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

PV=nRT

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.

Ideal Gas Law

If a sample of gas occupies a 400ml vessel which has a pressure of 5.2 atm, has the volume increased to 2.4L, what is the new pressure of the vessel?

PV=nRTnRT = constant therefore P1V1 = P2V2

.4L(5.2atm) = 2.4L(P2)

0.87atm = P2

Gas Law Problems

Suppose that in a gas thermometer the gas occupies 12.6ml at 20C. The thermometer is immersed in boiling water (100C). What is the volume of the gas at 100C?

PV=nRTRearrange V/T = nR/P where nR/P = constantTherefore V1/T1 = V2/T2

12.6ml/(293K) = V2/373K

16.04ml = V2

Another example

Calculate the volume in liters occupied by .55kg of dimethyl ether, C2H6O at 950mmHg and 15C.

PV=nRT

.55kg 1000g 1mol = 11.96mol 1kg 46.1g

V = 11.96mol(.0821atm L/mol K)(288K) / (950/760) V = 226L

Another Example

PV=nRT

n=mass/molar mass n=m/m

substitute PV=mRT/m

Also keep in mind that d=m/V (d=density)

rearrange P=mRT/mV therefore P=dRT/m

Ideal Gas Law…with a twist

An unknown diatomic gas has a density of 3.164g/L at STP. What is the identity of the gas?

m=dRT/P

m= (3.164g/L)(.0821atm L/mol K)(273K)/1atmm=70.91g

therefore the gas is Cl2

Another Example