Question

What mass of sucrose, C12H22O11, should you dissolve in 100.0 g of water to obtain a solution in which the mole fraction of C12H22O11 is 0.124?

Answer 1

Answer:

the sucrose mass is 264.g

Explanation:

The computation of the sucrose mass is shown below;

The Molar mass of $C_{12}H_{22}O_{11}$ is  342.3 g/mol

And, the molar mass of $H_2O$ is 18g/mol

The mass of $C_{12}H_{22}O_{11}$ be Y

Now

The moles of $C_{12}H_{22}O_{11}$ is

= Mass of $C_{12}H_{22}O_{11}$ ÷  molar mass of $C_{12}H_{22}O_{11}$

= Y ÷ 342.3 mol

And,

The moles of $H_2O$ is

= Mass of $H_2O$ ÷  molar mass of $H_2O$

= 100.0 ÷ 18

= 5.56mol

Now

The molar fraction of $C_{12}H_{22}O_{11}$ is

= Moles of $C_{12}H_{22}O_{11}$ ÷  (moles of$C_{12}H_{22}O_{11}$ + moles of $H_2O$)  = 0.124

= (Y ÷ 342.3) ÷ [(Y ÷ 342.3) + 5.56] = 0.124

Y ÷ 342.3 = 0.124 × [(Y ÷ 342.3 + 5.56]

Y = 0.124 × Y + (0.124 × 5.56 × 342.3)

Y = 269.4 g

hence, the sucrose mass is 264.g