Question

214.2 g of sugar syrup contains 34.2 g of sugar. Calculate (i) molarity of the solution and (ii)mole fraction of sugar in the syrup.

Answer 1

Step 1: Given Data

Mass of sugar =$34.2gram.$

Mass of solution = $214.2g$

Step 2: Formula used

The number of moles of sugar can be represented by the formula = $\frac{\mathrm{given}\mathrm{mass}}{\mathrm{molar}\mathrm{mass}}$.

$$\begin{gathered} =34.2/(mol.mass) \\ =34.2/342 \\ =0.1 \end{gathered}$$

Step 3: Calculating the Mass of water

$$\begin{gathered} =(214.2-34.2) \\ =180gor180/1000kg \end{gathered}$$

Step 4: Calculating the Number of moles in the water

(molar mass = 18 )

$$\begin{gathered} =180/18 \\ =10moles \end{gathered}$$

Step 5: Finding Molarity

Molarity = Number of moles of sugar/Mass of water per Kg

$$\begin{gathered} =0.1/180x1000 \\ =0.555M \end{gathered}$$

Step 6: Formula used

$\mathrm{Mole}\mathrm{fraction}\mathrm{of}\mathrm{sugar}=\frac{\mathrm{Number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{sugar}}{\mathrm{Total}\mathrm{moles}}$

Step 7: Calculating the Total number of moles of sugar syrup

number of moles of sugar syrup

=$10.0+0.1=10.1$

$$\begin{gathered} =0.1/10.1 \\ =0.0099 \end{gathered}$$

Hence, the molarity of sugar is$0.555M.$, the mole fraction of sugar syrup is $0.0099$.