The Ideal Gas Equation macroscopic propertiespressure, volume and temperature In order to understand gases scientists like Boyle and Charles had to look at what we call the macroscopic, large scale, properties of the gases such as pressure, volume and temperature. The reason for this is that it was all they could measure in their laboratories! All these factors are linked to each other in gases and changing one of them seems to have an effect on the other. amount of gas constantdefinite number of molecules In order to investigate these factors you need to keep the amount of gas constant so that it contains a definite number of molecules of gas. eliminate one other variable from your enquiries by keeping it constantinvestigate the effect of changing one variable on another. You can eliminate one other variable from your enquiries by keeping it constant and therefore investigate the effect of changing one variable on another.

Boyle’s Law Pressure/Pa Volume of the trapped mass of gas measured here. Air forced in from foot pump here. Bourdon pressure gauge. Use the apparatus shown below to record the change in volume of the trapped mass of gas as the pressure exerted on the gas is changed as read from the Bourdon pressure gauge. oil

The pressure (P) of a fixed mass of gas at constant temperature is inversely proportional to its volume (V). P  1/V P  1/V or PV = Constant PV = Constant or P 1 V 1 = P 2 V 2 This is a fairly simple rule to follow – if you decrease to volume of a gas trapped in a balloon by squashing it in both hands you feel an increase in pressure. They are therefore inversely proportional. look at the graph you can see that if the pressure doubles the volume halves If you look at the graph you can see that if the pressure doubles the volume halves etc etc.

T3T3 Volume Pressure T2T2 T1T1 Each linecertain temperature Each line shows the relationship at a certain temperature isotherm T 1 >T 3 Each line is called an isotherm (iso - same, therm - temperature) T 1 >T 3 left to right shows an expansion Moving down the line from left to right shows an expansion as the volume increases lower linedecrease in temperature. Moving down to a lower line would be indicate a decrease in temperature.

P T1T1 1/V T2T2 T3T3 This can also be drawn as a graph of Pressure against 1/Volume resulting in a straight line the gradient of which is steeper at higher temperatures as shown below.

This should make sense as when things get hot they expand as you have learned in Year 9. Effect is most noticeable in the longest dimension of solids. Least noticeable in solids and most noticeable in gases. V  T V/T = constant V 1 /T 1 = V 2 /T 2 Charles’ law (Not needed but useful to know) The volume of a fixed mass of gas at constant pressure is directly proportional to its absolute temperature (in Kelvin) V T/K

Combining all three of these laws we obtain: T must be measured in Kelvin The other units do not matter as long as they are the same on both sides of the equation. P 1 V 1 = P 2 V 2 T 1 T 2 PV = Constant T If we consider the same mass of gas in two different circumstances we can establish that…

The Ideal Gas Equation An ideal gas is one which obeys the gas laws perfectly regardless of the temperature and pressure and could therefore define the Kelvin temperature scale perfectly. Most of the gases obey the gas laws adequately provided well abovecritical temperature. critical temperatureThey are well above the critical temperature. Every gas has a temperature called its critical temperature, below which it can be liquefied by increasing the pressure alone, above this it cannot be liquefied. pressurearoundatmospheric pressure The pressure is around that of atmospheric pressure

We can deduce that for different masses of gas, the constant would be different. Therefore for 1 mole of a gas the constant has the value R – the Molar Gas Constant = 8.3 Jmol -1 K -1 If the amount of gas is not 1 mole we must scale things up/down accordingly. So for 1 mole of a gas If we now consider the situation when… PV = Constant T PV = R T For “n” moles of a gas, either more or less than 1, PV = nR T