At 298 K, the solubility of silver chloride in water is $1.434 \times 10^{-3} \mathrm{~g} \mathrm{~L}^{-1}$. The value of $-\log \mathrm{K}_{\mathrm{sp}}$ for silver chloride is \_\_\_\_. (Given mass of Ag is $107.9 \mathrm{~g} \mathrm{~mol}^{-1}$ and mass of Cl is $35.5 \mathrm{~g} \mathrm{~mol}^{-1}$)

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Equilibrium

At 298 K, the solubility of silver chloride in water is

1.434 \times 1 0^{- 3} g L^{- 1}

. The value of

- lo g K_{sp}

for silver chloride is ____.
(Given mass of Ag is

107.9 g mol^{- 1}

and mass of Cl is

35.5 g mol^{- 1}

)

Answer: 10

The molar mass of silver chloride is

107.9 + 35.5 = 143.4 g mo l^{- 1}

, so the molar solubility is

S = \frac{1.434 \times 1 0 ^{- 3}}{143.4} = 1 \times 1 0^{- 5} mol L^{- 1}

. For the dissolution giving one silver ion and one chloride ion,

K_{s p} = S^{2} = (1 0^{- 5})^{2} = 1 0^{- 10}

. Hence

- lo g K_{s p} = 10

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer