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Gibbs Free Energy & Spontaneity

Phenol associ...

Question

Phenol associates in $C_{6} H_{6}$ to double molecules. A solution of $2$ g of phenol in $100$ g $C_{2} H_{6}$ has its f.pt. lowered by $0.72$ K. $K_{f}$ for $C_{6} H_{6}$ is $5.12$ $K$ $m o l^{- 1} k g$ . Percentage degree of association of phenol is______ (write the integer at tens place, e.g., if percentage degree of dissociation is $x y %$ then answer would be $x$ ) .

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Solution

The molality of solution is $m = \frac{2 g}{94.1 g / m o l \times 0.1 k g} = 0.2125 g / m o l$
$i = \frac{Δ T_{f}}{K_{f} \times m} = \frac{0.72}{5.12 \times 0.2125} = 0.6616$
$i = 1 - \frac{α}{2} = 0.6616$
$α / 2 = 1 - 0.6616 = 0.3384$
$α = 2 \times 0.3384 = 0.6778$
Percentage degree of association of phenol is phenol is $66.78 %$ .

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2.0 g

100 g

{0.72}^{o} C

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