What is the degree of ionisation of 0.100 M CH3COOH (K_a = 1.8 x 10^-5) in a solution that is also 0.0500 M in HCl? Use the exact quadratic. Give alpha x 10^3 to two decimals.

JEE Main levelNumerical answerDifficulty 2 of 3ia100

What is the degree of ionisation of $0.100 M$ $CH X_{3} COOH$ ( $K_{a} = 1.8 \times 1 0^{- 5}$ ) in a solution that is also $0.0500 M$ in $HCl$ ? Use the exact quadratic. Give $α \times 1 0^{3}$ to two decimals.

Numerical answer type, tolerance 0.02.

Let

x

[CH X_{3} COO X^{-}]

x (0.0500 + x) / (0.100 - x) = 1.8 \times 1 0^{- 5}

, i.e.

x^{2} + 0.050018 x - 1.8 \times 1 0^{- 6} = 0

, so

x = 3.60 \times 1 0^{- 5} M

α = x /0.100 = 0.00036

, so

α \times 1 0^{3} = 0.36

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