3.4: Ideal Gas Law

Learning Objectives

I can explain the relationship between pressure, temperature, volume and number of moles of a gas sample using the ideal gas law.
I can explain the relationship between variables within an equation when one variable changes.

Language Objectives

I can verbally explain the relationship between pressure, temperature, volume and number of moles of a gas sample using the ideal gas law.
I can write the equation that represents the relationship between macroscopic properties of gases.

Essential knowledge

The macroscopic properties of ideal gases are related through the ideal gas law.
In a sample containing a mixture of ideal gases, the pressure exerted by each component (the partial pressure)is independent of the other components. Therefore, the total pressure of the sample is the sum of the partial pressures.
Graphical representations of the relationships between P, V, T, and n are useful to describe gas behavior.

equation(s):

PV=nRT
PA= Ptotal×XA where XA= moles A/total moles (mole fraction)
Ptotal=PA + PB+ PC + etc..... A, B and C are gases in a mixture

Notes:

The following gas laws are derived from the ideal gas law and they describe how a gas sample respond to changing conditions:

Ideal Gas Law

The ideal gas law, PV=nRT, is used to relate the pressure, volume, moles, and temperature of a sample of gas by using the gas constant, R, at a given state/conditions.

P = pressure in atm (atmosphere)

V = volume in L (Liters)

n = moles of gas

R = universal gas constant (0.08206 L.atm/mol.K)

T = temperature in Kelvin (Celcius + 273.15)

The Ideal Gas Constant, R

There are several R values listed on the equation sheet, they differ in the units for pressure.

R =62.36 L torr/mol K (for torr or mmHg) and R = 8.314 J/mol K (1 J = 1 L kPa)

Always check your units when completing an Ideal Gas Law calculation to make sure that the units all cancel out.

The ideal gas formula can be used to solve for molar mass or density of a gas as follows.

Dalton's Law of Partial Pressures:

According to Dalton's Law of Partial Pressure, the sum of all the partial pressures of each gas in a mixture of gasses is equal to the total pressure.

In mathematical notation, this is expressed by saying: Ptotal = PA+ PB+ PC... where A, B, and C are different gasses.

Mole Fractions χ:

Mole fraction is denoted by XA and equals moles A/total moles.

To find the partial pressure, multiply the mole fraction by the total pressure of the mixture.

Partial Pressure PA= XA* PTotal

Check Your Understanding:

If a mixture is 3.0 mol O2 and 4.0 mol H2. Calculate the mole fraction of H2, then find it is partial pressure knowing that the total pressure in the mixture is 1.5 atm.

Mole fraction of H2 = number of moles of H2 / total number of moles of gases = 3.0 /(3.0+ 4.0) = 3.0/7.0 = 0.43

PH2= XH2 * Ptotal = 0.43 * 1.5= 0.65 atm

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