 C?
B) A sample of gas has a volume of 200.0L?
CA Science Standards: Chemistry
3. e. Students know how to calculate the masses of reactants and products in a chemical reaction from the mass of one of the reactants or products and
the relevant atomic masses. 4. The kinetic molecular theory describes the motion of atoms and molecules and explains the properties of gases. As a basis for understanding this concept: a. Students know the random motion of molecules and their collisions with a surface create the observable pressure on that surface.
4. c. Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases. H/W ­ p.4
7
Gas Laws.notebook
May 05, 2014
How many liters of hydrogen gas can be produced
4/22/14
at 300.0 K and 104 kPa pressure if 20.0g sodium
metal is reacted with water according to the following equation?
How many liters of hydrogen gas can be produced
4/22/14
at 300.0 K and 104 kPa pressure if 20.0g sodium
metal is reacted with water according to the following equation?
Na(s) + H2O(l) ­­> NaOH(aq) + H2(g)
hints:
• balance equation
• choose which gas law to use
• solve for volume
• convert g to moles
• moles Na moles H2 • plug 'n chug
1) Calculate the value of the ideal gas constant, R, if exactly one mole of an ideal gas occupies a volume of 22.414 liters at 0.00˚C and 755 mm Hg 4/23/14
atmosphere pressure. Give R in L kPa/mol K.
(1 atm = 760 mm Hg = 101.325 kPa)
Na(s) + H2O(l) ­­> NaOH(aq) + H2(g)
hints:
• balance equation
• choose gas law to use
• solve for volume
• convert g to moles
• moles Na moles H2 • plug 'n chug
1) Calculate the value of the ideal gas constant, R, if exactly one mole of an ideal gas occupies a volume of 22.414 liters at 0.00˚C and 755 mm Hg atmosphere pressure. Give R in L kPa/mol K.
(1 atm = 760 mm Hg = 101.325 kPa)
Algebra:
2) Calculate Percent Error:
(not NOaH)
R =
Plug 'n Chug: R = Answer: R =
2) Calculate Percent Error:
Calculate the mass of carbon dioxide that would be needed to fill a 2.00 L bottle at 22.00 C and 757 mm Hg.
4/24/14
(1 atm = 760 mm Hg = 101.325 kPa)
1) Calculate the mass of carbon dioxide that would be needed to fill a 2.00 L bottle at 22.00 C and 757 mm Hg.
4/24/14
(1 atm = 760 mm Hg = 101.325 kPa)
8
Gas Laws.notebook
May 05, 2014
Dalton's Law of Partial Pressures
Ice:
00C
Disappearing Toys: DRY ICE
The total pressure of a mixture of gases is equal to the sum
of the partial pressures of the individual gases:
Dry ice:
­78.50C (­109.30F)
CO2(s) CO2(g)
"Sublimation"
Try:
(1) Not getting frostbite!
(2) Air hockey on your desk
(3) Coin torture
(4) Bubbling witch's brew
(5) Misdemeanor (let Rongley do it instead!)
Ptotal = PA + PB + PC T, _ P
= PA = PB Liquid Nitrogen:
−196°C (−321°F or 77 K) = PC Each gas behaves as if the other gases are absent
Start: p.451#5­9 2. A 283.3­g sample of X2(g) has a volume of 30 L at 3.2 atm and 27 °C. What is element X?
Step 1: Convert °C to Kelvin
T = °C + 273
T = 27 + 273
T = 300. K
5) 1,100 kPa
6) 0.39 L N2
7) n=0.122 mol N2
D = ?
9) 1 psi = 6.89286 kPa
V2 = 275.7 L He
# ballons = ?
Step 3: Find mass of 1 mol of X2
4 mol X2 = 283.3 g
1 mol X2 = 70.8 g
Step 2: Solve Gas Law equation for n
n = PV
RT
n = (3.2 atm)(30 L)
(0.08 atm L/mol K)(300 K)
Step 4: Find mass of 1 mol of X
1 mol X2 = 70.8 g
1 mol X = 35.4 g
Step 5: Identify the element with molecular mass 35.4 g
Chlorine has a molecular mass of 35.4 g
Answer: Element X is Chlorine
8) 5.3 x 10­3 mol SO2
9