Question

A solution contains 5.00 g of urea,\({\bf{CO}}\left( {{\bf{NH_2}}} \right){\bf{_2}}\), a non-volatile compound, dissolved in 0.100 kg of water. If the vapour pressure of pure water at 25 °C is 23.7 Tor, what is the vapour pressure of the solution?

Short answer

The Vapour Pressure of the Solution is 23.35 Tor.

Step-by-step solution

Vapour Pressure

Vapour pressure may be defined as the pressure when the liquid and vapour are at equilibrium. The equilibrium pressure level is thought to function as an indicator of the evaporation rate of a liquid.

Necessary Step

Mass of Urea= 5.0g

Molar Mass of Urea= 60 g/mole

Mass of Water= 0.100kg= 100g

Molar Mass of Water= 18 g/mole

Firstly,

\(\begin{align}Number\,of\,Moles &= \frac{{Mass}}{{Molar\,Mass}}\\Number\,of\,Moles\,of\,Urea &= \frac{5}{{60}} = 0.083mole\\Number\,of\,Moles\,of\,Water &= \frac{{100}}{{18}} = 5.55mole\\Mole\,Fraction &= \frac{{0.083}}{{0.083 + 5.55}} = 0.35\end{align}\)

\(\begin{align}{\bf{P}}\,{\bf{solution = {\rm X}}}\,{\bf{solvent + P}}\,{\bf{solvent}}\\{\bf{P}}\,{\bf{solution - P}}\,{\bf{solvent = {\rm X}}}\,{\bf{solvent}}\end{align}\)

Explanation

Vapour Pressure of Solution= 23.7 Tor

Vapour Pressure of Solvent= x g

\(\begin{align}P\,solution - P\,solvent &= {\rm X}\,solvent\\23.70 - x &= 0.35\\x &= 23.70 - 0.35\\x &= 23.35\end{align}\)

The Vapour Pressure is 23.35 Tor.