SATHEE: Equilibrium Question 757

Equilibrium Question 757

Question: The degree of dissociation of water at $25^{\circ} C$ is $1.9 \times 10^{- 7}$ % and density is 1.0 g $c m^{- 3}$ . The ionic constant for water is

Options:

A) $1.0 \times 10^{- 10}$

B) $1.0 \times 10^{- 14}$

C) $1.0 \times 10^{- 16}$

D) $1.0 \times 10^{- 8}$

Show Answer

Answer:

Correct Answer: B

Solution:

$\underset{(1 - α) c}{H_{2} O}, \to \underset{α c}{H^{+}}, + \underset{α c}{O H^{-}},$

$α = \frac{1.9 \times 10^{- 7}}{100};$ Density of water = $\frac{1.0 g}{c m^{2}}$

$∴ c = \frac{1}{18} \times 1000 = 55.56 m o l e s / l$

$∴ [H^{+}] = 55.56 \times 1.9 \times 10^{- 9} = 1.055 \times 10^{- 7}$

$∴ K_{w} = [H^{+}] [O H^{-}] = {(1.055 \times 10^{- 7})}^{2} = 1.0 \times 10^{- 14}$

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