The ideal gas equation

Starter What would happen if you kept filling a

balloon with gas?

What would happen if you put a full sealed balloon of gas into the refrigerator?

Why would this happen?

The ideal gas equationLearning outcomes:

State the ideal gas equation

Use SI units correctly

Manipulate the ideal gas equation to calculate the number of moles of a gas at a given volume, temperature and pressure

Specification reference 3.1.2.3

What is an ideal gas?An ideal gas is one which follows this

equation:

pV=nRT

Where: p = pressure in Pa (Nm-2) V = volume (in m3) n= number of moles T= temperature (in K) R = gas constant (8.31 JK-1mol-1)

No gas is actually ideal... But at room temperature and pressure (RTP) it works pretty well for most.

Really... Where does that equation come fromThe ideal gas equation is a combination of;

Boyle’s law – it states that the product of pressure and volume is a constant so long as the temperature stays constant

Charles’ law – it states that volume is proportional to the temperature so long as the pressure is constant

Gay-Lussac’s law – it states that pressure is proportional to the temperature as long as the volume remains constant

All these equations are in the book – you are not expected to know them

Using the ideal gas equationKey things – you must use the correct units

(and convert values if they aren’t correct)

To convert °C to Kelvin, add 273

To convert kPa to Pa, multiply by 1000

To convert dm3 into m3, divide by 1000To convert cm3 into m3, divide by 106

Rearrange... Make:

VolumePressureTemperatureNumber of moles... the subject of the equation

Answers

Worked example Volume from the ideal gas equation. If a gas has a temperature of 20.0°C, at a pressure

of 100 000Pa, and n= 1 for one mole of gas, what is the volume?

V = nRT/P

V = 1 x 8.31 x 293/100 000

V = 0.0243 m3

Convert to cm3 by multiplying by 106

Question Calculate the volume of 2 moles of gas if the

temperature is 30°C, and the pressure is 100 000Pa.

Calculate the pressure of 0.5 moles of a gas if the volume is 11 000cm3, and the temperature is 25°C.

Calculate the volume in m3 of 2.5x10-2 moles of oxygen gas at a pressure of 150kPa and a temperature of 50°C

Worked exampleFinding the number of moles:How many moles of hydrogen molecules are present

in a volume of 100cm3 at a temperature of 20.0°C and a pressure of 100kPa?

R = 8.31 JK-1mol-1

Convert base units 100kPa = 100 000Pa100cm3 = 100 x 10-6

20°C = 293Kn = PV/RT = 100 000 x 100x10-6/8.31 x 293= 0.00411 moles

Questions Calculate how many moles of hydrogen

molecules are present in a volume of 48 000cm3, at 100 000Pa and 25°C.

State how many moles of carbon dioxide molecules would be present under the same conditions. Explain your answer.

Useful things to calculateIf you know the number of moles present in

any given mass of gas, you can find the mass of one mole of gas and thus the Mr of that gas.

Once you have calculated the number of moles, you can rearrange the equation n = m/Mr (Mr = mass/n) and then find the relative formula mass of that gas.

Homework Complete the activity on kerboodle

http://www.kerboodle.com/app/courses/18514/modules/Resources/node/12362/page/1/content/91127

Link also on show my homework

Once you have done that, complete the ideal gas questions on the worksheet