Theoretical Example of Vapour Pressure of Liquids

The gas phase pressure of a liquid is called its vapour pressure p and increases with increasing temperature of the liquid

Where ΔH⁰_vap is the enthalpy of vaporization, the amount of heat required to vaporize a mole of liquid in its standard state; R is the gas constant; and T₁ and T₂ are low and high temperatures having p₁ and p₂ vapour pressures. Rearrange the equation to get T₂ as the subject of the equation.

Solution

This question is not as easy as it first appears. The method suggested is one of several but with this type of question it is easy to make a mistake and obtain an incorrect solution, a step by step method is best.

(1 )split the term in brackets into two terms; (2) cancel out top and bottom separately for each term inside the right hand bracket; (3) expand the bracket by multiplying it out;

then (4) rearrange the equation so that the term containing T₂ becomes the subject;

(5) multiply by R/ ΔH⁰_vap throughout and

(6) then cancelling out top and bottom within each term;

(7) before we can take the reciprocal on both sides we need to bring the right hand side to the common denominator T₁ ΔH⁰_vap, and finally

(8) we can now take reciprocals on both sides of the equation.