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$\begin{array}{ll} ATP + H_{2} O \to ADP + {PO}_{4}^{3 -}; Δ_{r} G^{\circ} = - 31 kJ / mol \\ Glucose + Fructose \to Sucrose; Δ_{r} G^{\circ} = 23 kJ / mol \end{array}$
A 100 ml solution is 0.5 (M) with respect to glucose and 0.8 (M) with respect to fructose. To this how many liters of gastric juice containing l0^-2 (M) ATP is to be added to obtain maximum molarity of sucrose?

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2.71 L

3 L

37.1 L

3.71 L

answer is D.

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Detailed Solution

Glucose + Fructose $\to$ Sucrose

$5 \times 10^{- 2} mol 8 \times 10^{- 2} mol$

Glucose is the L.R. and maximum amount of sucrose to be obtained = 5 × 10^-2mol

$∴ Energy required = 23 \times 5 \times 10^{- 2} kJ$

Let V ml of ATP solution is required

$\begin{array}{l} V \times 10^{- 5} \times 31 = 23 \times 5 \times 10^{- 2} \\ ∴ V = \frac{23 \times 5}{31} \times 10^{3} = 3.71 \times 10^{3} mL = 3.71 L \end{array}$

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