Molar Volume

1
Molar Volume

• Pg 66-74
• Also advanced material not found in text

2
Avogadros Hypothesis

• At a constant temperature and pressure, a given
  volume of gas always has the same number of
  particles.
• The coefficients of a balanced reaction is the
  same ratio as the volumes of reactants and
  products

3
2CO (g) O2 (g)? 2CO2(g)

• For the above example, it is understood that half
  the volume of oxygen is needed to react with a
  given volume of carbon monoxide.
• This can be used to carry out calculations about
  volume of gaseous product and the volume of any
  excess reagents.

4
Example

• 10 mL of ethyne (C2H2) is reacted with 50 mL of
  hydrogen to produce ethane (C2H6), calculate the
  total volume and composition of the remaining gas
  mixture, assuming constant T and P.

1st get balanced equation C2H2(g) 2H2(g) ?
C2H6(g)
2nd look at the volume ratios 1 mol ethyne to 2
mol of hydrogen, therefore 1 vol to 2 vol
3rd analyse If all 10 mL of ethyne is used, it
needs only 20 mL of hydrogen, therefore hydrogen
is in excess by 50 mL-20 mL 30 mL. In the end
youll have 10 mL Ethane and the leftover 30 mL
hydrogen
5
Molar volume

• The temperature and pressure are specified and
  used to calculate the volume of one mole of gas.
• Standard temperature and pressure (STP) is at sea
  level 1 atm 101.3 kPa and 0oC 273 K this
  volume is 22.4 L

Molar gas volume, Vm. It contains 6.02 x 1023
molecules of gas
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Example

• (a) Calculate how many moles of oxygen molecules
  are there in 5.00 L at STP
• n VSTP 5.00 L 0.223
  mol
• 22.4 L/mol 22.4 L/mol
• (b) How many oxygen molecules are there in 5.00L
  at STP?
• 0.223 mol x 6.02 x 1023 molecules 1.34 x 1023
  molecules
• mol

7
Avogadros Law

• Mathematical relationship between the volume of a
  gas (V) and the number of moles of gas present
  (n).
• n1 n2
• V1 V2
• One mole of gas occupies the same volume as one
  mole of another gas at the same temp and pressure
• Molar volumes unit is L/mol

8
Practice

• (a) How many moles are present in 44.8 L of
  methane gas (CH4) at STP? (b) What is the mass
  of the gas? (c) How many molecules are present?
• 22.4 L 1 mol of any gas at STP
• So 44.8L x 1mol 2.00 mol
• 22.4L

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(b) What is the mass of the gas?

• 2.00 mol CH4 x 16.05 g 32.10 g CH4
• mol CH4
• (c) How many molecules are present?
• 2.00 mol x 6.02 x1023 molecules 1.20 x1024
  molecules
• mol

10
Boyles Law (1659)

• Boyle noticed that the product of the volume of
  air times the pressure exerted on it was very
  nearly a constant, or PVconstant.
• If V increases, P decreases proportionately and
  vice versa. (Inverse proportions)
• Temperature must be constant.
• Example A balloon under normal pressure is blown
  up (1 atm), if we put it under water and exert
  more pressure on it (2 atm), the volume of the
  balloon will be smaller (1/2 its original size)
• P1V1P2V2

11
Charles Law (1787)

• Gas expands (volume increases) when heated and
  contracts (volume decreases) when cooled.
• The volume of a fixed mass of gas varies directly
  with the Kelvin temperature provided the pressure
  is constant. V constant x T
• V1 V2
• T1 T2

12
Gay-Lussacs Law

• The pressure of a gas increases as its
  temperature increases.
• As a gas is heated, its molecules move more
  quickly, hitting up against the walls of the
  container more often, causing increased pressure.
• P1 P2
• T1 T2

13
Laws combined

• P1V1 P2V2
• T1 T2
• T must be in Kelvins, but P and V can be any
  proper unit provided they are consistently used
  throughout the calculation

14
Practice

• If a given mass of gas occupies a volume of 8.50
  L at a pressure of 95.0 kPa and 35 oC, what
  volume will it occupy at a pressure of 75.0 kPa
  and a temperature of 150 oC?

1st convert oC to K 35 273 308 K 150
273 423 K
2nd rearrange equation and solve problem V2
V1 x P1 x T2 8.50 x 95.0 x 423 14.8 L P2
x T1 75.0 x 308
15
Temperature

• Kelvin temperature is proportional to the average
  kinetic energy of the gas molecules.
• It is a measure of random motion of the gas
  molecules
• More motion higher temperature

16
Ideal gas behaviour

• Ideal behaviour is when a gas obeys Boyles,
  Charles and Gay-Lussacs laws well
• At ordinary temperature and pressures, but there
  is deviation at low temperature and high pressures

17
Ideal gas

• where all collisions between molecules are
  perfectly elastic and in which there are no
  intermolecular attractive forces.
• Its like hard spheres bouncing around, but NO
  interaction.

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Ideal gas law

• PV nRT
• P pressure (kPa)
• Volume (L)
• n number of moles
• Runiversal gas constant 8.3145 J mol-1 K-1
• T temperature (K)

19
Example

• 3.376 g of a gas occupies 2.368 L at 17.6 oC and
  a pressure of 96.73 kPa, determine its molar
  mass.
• PV nRT rearrange equation for n
• Temp 17.6 oC 273 290.6 K

n PV/RT (96.73 x 2.368) / (8.314 x 290.6)
0.09481 mol Molar mass mass/ mole
3.376 g / 0.09481 mol 35.61
g/mol
20
http//www.mhhe.com/physsci/chemistry/essentialche
mistry/flash/gasesv6.swf

• Visit this flash to see how temp, pressure and
  volume are related

21
Practice

• Pg 73 38 43
• Scanned handout online with notes additional
  questions.