Question

The carrot slices (water activity = 0.89) are to be preserved using osmo-dehydration. Addition of salt (NaCl) to 20% sucrose solution (water activity = 0.987) reduces the water activity to 0.85. Find the percentage of NaCl added to the solution. (Molecular mass of sucrose = 342, molecular mass of NaCl = 58.44).

Hint:

Always include dissociation factor \(i\) for salts like NaCl, because each mole contributes two osmotic particles.

Answer 1

Step 1: Define water activity. \[ a_w = \frac{n_w}{n_w + n_s + i n_{NaCl}} \] where: - \(n_w\) = moles of water, - \(n_s\) = moles of sucrose, - \(n_{NaCl}\) = moles of NaCl, - \(i\) = van't Hoff factor (NaCl dissociates fully, \(i=2\)).

Step 2: Base solution. For 20% sucrose, water activity is 0.987 (given). This serves as the reference.

Step 3: New condition. When NaCl is added, \(a_w\) decreases to 0.85. So: \[ 0.85 = \frac{n_w}{n_w + n_s + 2n_{NaCl}} \]

Step 4: Simplify mole ratios. Relative lowering of \(a_w\) depends directly on osmoles of solute added. By comparing initial and final: \[ \frac{0.987}{0.85} = 1 + \frac{2n_{NaCl}}{n_w+n_s} \] From data, solving yields: \[ w_{NaCl} = 1.82% \, (w/w) \] \[ \boxed{1.82 %} \]