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Ideal Gas Equation

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Ideal Gas Equation
4. States of Matter
I The gaseous state:
(i) Ideal gas behaviour and deviations from it
(II) pV = nRT and its use in determining a value for Mr
II The liquid state
The kinetic concept of the liquid state and simple kinetic-molecular
descriptions of changes of state
III The solid state
Lattice structures
Learning Outcomes
Candidates should be able to:
(a) state the basic assumptions of the kinetic theory as applied to an ideal gas
(b) explain qualitatively in terms of intermolecular forces and molecular size:
(i) the conditions necessary for a gas to approach ideal behaviour
(ii) the limitations of ideality at very high pressures and very low temperatures
(c) state and use the general gas equation pV = nRT in calculations, including
the determination of Mr
(d) *describe, using a kinetic-molecular model, the liquid state; melting;
vaporisation and vapour pressure
(e) *describe, in simple terms, the lattice structure of a crystalline solid which is:
(i) ionic, as in sodium chloride, magnesium oxide
(ii) simple molecular, as in iodine
(iii) giant molecular, as in graphite; diamond; silicon(IV) oxide
(iv) hydrogen-bonded, as in ice
(v) metallic, as in copper
[the concept of the ‘unit cell’ is not required]
(f) explain the strength, high melting point and electrical insulating properties of
ceramics in terms of their giant molecular structure
(g) relate the uses of ceramics, based on magnesium oxide, aluminium oxide
and silicon(IV) oxide, to their properties (suitable examples include furnace
linings; electrical insulators; glass; crockery)
(h) describe and interpret the uses of the metals aluminium, including its alloys,
and copper, including brass, in terms of their physical properties
(i) understand that materials are a finite resource and the importance of
recycling processes
(j) outline the importance of hydrogen bonding to the physical properties
of substances, including ice and water
(k) suggest from quoted physical data the type of structure and bonding
present in a substance
• Avogadro’s law:
Equal volumes of any gas measured at the
same temperature and pressure contain
the same numbers of particles (atoms and
molecules
In order for volumes of gases to be comparable, they must be
measured under the same conditions of temperature and pressure.
Alternatively the volumes at the required temperature can be worked
out using the Ideal Gas Equation.
• Remember Boyle’s Law: PV = constant
• Charles Law: V = constant
T
• PV = constant (for a fixed mass of gas)
T
If we take 1 mole of gas the constant is given the symbol R
and is called the gas constant, and for n moles of gas we
have
PV = nRT
R is a constant, 8.314 KJ-1mol-1
P, pressure must be in Pascals, Pa; V, volume must be in m3 (1m3 = 106 cm3
= 103 dm3), T, temperature must be in Kelvin, K
Kinetic theory is an attempt to explain the
observed properties of gases
- The particles are moving randomly
- We can neglect the volume of the particles themselves in comparison
to the total volume of the gas
- The particles do not attract one another
- The average kinetic energy of the particles is proportional to the
temperature of the gas
- No energy is lost in collisions between particles
- Bombardment of the walls of the container explains pressure and
increasing temperature makes them hit walls harder, so pressure
increases
• Deviations from Ideal Gas Behaviour
When gases are put under high pressure or cooled down
the gas molecules get closer together (or move slower at
lower temperatures) and they become attracted to each
other using intermolecular forces and start to form a
liquid. So there are no gases at 0 K!
What volume is needed to store 0.050 moles of
helium gas at 202.6kPa and 400K?
What pressure will be exerted by 20.16g hydrogen
gas in a 7.5L cylinder at 20oC?
A 50L cylinder is filled with argon gas to a pressure
of 10130.0kPa at 30oC. How many moles of argon
gas are in the cylinder?
To what temperature does a 250mL cylinder
containing 0.40g helium gas need to be cooled in
order for the pressure to be 253.25kPa?
What volume is needed to store 0.050 moles of helium gas
at 202.6kPa and 400K?
PV = nRT
P = 202.6 kPa
n = 0.050 mol
T = 400K
V=?L
R = 8.314 J K-1 mol-1
202.6V=0.050x8.314x400
202.6 V = 166.28
V = 166.28 ÷ 202.6
V = 0.821 L (821mL)
What pressure will be exerted by 20.16g hydrogen gas
in a 7.5L cylinder at 20oC?
PV = nRT
P = ? kPa
V = 7.5L
n = mass ÷ MM
mass=20.16g
MM(H2)=2x1.008=2.016g/mol
n=20.16 ÷ 2.016=10mol
T=20o=20+273=293K
R = 8.314 J K-1 mol-1
Px7.5=10x8.314x293
Px7.5 = 24360.02
P = 24360.02 ÷ 7.5 = 3248kPa
A 50L cylinder is filled with argon gas to a pressure of 10130.0kPa
at 30oC. How many moles of argon gas are in the cylinder?
PV = nRT
P = 10130.0kPa
V = 50L
n = ? mol
R = 8.314 J K-1 mol-1
T=30oC=30+273=303K
10130.0x50=nx8.314x303
506500=nx2519.142
n=506500 ÷ 2519.142=201.1mol
To what temperature does a 250mL cylinder containing 0.40g helium
gas need to be cooled in order for the pressure to be 253.25kPa? PV = nRT
P = 253.25kPa
V=250mL=250 ÷ 1000=0.250L
n=mass ÷ MM
mass=0.40g
MM(He)=4.003g/mol
n=0.40 ÷ 4.003=0.10mol
R = 8.314 J K mol-1
T=?K
253.25x0.250=0.10x8.314xT
63.3125 = 0.8314xT
T=63.3125 ÷ 0.8314=76.15K
• Calculations
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