Assume a living cell with 0.9% (w/w) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data upto first decimal place only) The cell will :

shrink since solution is 0.45 \%(\omega / \omega) as a result of association of glucose molecules (due to hydrogen bonding)

shrink since solution is 0.5 \%(\omega / \omega)

show no change in volume since solution is 0.9 \%(\omega / \omega)

swell up since solution is 1 \%(\omega / \omega)

Solutions PYQ — JEE Main 2025 · 28 Jan · Shift 2 · Q13 with Solution

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Correct answer: NO OPTION IS CORRECT; THE EXTERNAL SOLUTION IS ABOUT 90.9% (W/W) GLUCOSE, SO THE CELL WILL SHRINK.

The cell contains a $0.9\%$ $(w/w)$ glucose solution.

This means:

So inside the cell, the solution is quite dilute.

The outside solution has equal mole fraction of glucose and water.

That means equal number of moles of glucose and water:

$n_{\text{glucose}} = n_{\text{water}}$

Take:

$1\text{ mol glucose} = 1\text{ mol water}$

Now calculate their masses:

Thus,

$m_{\text{glucose}} = 180\text{ g}$ $m_{\text{water}} = 18\text{ g}$

Total mass of solution:

$180 + 18 = 198\text{ g}$

Therefore, mass percent of glucose is

$\% (w/w) = \frac{180}{198}\times 100$

$= 90.9\% \approx 90.9\%$

So the outside solution is much more concentrated (hypertonic) than the cell contents.

Hence, water will move out of the cell by osmosis.

Therefore, the cell will shrink.

None of the given percentages is correct. The actual outside concentration is about $90.9\%$ $(w/w)$ , so the cell should shrink.

The cell will shrink, but none of the options gives the correct reason/value.

If forced to choose based only on direction of osmotic flow, the statement "shrink" is right, but the quoted percentages in A and B are wrong.

So strictly, no option is correct.