nRT The Ideal Gas Equation Objective To be able to use the Ideal Gas Equation pV nRT Outcomes To know the ideal gas equation To use the ideal gas equation To rearrange the ideal gas equation ID: 726537
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Slide1
Ideal Gas Equation pV= nRTSlide2
The Ideal Gas Equation
Objective:
To be able to use the Ideal Gas Equation (
pV
=
nRT
)
Outcomes:
To know the ideal gas equation
To use the ideal gas equation
To rearrange the ideal gas equation
To use the ideal gas equation to find molecular
formuale
of gases and volatile liquidsSlide3
Molar volumes of gases
If the temperature and pressure are fixed at convenient standard values, the molar volume of a gas can be determined.
Standard temperature is 273 K
(0
o
C) and
pressure is 101.3 kPa.
At standard temperature and pressure (s.t.p) 1 mole of any gas occupies a volume of 22.4 dm3. This is the molar gas volume.
At room temperature and pressure (
r.t.p) 1 mole of any gas will occupy a volume of 24 dm3 mol-1 . R. T.P is 293 K (20o C) and 101.3 kPa. This is the molar gas volume.
Last lesson we learnt thisSlide4
Ideal gas equation
The
ideal gas equation
relates pressure, volume, number of moles and temperature for a gas.
pV
=
nRT
p
= pressure in Pa
V = volume in m3
How is the number of moles in a gas at other temperatures and pressures calculated?
n
= number of moles
R
= gas constant: 8.31JK
-1
mol-1T = temperature in Kelvin
A gas that obeys this law under all conditions is called an
ideal gas
.Slide5
Ideal gas equation: converting units
It is very important when using the ideal gas equation that the values are in the correct units.
The units of pressure, volume or temperature often need to be converted before using the formula.
Pressure
to convert
kPa
to Pa:
× 1000
Volume
to convert dm
3
to m
3
:
to convert cm
3
to m
3:
÷
1000 (10
3
)
÷
1
000
000 (106)
Temperatureto convert °C to Kelvin:
+ 273Slide6
Starters for 10Slide7
Finding the molecular formula of a gas using
pV
=
nRT
At a temperature of 60oC and a pressure of 250 kPa, a gaseous hydrocarbon occupied a volume of 1100 cm3
and had a mass of 1.60 g. Find the molecular formula of the hydrocarbon.n = pV/RT = (250 x 103) x (1.1 x 10
-3) / (8.31 x 333) = 0.0993 moles0.0993 moles = 1.60 g so Mr= 1.60 / 0.0993 = 16.1 gMolar mass is 16 gThe only hydrocarbon with a molar mass of 16 is methane, CH4Slide8
Finding the molecular formula of a gas using
pV
=
nRT
A cylinder of gas X weighed 242.487 g. After it was used to release some gas into a gas syringe, the cylinder weighed 242.313 g.Calculate the mass of the gas releasedThe reading on the gas syringe was 75 cm3
, the temperature was 27oC and the atmospheric pressure was 100 kPa. Calculate the number of moles of gas released into the syringe.Use your answers to parts a) and b) to calculate the Mr of the gas.
Old AQA page 49Slide9
Find the molar mass of a volatile liquidA volatile liquid evaporates easily.
You can use the ideal gas equation to find the molar mass of an unknown volatile liquid.
Put a known
mass
of the liquid in a flask, then attach it to a sealed gas syringe . Gently warm the apparatus in a water bath until the liquid completely evaporates.Record the volume of gas in the syringe and the temperature of the water bath
Use the ideal gas equation to work out how many moles of the liquid were in your sample and the equation molar mass = mass / moles to calculate the molar massSlide10
Example
Calculate the volume in cm
3
occupied by 0.0200
mol of oxygen in 298 K and 100 kPa pressure.pV =
nRT=4.95 x 10-4 m3
Volume = 4.95 x 10-4 x 106 = 495 cm3(x 1000 000)Slide11
ExampleCalculate the volume which 2.2 g of carbon monoxide would occupy at a temperature of 20
o
C and a pressure of 6500 Pa.
n = 2.2 / 28
pV = nRT = 6500 x V = 0.07857 x 8.31 x 293V= 0.07857 x 8.31 x 293 / 6500
V =0.02943 m3 = 29430 cm3= 29.43 dm3Slide12
Example
What is the volume of 2.50 g of hydrogen gas at a temperature of 293 K and a pressure of 100
kPa
Moles = 2.50/2 = 1.25
pV = nRT V= nRT
/P= 1.25 x 8.31x 293 / 100 000= 3043.538 / 100 000=0.0304353 m3 = 30435 cm
3 = 30.4 dm3Slide13
The Ideal Gas Equation
Objective:
To be able to use the Ideal Gas Equation (
pV
= nRT)Outcomes:To know the ideal gas equation
To use the ideal gas equationTo rearrange the ideal gas equationTo use the ideal gas equation to find molecular formuale of gases and volatile liquids