JEE MAIN - Chemistry (2023 - 11th April Morning Shift - No. 17)

0.004 M K$$_2$$SO$$_4$$ solution is isotonic with 0.01 M glucose solution. Percentage dissociation of K$$_2$$SO$$_4$$ is ___________ (Nearest integer)
Answer
75

Explanation

Given that isotonic solutions have the same osmotic pressure, we equate the osmotic pressures of the K2SO4 and glucose solutions :

$i \times 0.004 \, \text{M} = 0.01 \, \text{M}$

Here, $i$ is the van't Hoff factor, which accounts for the number of ions the compound dissociates into in the solution. Solving this equation for $i$, we get $i = 2.5$.

For the compound K2SO4, which dissociates into 3 ions (2K+ and 1 SO42-), the formula for $i$ is given by

$i = 1 + (n-1)\alpha$

where $n$ is the number of ions the solute dissociates into and $\alpha$ is the degree of dissociation.

Substituting $n=3$ and $i=2.5$ into this formula and solving for $\alpha$ gives

$\alpha = \frac{i-1}{n-1} = \frac{2.5-1}{3-1} = 0.75$

To convert this into a percentage, we multiply by 100, yielding a percentage dissociation of 75%.

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