Ideal Gas LawIdeal Gas Law

Ideal GasesIdeal Gases– are at high temperatures and low are at high temperatures and low pressures.pressures.

– have no forces of attraction between have no forces of attraction between particles. particles.

– Collide elastically (no loss in kinetic Collide elastically (no loss in kinetic energy).energy).

Real GasesReal Gases It is rare that we see a gas behaving It is rare that we see a gas behaving in an ideal manner.in an ideal manner.

Most gases actually show very small Most gases actually show very small attractive and repulsive forces between attractive and repulsive forces between particles and collide inelastically particles and collide inelastically (kinetic energy is lost).(kinetic energy is lost).

Ideal Gas Law :Ideal Gas Law :

PV = nRTPV = nRTWhere Where P = pressureP = pressureV = volume in LitersV = volume in Litersn = number of molsn = number of molsR = ideal gas R = ideal gas constantconstantT = temperature (Kelvin)T = temperature (Kelvin)

Calculate R, the Ideal Calculate R, the Ideal Gas Constant…Gas Constant…

Using 1 mol of gas at STP and molar Using 1 mol of gas at STP and molar volumevolume

R = R = 0.0821 0.0821 atmatm·L·L

mol·Kmol·K

= = 62.4 62.4 mmHgmmHg·L·L

mol·Kmol·K

= = 8.314 8.314 kPakPa·L·L

mol·Kmol·K

Example…Example…

Calculate the number of moles Calculate the number of moles of gas contained in a 3.0L of gas contained in a 3.0L vessel at 33°C and a pressure vessel at 33°C and a pressure of 1.50 atm.of 1.50 atm.

PV=nRTPV=nRT

(1.50 atm) (3.0 L) = n ((1.50 atm) (3.0 L) = n (0.0821atm0.0821atm·L/mol·K·L/mol·K))(306K)(306K)

n = 0.18 molesn = 0.18 moles

Variations…Variations…

We donWe don’’t always know the t always know the number of moles, but we number of moles, but we have the mass. have the mass. –n = m/M so…n = m/M so…

PVM = mRT PVM = mRT

–d= m/V so…d= m/V so…

PM = dRTPM = dRT

Example…Example… Calculate the grams of oxygen Calculate the grams of oxygen gas present in a 2.50L sample gas present in a 2.50L sample kept at 1.66 atm pressure and a kept at 1.66 atm pressure and a temperature of 10.0temperature of 10.0°C.°C.

PVM = mRT PVM = mRT (1.66 atm)(2.50 L)(32 g/mol) = m (1.66 atm)(2.50 L)(32 g/mol) = m (0.0821atm(0.0821atm·L/mol·K·L/mol·K)(283 K))(283 K)

m = 5.72 gm = 5.72 g

Examples…Examples… What is the density of NHWhat is the density of NH33 at at

800 mmHg and 25800 mmHg and 25°C?°C?

PM = dRTPM = dRT(800 mmHg)(17 g/mol) = d ((800 mmHg)(17 g/mol) = d (62.4 mmHg62.4 mmHg·L/mol·K·L/mol·K))(298 K)(298 K)

d = 0.7 g/Ld = 0.7 g/L