# Gas Laws Boyles Charles Avogadros GayLussacs Combined Gas

Gas Laws Boyle’s, Charles’, Avogadro's, Gay-Lussac’s Combined Gas law and The Ideal Gas Law

Ideal Gas Law PV=n. RT The ideal gas law can be applied to most gas law problems. Keep in mind that if a condition does not change, it can be considered a constant.

Gas Law Problems If a sample of gas occupies a 400 ml vessel which has a pressure of 5. 2 atm, has the volume increased to 2. 4 L, what is the new pressure of the vessel? PV=n. RT = constant therefore P 1 V 1 = P 2 V 2. 4 L(5. 2 atm) = 2. 4 L(P 2) 0. 87 atm = P 2

Another example Suppose that in a gas thermometer the gas occupies 12. 6 ml at 20 C. The thermometer is immersed in boiling water (100 C). What is the volume of the gas at 100 C? PV=n. RT Rearrange V/T = n. R/P where n. R/P = constant Therefore V 1/T 1 = V 2/T 2 12. 6 ml/(293 K) = V 2/373 K 16. 04 ml = V 2

Another Example Calculate the volume in liters occupied by. 55 kg of dimethyl ether, C 2 H 6 O at 950 mm. Hg and 15 C. PV=n. RT. 55 kg 1000 g 1 kg 1 mol 46. 1 g = 11. 96 mol V = 11. 96 mol(. 0821 atm L/mol K)(288 K) / (950/760) V = 226 L

Ideal Gas Law…with a twist PV=n. RT n=mass/molar mass n=m/m substitute PV=m. RT/m Also keep in mind that d=m/V (d=density) rearrange P=m. RT/m. V therefore P=d. RT/m

Another Example An unknown diatomic gas has a density of 3. 164 g/L at STP. What is the identity of the gas? m=d. RT/P m= (3. 164 g/L)(. 0821 atm L/mol K)(273 K)/1 atm m=70. 91 g therefore the gas is Cl 2

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