GATE 2023 AG – Question 64
Carrot slices have water activity.89. Adding NaCl to 20% sucrose solution(initial activity.987) lowers solution activity to .85. Find added NaCl percentage, to two decimals. Sucrose/NaCl molar masses342/58.44 g/mol.
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Correct answer: 16.40 to 16.60
Explanation
Use a 100 g starting sucrose-solution basis:20 g sucrose and 80 g water. With the ideal dissociated-salt approximation and the initial sucrose activity factored out,$a_{final}=a_{sucrose}n_w/(n_w+2n_s)$. Thus $n_s=(80/18)[(.987/.85)-1]/2=.35817$ mol and NaCl mass is 20.93098 g. Its fraction in final solution is $100(20.93098)/(100+20.93098)=\mathbf{17.31\%}$. The official range16.40–16.60% requires a different salt-activity/nonideality convention not specified by these data. Therefore preserve the key and identify that model gap rather than treat the ideal calculation as the accepted answer.