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Chemistry 20 Lesson 2-06 2013 T. de Bruin

Chemistry 20 – Ideal gas law

� If we combine all the information contained in Boyle’s, Charles’ and Avogadro’s laws, we can derive anexpression that describes the temperature, pressure and volume of a gas.

� This relationship is known as the ideal gas law and is mathematically described with the formula below:

PV=nRTwhere: P = pressure (kPa)

V = volume (L)n = amount of moles (mol)T = temperature in Kelvin (K)

R = universal gas constant 8.314 kPa Lmol K

··

The universal gas constant is a value relating the molar volume of a gas totemperature and pressure. It is a mathematical “correction factor” to account fornon-ideal behaviour of real gases.

� An ideal gas behaves perfectly and predictably under all conditions of pressure, temperature and volume.That is:

· Ideal gases do not condense into liquids.

· Ideal gases have particles (molecules/atoms) of zero size (point masses) that have no forces ofattraction (such as London Force, dipole-dipole).

� The name ideal gas law implies that there must be some gases whose behaviour is non-ideal. In fact thereis no such thing as an ideal gas that obeys the PV=nRT equation perfectly under all conditions;all real gases deviate slightly from the behaviour predicted by the law for the followingreasons:

· The kinetic-molecular theory assumes that the volume of the gas particles themselves isnegligible compared with the total gas volume. This does not hold true at either high pressuresor very low temperatures. The smaller the volume of gas, the more important the size of the gasmolecule becomes.

· A second problem with real gases is the assumption that there are no attractive forces betweenmolecules. At lower pressures, this assumption is a good one because the gas particles are farapart and the attractive forces between them are negligible. At higher pressures, however, theparticles are much closer together and the attractive forces between them become moreimportant.


Consider the following graph of pressure vs. volume for an ideal and real gas:

� If we subject an ideal gas to increasing pressure, it always remains a gas.

� If we subject a real gas such as SO2 to increasing pressure, we find that at a certain point (different for eachreal gas) intermolecular forces of attraction (London, dipole-dipole, hydrogen bonding) are strong enoughto cause the gas molecules to attract each other and turn into a liquid (and then a solid if the pressure ishigh enough). This is because the pressure forces the gas molecules closer and closer together, allowingintermolecular forces to attract gas molecules together.

� Real gases deviate most from ideal gases at low temperatures and/or high pressure. This is because theseconditions bring the gas molecules so close together, they start interacting with each other (attracting,repelling and colliding).

� As you increase the temperature and/or decrease the pressure of a real gas, the particles (molecules oratoms) separate far apart enough from each other so that intermolecular interactions become negligible.Thus a real gas starts to behave more ideally.

· Small gas molecules behave more ideally than larger gas molecules.

Gas Molar Mass g/molBoiling Point ˚Cl à g phase change*

He 4.00 -269 most idealH2 2.02 -253N2 28.02 -196CO2 44.01 -78C3H8 (propane) 44.11 -33 least ideal

* ideal gases never turn into liquids (or solids).

· Of all real gases helium (He) most closely resembles an ideal gas as it is monoatomic with a completely filledvalence energy level (even charge distribution of electrons around the nucleus). Since hydrogen is diatomic, itis subject to stonger London force that helium, thus changing into a liquid easier than helium.


Technologoical Applications of Real Gase Behaviour

Butane Lighters

· A butane lighter is a great example of real gas behaviour and its technologicalapplication.

· Butane (C4H10) is forced into the reservoir under pressure. The pressure causesLondon Force (butane is nonpolar) to change the butane gas into a liquid as thegas molecules are attracted to each other under pressure.

· By pressing the trigger, the internal pressure is reduced, allowing some of thebutane to change back into a gas. A flint or electric spark mechanism thenignites the gaseous butane.

· The approximately 10 mL of (pressurized) liquid butane in the lighter will turninto approximately 1 000 mL of gaseous butane!

Liquified Natural Gas (LNG) Transportation

· Natural gas (methane, CH4) is a very common fuel used world-wide.· Transporting gas-phase chemicals is very inefficient because gases occupy a

large volume of space.· By pressurizing and cooling natural gas to its condensation point (that point at

which it turns into a liquid), you can transport enormously larger amounts ofnatural gas than if it was in its gas phase

· Specialized transport ships are used for this, acting as giant pressurized thermos bottles to keep themethane in the liquid phase.


Lesson summaryAny sample of gas can be described by four variables: pressure, volume, temperature and moles. The ideal gaslaw relates these four variables to each mathematically: PV=nRT.

Example Problem

Determine the volume occupied by 15.5 g of propane (C3H8) at 23.3 ˚C and 99.75 kPa.

Solution:

m = 15.5 g

M = 44.11 g/mol

T = 296.65 K

P = 99.75 kPa

V = ?

Since PV=nRT requires moles (n) which we are not given, we will firsthave to calculate it using:

gmol

m 15.5gn 0.3513942417mol

M 44.11= = =

Now we can use the ideal gas law to solve for V:

kPa L0.3513942417mol 8.314 296.65KnRT mol KVP 99.75kPa

·· ·

·= =

V = 8.69 L


Chemistry 20 – Ideal Gas Problems

1. A sample of 4.25 moles of hydrogen at 20.0 °C occupies a volume of 25.0 L. What is the pressure of thissample?

2. What volume will 30.0 g of NO (g) occupy at 3.26 atm and 19.0 °C?

3. What is the temperature of 45.3 g of ammonia gas if it occupies 64.2 L at 150 kPa?

4. What mass of sulfur trioxide is present in a 4.8 L container at 55 °C and 150 kPa?


5. A 70.0 L tank on a car is drained of liquid gasoline. How many moles of octane vapour are present in thistank at SATP?

6. A balloon is filled with 0.61 mol of air at 101.5 kPa. At what temperature will the volume of the balloonbe 15 L?

7. What is the volume of a hot air balloon if it contains 1.05 × 105 mol at 102 kPa and 100 °C?

Numerical Response ProblemsRecord all answers to three digits in the spaces provided below and record in the boxes as shown below.

Numerical Response directions.

· If an answer is a value between 0 and 1 (e.g. 0.25), then be sure to record the 0 before the decimal place.· Boxes 2 or 3 could be a decimal point.· Enter the first digit of your answer in the left-hand box and leave any unused boxes blank.· Example calculation question and solution.

· The average of the values 21.0, 25.5 and 24.5 is ______.

(Record your three digit answer in the numerical-response section on your answer sheet)

Average = (21.0 + 25.5 + 24.5)/3

= 23.6666666

=23.7 (round to three digits)

Problems

1. Automotive tires are now being filled with pure nitrogen gas to increase tire performance. Determinethe mass of nitrogen present in a tire containing 20.3 L of air at 20.0 oC and 327 kPa.

2. Calculate the mass of neon gas in a neon sign with a volume of 50.0 L at 10.0 °C and 3.10 kPa.

3. Calculate the volume of 8.40 g of nitrogen at 200 °C and 130 kPa.

4. Hydrogen gas is generated by the decomposition of water to fill a 1.10 kL weather balloon at20.0 °C and 100 kPa. What is the mass of hydrogen required?

5. Calculate the volume of 16.0 g of oxygen at 22.0 °C and 97.5 kPa.

Chemistry 20 – Ideal Gas Problems – Answer Key

1. 2.

3. 4.

5. 6.

Numerical Response Problems

1.7 6 . 3

2.1 . 3 3

3.9 . 0 7

4.9 1 . 2

5.1 2 . 6

( ) ( )kPa L4.25mol 8.314 293.15Kmol K

25.0 L414kPa

PV nRTnRTPV

P

P

=

=

æ öç ÷è ø=

=

g

g

NO

NO

g g14.01 16.00mol mol

g30.01mol

30.0gg30.01

mol1.00mol

M

M

mnM

n

n

= +

=

=

=

=

3

3

NH

NH

g g14.01 3 1.01mol mol

g17.04mol

45.3gg17.04

mol2.66 mol

M

M

mnM

n

n

æ ö= + ç ÷è ø

=

=

=

=

( ) ( )

( )

150 kPa 64.2 LkPa L2.66mol 8.314mol K

435K

PV nRTPVTnR

T

T

=

=

=æ öç ÷è ø

=

g

g

( )( )

( )

150 kPa 4.8 LkPa L8.314 328.15Kmol K

0.264 mol

PV nRTPVnRT

n

n

=

=

=æ öç ÷è ø

=

g

g

( )

3

3

SO

SO

g g32.07 3 16.00mol molg80.07

mol

g0.264 mol 80.07mol

21g

M

M

mnM

m nM

m

m

æ ö= + ç ÷è ø

=

=

=

æ ö= ç ÷è ø

=

( )( )

( )

100 kPa 70.0LkPa L8.314 298.15Kmol K

2.82 mol

PV nRTPVnRT

n

n

=

=

=æ öç ÷è ø

=

g

g

( ) ( )

( )2

101.5kPa 15LkPa L0.61mol 8.314mol K

3.0 10 K 27 º C

PV nRTPVTnR

T

T or

=

=

=æ öç ÷è ø

= ´

g

g

( ) ( )5

6

kPa L1.05 10 mol 8.314 373.15Kmol K

102kPa3.19 10 L

PV nRTnRTV

P

V

V

=

=

æ ö´ ç ÷è ø=

= ´

g

g

( ) ( )

( )

kPa L1.00 mol 8.314 292.15 Kmol K

kPa3.26 atm 101.325atm

7.35 L

PV nRTnRTV

P

V

V

=

=

æ öç ÷è ø=

æ öç ÷è ø

=

g

g

Chemistry 20 formative problem set - Ideal Gas Law

Formula: PV=nRT You may also need mn=

MThe pressure must be in kPa and the temperature must bein Kelvin. Check your data book for the conversion factors.

1. A cylinder of neon gas has a volume of 9.76 L. If thecylinder contains 61.2 g of neon at 23.0 °C, what is thepressure in the cylinder?

2. An experiment calls for 70.025 g of carbon monoxide at55.0 °C and 157.00 kPa. Determine the volumeoccupied by the carbon monoxide.

3. The maximum safe pressure that a certain 4.00 Lvessel can hold is 425.95 kPa. If the vessel contains0.410 moles of a gas, determine is the maximumtemperature (in degrees Celsius) to which this vesselcan be subject.

4. We wish to compress 3.15 g of methane gas (CH4) intoa heavy-walled 2.00 L flask at 19.0 °C. Calculate thepressure of the gas.

5. Calculations show that a chemical reaction should yield5.67 g of carbon dioxide gas. Determine the volumeexpected at SATP?

6. A 2.50 L flask was used to collect a 5.65 g sample ofpropane gas, C3H8 . After the sample was collected, thegas pressure was found to be 235.75 kPa. Calculate thetemperature of the propane in the flask.

7. If 458 mL of gas measured at 30.5 °C and 98.95 kPahas a mass of 0.384 g, what is its molecular mass?

8. A volume of 0.972 L of a gas measured at 50.0 °C and80.97 kPa has a mass of 0.525 g. Calculate itsmolecular mass.

9. Methane gas (CH4) is sold in a 43.8 L cylindercontaining 5.54 kg of the gas. Calculate thepressure inside the cylinder at 20.0 ºC.

10. Many laboratory gases are sold in steel cylinderswith a volume of 43.8 L. Determine the mass ofargon inside a cylinder whose pressure is 17 180kPa at 20.0 ºC?

Critical thinking

11. A sample of methane gas (CH4) is at 50.0 ºC and2.03 MPa. Would you expect it to behave more orless ideally if (include your reasoning):

a) The pressure was reduced to 100 kPa?

b) The temperature was reduced to -50 ºC?

12. In the diagram below, show using a line, theapproximate level of the movable piston indrawings (a), (b), and (c) after the indicatedchanges have been made to the gas.

Diagram for problem 12.

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