GASESGASESChemistry I Honors – Chapter 13Chemistry I Honors – Chapter 13

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Importance of Gases Importance of Gases (don’t copy)(don’t copy)

Airbags fill with NAirbags fill with N22 gas in gas in an accident. an accident.

Gas is generated by the Gas is generated by the decompositiondecomposition of sodium of sodium azide, NaNazide, NaN33..

2 NaN2 NaN33--->2 Na + 3 N--->2 Na + 3 N222

General Properties of General Properties of GasesGases1. There is a lot of “free” 1. There is a lot of “free” space in a gas.space in a gas.2. Gases can be expanded 2. Gases can be expanded infinitely. (they will fill infinitely. (they will fill whatever “container” they are whatever “container” they are in.)in.)3. Gases fill containers 3. Gases fill containers uniformly and completely.uniformly and completely.4. Gases diffuse and mix 4. Gases diffuse and mix rapidly.rapidly.

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PressurePressurePressure is the amount of force Pressure is the amount of force per unit area.per unit area.

1.1.GasGas Pressure Pressure is the pressure is the pressure caused by particles of gas caused by particles of gas striking an object.striking an object.

2.2.Atmospheric Atmospheric pressure pressure is the is the pressure of the column of pressure of the column of atmosphere above you, atmosphere above you, pressing down on you. pressing down on you.

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Atmospheric Pressure

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(COPY)(COPY)• Measured with a Measured with a

BAROMETER BAROMETER (developed by (developed by Torricelli in 1643)Torricelli in 1643)

• Hg rises in tube until Hg rises in tube until force of Hg (UP) force of Hg (UP)

balances the force of balances the force of atmosphere (DOWN). atmosphere (DOWN).

(Just like a straw in a soft drink)(Just like a straw in a soft drink)

(DON’T COPY)(DON’T COPY)Q: Why is Hg so good for Q: Why is Hg so good for

use in barometer?use in barometer?A: A: If you tried to use water, it If you tried to use water, it

would rise about 34 feet high!would rise about 34 feet high!

Atmospheric. Atmospheric. PressurePressure

COPYCOPYThe column height (of the The column height (of the

barometer) measures barometer) measures atmospheric pressureatmospheric pressure

1 standard atmosphere 1 standard atmosphere (atm) *(atm) *

= = 101.3 kPa 101.3 kPa (SI unit is (SI unit is PASCAL)PASCAL)

= 760 mm Hg = 760 mm Hg

= 14.7 pounds/in= 14.7 pounds/in2 2 (psi)(psi) * *

These are the 2 units we will use most of the time

From the height of mercury in the barometer

Pressure Conversions

A. What is 2.71 atm expressed in kPa?

B. The pressure in a tire reads 262 kPa.

What is this pressure in atm?

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Properties of Properties of GasesGases

Gas properties can be Gas properties can be modeled using math. modeled using math.

The factors that affect gases The factors that affect gases are:are:

V = volume of the gas (L)V = volume of the gas (L)T = temperature (K)T = temperature (K)n = amount (moles)n = amount (moles)P = pressure P = pressure (atm, kPa, mm (atm, kPa, mm

Hg, Hg, or psi)or psi)

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All temperatures must be in Kelvins! No exceptions!

Converting Temperatures to KelvinKelvin = ˚Celsius + 273

ORK = ˚C + 273

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Copy onto P. Table

Example: convert 25 ˚C to Kelvins.

K = 25 ˚C + 273 = 298 K

Properties of Gases, Properties of Gases, cont.cont.

We can study the relationship between 2 variables if we keep the others the same.

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VARIABLES: Moles, temperature, pressure, and

volume

The relationship between:n (moles) & P (pressure)Pressure is caused by the particles striking the walls of the container.

If the gas is in a rigid container, the volume is constant (not changing)

If you increase the number of gas particles (n), you increase the pressure. Animation

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SAMPLE PROBLEMn (moles) & P (pressure)Question: A container containing 2 moles of helium gas exerts a pressure of 0.75 atm on the container walls. Another 2 moles of helium are pumped into the container. What is the new pressure inside the container?

Analysis: The number of (moles of) gas particles doubles, so the pressure doubles.

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Boyle’s Law: Boyle’s Law: The relationship between: P (pressure) & V (volume)

All other variables kept the same (T, n, etc.)

This relationship is seen in a flexible/adjustable container

Ex: a rising balloon or a cylinder with a piston

Animation13

Boyle’s LawBoyle’s Law P P αα 1/V 1/V

This means This means Pressure and Pressure and Volume are Volume are INVERSELY INVERSELY

PROPORTIONALPROPORTIONALP goes up as V P goes up as V

goes down.goes down.

PP11VV11 = P = P22 V V22 14

Robert Boyle Robert Boyle (1627-1691). (1627-1691). Son of Earl of Son of Earl of Cork, Ireland.Cork, Ireland.

Copy onto P. Table

Boyle’s LawBoyle’s LawBoyle’s LawBoyle’s LawA bicycle pump is a A bicycle pump is a

good example of good example of Boyle’s law. Boyle’s law.

As the volume of the As the volume of the air trapped in the air trapped in the pump is reduced, its pump is reduced, its pressure goes up, pressure goes up, and air is forced into and air is forced into the tire.the tire.

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Sample Problem 14.1 (p 419)A balloon contains 30.0 L of helium gas at

103kPa. What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kPa?

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Givens:P1= 103 kPa P2 = 25.0kPa

V1 = 30.0L

Unknown:V2 = ?

SOLUTION STEP 1: Identify & label all your variables (given & unknown)

SOLUTION STEP 2: Find the formula that has all the variables you are using.

SOLUTION STEP 3: Rearrange the formula to solve for the unknown.

PP11VV11 = P = P22 V V22

SOLUTION, cont.SOLUTION STEP 4: substitute values

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SOLUTION STEP 5: Calculate an answer

V2 = 123.6

V2 = 124 L

SOLUTION STEP 6: Evaluate your answer. Does it make sense?

Charles’s LawCharles’s LawThe relationship between: V (volume) & T (temperature)

All other variables kept the same (P, n, etc.)

Example: balloon

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Charles’s Charles’s LawLaw

V V αα T TV and T are V and T are

directly directly proportional.proportional.VV11 V V22

==

TT11 T T22

If one temperature goes If one temperature goes up, the volume goes up!up, the volume goes up!

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Jacques Charles (1746-Jacques Charles (1746-1823). Isolated boron 1823). Isolated boron and studied gases. and studied gases. Balloonist.Balloonist.

Sample Problem 14.2 Using Charles Law (p 421)A balloon inflated in a room at 24˚C has a

volume of 4.00L. The balloon is then heated to a temperature of 48˚C. What is the new volume if the pressure remains constant?

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Givens: T1 = 24˚C + 273 = 297K T2 = 48 + 273

=321K V1 = 4.00 L

Unknown: V2

Solution

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V1 = V2 V2 = V1T2

T1 T2 T1

V2 = 4.00L*321K 297K V2 =

CW/HWPractice Problems, pp 419-423 # 7-10

p 439 #47-49

Charles’s LawCharles’s Law

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What will happen if the syringe is put in a hot water bath?A cold water bath?

Gay-Lussac’s LawGay-Lussac’s LawIf n and V are constant, If n and V are constant,

then P then P αα T TP and T are directly P and T are directly

proportional.proportional.

PP11 P P22

==

TT11 T T22 If one temperature If one temperature

goes up, the pressure goes up, the pressure goes up!goes up!

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Joseph Louis Gay-Joseph Louis Gay-Lussac (1778-1850)Lussac (1778-1850)

Practice Problem (G-L)A 20 L cylinder containing 6 atm of gas at 27 °C. What would the pressure of the gas be if the gas was heated to 77 °C?

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GIVENS UNKNOWN20 L = V ? = P6 atm = P27 °C + 273 = 300.K = T77 °C + 273 = 350.K= T2

1

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Section 14.1 Assessmentp 4171. Why is a gas easy to compress?2. List 3 factors that can affect gas pressure.3. Why does a collision with an air bag cause less

damage than a collision with a steering wheel?4. How does a decrease in temp affect the pressure of a

contained gas?5. If the temp is constant, what change in volume would

cause the pressure of an enclosed gas to be reduced to ¼ of its original value?

6. Assuming the gas in a container remains at a constant temp, how could you increase the gas pressure in a container a hundredfold?

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Combined Gas LawSince all 3 gas laws are related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!

P1 V1 = P2 V2

T1 T2

26No, it’s not related to R2D2

Combined Gas LawIf you only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

=

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P1 V1

T1

P2 V2

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Combined Gas Law Problem

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A sample of helium gas has a volume of 180 mL, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature(°K) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm?

Set up Data Table

P1 = 0.800 atm V1 = 180 mL T1 = 302 K

P2 = 3.20 atm V2= 90 mL T2 = ??

SolutionP1 = 0.800 atm V1 = 180 mL T1 =

302KP2 = 3.20 atm V2= 90 mL T2 = ??P1 V1 P2 V2

= P1 V1 T2 = P2 V2 T1

T1 T2

T2 = P2 V2 T1

P1 V1

T2 = 3.20 atm x 90.0 mL x 302 K

0.800 atm x 180.0 mLT2 = 604 K - 273 = 331 °C 29

= 604 K

Learning Check A gas has a volume of 675 mL at 35°C and 0.850 atm pressure. What is the temperature when the gas has a volume of 0.315 L and a pressure of 802 mm Hg?

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One More Practice Problem

A balloon has a volume of 785 mL on a fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?

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And now, we pause for this commercial message from STP

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OK, so it’s really not THIS kind of STP…

STP in chemistry stands for Standard Temperature and

Pressure

Standard Pressure = 1 atm (or an equivalent)

Standard Temperature = 0 deg

C (273 K)

STP allows us to compare amounts of

gases between different pressures and temperatures

STP allows us to compare amounts of

gases between different pressures and temperatures

Try This OneA sample of neon gas used in a neon sign has a volume of 15 L at STP. What is the volume (L) of the neon gas at 2.0 atm and –25°C?

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Avogadro’s Avogadro’s HypothesisHypothesis

Equal volumes of gases at Equal volumes of gases at the same T and P have the the same T and P have the same number of molecules.same number of molecules.

V and n are directly relatedV and n are directly related..

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twice as many twice as many moleculesmolecules

IDEAL GAS LAWIDEAL GAS LAW

Brings together gas Brings together gas properties.properties.

BE SURE YOU KNOW BE SURE YOU KNOW THIS EQUATION!THIS EQUATION!

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P V = n R TP V = n R T

Using PV = nRTUsing PV = nRTP = PressureP = Pressure n = number of molesn = number of molesV = VolumeV = Volume T = TemperatureT = TemperatureR is a constant, called theR is a constant, called the Ideal Gas ConstantIdeal Gas Constant = =

8.31 L*kPa8.31 L*kPa K*molK*mol

NOTE: We must NOTE: We must convert the convert the units to match R.units to match R.

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Using PV = nRTUsing PV = nRTEx: p 439, Q#55Ex: p 439, Q#551.24 moles of gas at 35 C and 96.2 kPa 1.24 moles of gas at 35 C and 96.2 kPa

pressure. What is the volume the gas pressure. What is the volume the gas occupies?occupies?

V=?V=?n= 1.24 moln= 1.24 molT = 35 + 273 = 308KT = 35 + 273 = 308KP = 96.2kPaP = 96.2kPaR=8.31L*kPa/K*molR=8.31L*kPa/K*mol(96.2kPa)V = (1.24 mol ) (8.31L*kPa/K*mol) (96.2kPa)V = (1.24 mol ) (8.31L*kPa/K*mol)

(308K)(308K)V=33.0LV=33.0L

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Learning Check

Dinitrogen monoxide (N2O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (mm Hg) in the tank in the dentist office?

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Learning Check

A 5.0 L cylinder contains oxygen gas at 20.0°C and 735 mm Hg. How many grams of oxygen are in the cylinder?

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Gases in the Air (don’t copy)The % of gases in air Partial pressure (STP)

78.08% N2 593.4 mm Hg

20.95% O2 159.2 mm Hg

0.94% Ar 7.1 mm Hg

0.03% CO2 0.2 mm Hg

PAIR = PN2 + PO2 + PAr + PCO2 = 760 mm Hg

(Total Pressure = 760mm Hg)

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Dalton’s Law of Partial Dalton’s Law of Partial PressuresPressures

What is the total pressure in the flask?What is the total pressure in the flask?

PPtotaltotal in gas mixture = P in gas mixture = PAA + P + PBB + ... + ...

Therefore, Therefore,

PPtotaltotal = P = PHH22OO + P + POO22 = 0.48 atm = 0.48 atm

Dalton’s Law: total P is sum of PARTIAL Dalton’s Law: total P is sum of PARTIAL pressures. pressures.

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2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

0.32 atm 0.32 atm 0.16 0.16 atmatm

Health NoteWhen a scuba diver is several hundred feet under water, the high pressures cause N2 from

the tank air to dissolve in the blood. If the diver rises too fast, the dissolved N2 will form

bubbles in the blood, a dangerous and painful condition called "the bends". Helium, which is inert, less dense, and does not dissolve in the blood, is mixed with O2 in

scuba tanks used for deep descents.

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GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSIONdiffusiondiffusion is the is the

gradual mixing of gradual mixing of molecules of molecules of different gases.different gases.

effusioneffusion is the is the movement of movement of molecules through molecules through a small hole into an a small hole into an empty container.empty container.

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HONORS HONORS onlyonly

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSION (Don’t Copy)EFFUSION (Don’t Copy)

Graham’s law governs Graham’s law governs effusion and diffusion effusion and diffusion of gas molecules.of gas molecules.

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Thomas Graham, 1805-1869. Thomas Graham, 1805-1869. Professor in Glasgow and London.Professor in Glasgow and London.

Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.

Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.

M of AM of B

Rate for B

Rate for A

HONORS HONORS onlyonly