Ideal vs. Real Gases

No gas is ideal. As the temperature of a gas increases and the pressure on the gas decreases the gas acts more ideally.

Equation of State of an Ideal Gas Robert Boyle ( 1662 ) found that at fixed temperature –Pressure and volume of a gas is inversely proportional PV = constantBoyle’s Law J. Charles and Gay-Lussac ( circa 1800 ) found that at fixed pressure –Volume of gas is proportional to change in temperature Volume Temp o C All gases extrapolate to zero volume at a temperature corresponding to – o C (absolute zero). He CH 4 H2OH2O H2H2

Kelvin Temperature Scale Kelvin temperature (K) is given by K = o C where K is the temperature in Kelvins, o C is temperature in Celcius Using the ABSOLUTE scale, it is now possible to write Charles’ Law as V / T = constant Charles’ Law Gay-Lussac also showed that at fixed volume P / T = constant Combining Boyle’s law, Charles’ law, and Gay-Lussac’s law, we have P V / T = constant Gay-Lussac

Ideal Gas Equation P V = n R T Universal Gas Constant Volume No. of moles Temperature Pressure R = atm L / mol K R = kPa L / mol K Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 366

PV = nRT P = pressure V = volume T = temperature (Kelvin) n = number of moles R = gas constant Standard Temperature and Pressure (STP) T = 0 o C or 273 K P = 1 atm = kPa = 760 mm Hg Solve for constant (R) PV nT = R Substitute values: (1 atm) (22.4 L) (1 mole)(273 K) R = atm L / mol K or R = 8.31 kPa L / mol K R = atm L mol K Recall: 1 atm = kPa (101.3 kPa) ( 1 atm) = 8.31 kPa L mol K 1 mol = 22.4 STP

Gas Law Calculations Boyle’s Law PV = k Boyle’s Law PV = k Charles’s Law V T Charles’s Law V T Combined Gas Law PV T Combined Gas Law PV T Ideal Gas Law PV = nRT Ideal Gas Law PV = nRT = k T and V change P, n, R are constant P, V, and T change n and R are constant P and V change n, R, T are constant

The production of oxygen by thermal decomposition Zumdahl, Zumdahl, DeCoste, World of Chemistry  2002, page 423