Question

the concentration of sug

The concentration of sugars in a maple syrup is about 66 g per 1 L. Estimate the boiling point (Kb for water (-0.51 oC/m) of such a sugar solution. Use molecular weight of sucrose (C22011H22, 342 g mol-l) in your calculations, and assume that the weight of 1 L of syrup equals to 1000 9. Select one: O a. 100.1°C O b. 110°C O c. 101.1°C O d. 101°C

Answer 1

Answer:-

Given:-

As we know that the concentration of sugar (sucrose) in a maple syrup is about 66 g per 1 L which shows that 66 g sugar (sucrose) is dissolved in 1 L water.

therefore

wt. of sugar (sucrose) i.e solute (W_B) = 66 g

molar mass of  sugar (sucrose) (M_B) = 342.0 g.mol^-1

wt. of water i.e solvent (W_A) = 1 L = 1000 g (since 1 L = 1000 g )

molal elevation constant of water (K_b) = 0.51 ⁰C / m

Also we know that

boiling point of pure water ( T_H2O) = 100 ⁰C

elevation in boiling point of sugar solution ($\Delta$T_b) = ?

boiling point of sugar solution ( T_solution) = ?

Von't Hoff factor (i) = 1 ( because sugar does not dissociated into ions therefore no. of solute particles (i) = 1)

So

molality of sugar solution (m) = wt. of sugar (sucrose) i.e solute (W_B) in (g )$\times$ 1000 / molar mass of  sugar (sucrose) (M_B) in (g.mol^-1 ) $\times$ wt. of water i.e solvent (W_A) in (g)  

molality of sugar solution (m) = 66 g $\times$ 1000 / 342.0 g.mol^-1  $\times$ 1000 g  

molality of sugar solution (m) = 0.1930 m

So according to the formula

elevation in boiling point of sugar solution ($\Delta$T_b) = i $\times$ molal elevation constant of water (K_b) $\times$ molality of sugar solution (m)

elevation in boiling point of sugar solution ($\Delta$T_b) = 1 $\times$ 0.51 ⁰C / m $\times$ 0.1930 m

elevation in boiling point of sugar solution ($\Delta$T_b) = 0.098 ⁰C = 0.1 ⁰C

elevation in boiling point of sugar solution ($\Delta$T_b) = 0.1 ⁰C

Also we know that

boiling point of solution ( T_solution) = boiling point of pure solvent ( T_solvent) + elevation in boiling point of solution ($\Delta$T_b)

therefore

boiling point of sugar solution ( T_solution) = boiling point of pure water ( T_H2O) + elevation in boiling point of sugar solution ($\Delta$T_b)

boiling point of sugar solution ( T_solution) =  100.0 ⁰C +   0.1 ⁰C

boiling point of sugar solution ( T_solution) = 100.1 ⁰C (i.e the answer)