A weak monobasic acid in 0.1 M solution has pH 3.00 (so K_a may be taken as 1.0x10^-5). Solving the quadratic exactly, the pH of its 0.001 M solution is nearest to

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A weak monobasic acid in $0.1 M$ solution has pH 3.00 (so $K_{a}$ may be taken as $1.0 \times 1 0^{- 5}$ ). Solving the quadratic exactly, the pH of its $0.001 M$ solution is nearest to

x^{2} + K_{a} x - K_{a} c = 0

with

K_{a} = 1 0^{- 5}

c = 1 0^{- 3}

x = (- 1 0^{- 5} + 1 0^{- 10} + 4 \times 1 0^{- 8}) /2 = 9.512 e - 05 M

, so

pH = 4.02

. The approximation

K_{a} c

gives 4.00, because it ignores that the acid is about 9.5% ionised at this dilution.