Subtopic: Water activity, sorption and desorption isotherms
Question Statement:
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. Percentage of NaCl added to the solution is ______________ (rounded off to 2 decimal places). Consider molecular mass of Sucrose = 342 and molecular mass of NaCl = 58.44
Official Answer Key:
16.40 to 16.60
Step-by-Step Solution & Explanation
Basis: 100 g of 20% sucrose solution = 20 g sucrose + 80 g water (this reproduces the stated aw=0.987 via Raoult's law: n_water/(n_water+n_sucrose) = (80/18)/[(80/18)+(20/342)] = 4.444/(4.444+0.0585) = 0.9870 ✓, confirming the basis).
Adding x g of NaCl (which fully dissociates into 2 ions in solution, so contributes 2×(x/58.44) moles to the mixture) and solving via Raoult's law for the target a_w=0.85:
n_water/(n_water + n_sucrose + 2×n_NaCl) = 0.85
Solving numerically for x gives x ≈ 21.2 g, i.e. ≈17.3–17.5% of the new total solution mass (or ≈21.2% of the original 100 g solution basis) is NaCl — this is close to, but not exactly matching, the official range of 16.40–16.60%. The residual gap likely reflects a difference in basis convention (e.g., “% NaCl” defined relative to the water mass alone, or a slightly different dissociation/activity-coefficient assumption) that could not be pinned down with full certainty from the problem statement alone; the official range is reported here for the final answer.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.