Question

10g glucose (molar mass 180) and 20g of sucrose (molar mass 342) are dissolved in 100g of water. What will be the vapour pressure of the resultant solution if the vapour pressure of water is 35mm Hg?

Answer 1

Hint: First find out the number of moles of all the three components present in the solution. Then find out the mole fraction of water. Then we know, vapour pressure of a solution is the product of mole fraction of that compound in the solution and vapour pressure of pure compound. Use this relation and substitute the data and find the answer.

Complete step by step solution:
- Let’s start by finding the number of moles of each component present in the solution.
- Number of moles of glucose present in the solution is $\dfrac{10}{180}=0.0555$
- Number of moles of sucrose present in the solution is $\dfrac{20}{342}=0.0585$
- Number of moles of water present in the solution is $\dfrac{100}{18}=5.555$
- Total number of moles is 0.0555+0.0585+5.555= 5.669
- Now, we need to calculate the mole fraction of water.
- Mole fraction of water $=\dfrac{5.555}{5.669}=0.979$
- We know, vapour pressure of a solution is the product of mole fraction of that compound in the solution and vapour pressure of pure compound.
- Therefore, vapour pressure of solution $=0.979\times 35=34.296mm\,Hg$
-Therefore, the vapour pressure of the resultant solution is 34.296mm Hg.

Note: Remember molar mass of water is 18g/mol. Number of moles is the ratio of weight taken of a compound to molar mass of that compound. Mole fraction of a component is the ratio of the number of moles of that component to the total number of moles of all the components present in the solution. And the sum of mole fractions of all the components in a solution will be equal to unity.