Question

QUESTION 2.5

A solution of glucose in water is labelled as $10\%w/w$. What should be the molality and mole fraction of each component in the solution? If the density of solution is $1.2gm{L}^{-1}$, then what shall be the molarity of the solution?

Answer 1

Step 1:

10% w/w glucose solution means 10 g glucose present in 100 g of solution which contains 90 g of water.

Molality is the number of moles of glucose present in 1 kg of water.

Molar mass of glucose $\left(C_6{H}_{12}{O}_6\right)$ = $6\times 12+12\times 1+6\times 16=180g{mol}^{-1}$

Number of moles = $\frac{Givenmassingrams}{Molecularmass}$

Number of moles of glucose = $\frac{10}{180}mol$ = 0.056 mol

$Molalityofsolution=\frac{Numberofmoles}{weightofsolvent}$

$\therefore$ Molality of solution = $\frac{0.056mol}{0.09kg}=0.62M$

Number of moles of water = $\frac{90g}{18g{mol}^{-1}}=5mol$

Step 2:

$Molefraction=\frac{Numberofmolesofsolute}{Numberofmolesofsolute+numberofmolesofsolvent}$

Mole fraction of glucose, $x_g=\frac{0.056}{0.056+5}=0.011$

Mole fraction of water, $x_w=1-x_g$ $=1-0.011=0.989$

Step 3:

If density of solution is 1.20 g/mL, then the volume of the 100 g solution can be given as:

$\frac{100g}{1.2g{mL}^{-1}}$ = $83.33mL=83.33\times {10}^{-3}L$

$\therefore$ Molarity of the solution = $\frac{0.056mol}{83.33\times {10}^{-3}L}=0.67M$