GATE 2023 BT Q.49: solution and answer

GATE 2023 · BTQ.49 · 2 marks · NAT

Aqueous two-phase extraction is used to recover $α$ -amylase from a solution. A polypropylene glycol-dextran mixture is added and the solution separates into upper and lower phases. The partition coefficient is 4.0 and the ratio of upper to lower phase volume is 5.0. The enzyme recovery or yield (in percentage, rounded off to the nearest integer) is ________.

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Answer and solution

ANSWER

The enzyme recovery in the upper phase is $\frac{K R}{1 + K R} = \frac{20}{21} = 95.24%$ , so the answer is 95.

Official answer: 94 to 96Source: Official answer key, GATE 2023 BT (IIT Kanpur)

Define the symbols. The partition coefficient is $K = \frac{C _{U}}{C _{L}} = 4.0$ , where $C_{U}$ and $C_{L}$ are the enzyme concentrations in the upper and lower phases. The volume ratio is $R = \frac{V _{U}}{V _{L}} = 5.0$ , where $V_{U}$ and $V_{L}$ are the upper- and lower-phase volumes. By the usual convention $K$ is written upper-over-lower, and $K > 1$ means the enzyme favours the upper phase, so the product is recovered from the upper phase.
Mass balance on the enzyme. The total enzyme is shared between the two phases: $total = C_{U} V_{U} + C_{L} V_{L}$ .
Fraction of the enzyme recovered in the upper phase: $Y_{U} = \frac{C _{U} V _{U}}{C _{U} V _{U} + C _{L} V _{L}} = \frac{K R}{1 + K R}$ (divide the numerator and the denominator by $C_{L} V_{L}$ , using $\frac{C _{U}}{C _{L}} = K$ and $\frac{V _{U}}{V _{L}} = R$ ).
Substitute: $K R = 4.0 \times 5.0 = 20$ .
$Y_{U} = \frac{20}{1 + 20} = \frac{20}{21} = 0.9524$
Yield $= 95.24% \approx 95%$ (rounded to the nearest integer).

KEY IDEA

In a two-phase partition, the fraction of solute in the upper phase depends only on the product $K R$ (partition coefficient times the upper-to-lower volume ratio): $Y_{U} = \frac{K R}{1 + K R}$ . A large upper-phase volume raises the yield even when $K$ is modest. Here $K R = 20$ , so only $1/21$ of the enzyme stays in the lower phase.

WATCH OUT FOR

Using $K$ alone and writing $\frac{K}{1 + K} = 80%$ , which ignores the volume ratio. Another slip is inverting $R$ ( $V_{L} / V_{U} = 0.2$ ), which gives $\frac{0.8}{1.8} = 44%$ . A third is reporting the lower-phase fraction, $\frac{1}{1 + K R} = 4.76%$ , as the yield.

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GATE 2023 BT Q.49: solution and answer

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