3.7 Gas Laws

Boyle’s law At a constant temperature, the volume of a given mass of any gas is inversely proportional to the pressure on the gas. V = 1 * constant P V P

Charles’ Law [1787] The volume of a fixed mass of any gas at constant pressure is proportional to the Kelvin temperature. V = T * Constant V Temp [K]

Kinetic Theory of Gases James Clerk Maxwell & Ludwig Boltzmann came up with this idea independently near end of 19th century 1.Gases are made up of particles whose diameters are negligible compared to the distances between them. 2.There are no attractive or repulsive forces between these particles.

3.The particles are in constant rapid random straight-line motion, colliding with each other and the walls of the container. 4.All collisions are perfectly elastic. 5.The average kinetic energy of the particles is proportional to the Kelvin temperature.

Boyle’s Law Explained Constant temperature so the particles have a fixed average velocity. Decreasing the volume leads to the particles colliding with the walls more often. Pressure is proportional to the number of collisions of particles with the wall. Thus the pressure increases

Charles’ Law explained Constant pressure so particles collide a set number of times per second with walls of the container Temperature is increased so average velocity of particles increases proportionately - (so the particles will collide with the walls more often – if nothing was done - the pressure would increase)

The volume of the gas must therefore increase proportionately if the particles are to hit the walls with the same frequency (because Pressure proportional to number of collisions) Reverse is true if temperature is lowered

Gay Lussac’s Law When gases react, the volumes in which they do so bear a simple ratio to one another and to the volumes of the products (if gaseous), all volumes being measured under the same conditions of temperature and pressure. Reaction Ratio 2 CO + O2 = 2 CO2 2 : 1 : 2

Reaction Ratio NH3 + HCl = NH4Cl(s) 1 : 1 : - NH4Cl is a solid CH4 + 2 O2 = CO2 + 2H2O(l) 1 : 2 : 1 : - H2O is a liquid

Avogadro’s Law (1811) Equal volumes of gases under the same conditions of temperature and pressure contain equal numbers of molecules. V  n [n is number of molecules] V = n * constant

Equation of State for an Ideal Gas (Ideal Gas Law) Boyle’s V  1/P [at constant T and n] Charles’ V  T [at constant P and n] Avogadro’s V  n [at constant T and P] Combining all 3 V  1 * T * n P

V = R * 1 * T * n P Written as an equation this becomes Where R is a constant known as the Gas Constant

Rearrange ......... Equation of State for an Ideal Gas PV = nRT P = pressure [usually Nm-2 (Pa)] V = volume in cubic metres [ L(dm3) / 1000] e.g. 20 L (dm3)= 0.02 m3 n = number of moles [mass / RMM or volume of gas / 22.4 L (dm3) or number of molecules / 6*1023 ] R = Gas Constant = 8.31 JK-1mol-1 (no need to remember this as it will be given) T = Kelvin temperature = (oC + 273)

Rearrange again ........ P V = nR T P1 V1 = n1 R1 T1 But P2 V2 = n2 R2 T2 R1 and R2 are the same since R is a constant n1 and n2 are the same since it is the same sample of gas

 P1 V1 = P2 V2 T1 T2 This can be used to calculate the Pressure or Volume or Temperature of a gas under varying conditions. Most commonly used to calculate changes in volume. E.g. to calculate a volume at STP given the volume at RTP Subscript 1 [P1 T1] usually represents STP.

Deviation from Ideal Gas Behaviour No ideal gas actually exists At high temperatures and low pressures gases are closest to ideal behaviour. Gases deviate from ideal behaviour because there are attractive forces between the particles especially when they get close together [compared to their diameters.]

Deviation from ideal gas behaviour is most obvious when The temperature is low [particles slow] Pressure is high [particles pushed close] The molecules are large [distances small and moving slow] If the particles are polar [attractive forces]

Compare HCl and H2 Hydrogen behaves as an ideal gas over a wider range of conditions than HCl because it is (a) smaller (b) non-polar. δ+ δ-