EXN.1.SL.TZ0.5

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The $p H$ of a solution is given by the formula $p H = - \log_{10} C$ where $C$ is the hydrogen ion concentration in a solution, measured in moles per litre ( ${Ml}^{- 1}$ ).

Find the $p H$ value for a solution in which the hydrogen ion concentration is $5.2 \times 10^{- 8}$ .

[2]

Write an expression for $C$ in terms of $p H$ .

[2]

b.i.

Find the hydrogen ion concentration in a solution with $p H 4.2$ . Give your answer in the form $a \times 10 k$ where $1 \leq a < 10$ and $k$ is an integer.

[2]

b.ii.

Markscheme / solution

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

$p H = - \log_{10} (5.2 \times 10^{- 8}) = 7.29 (7.28399 \dots)$ (M1)A1

[2 marks]

$C = 10^{- p H}$ (M1)A1

Note: Award M1 for an exponential equation with $10$ as the base.

[2 marks]

b.i.

$C = 10^{- 4.2} = 6.30957 \dots \times 10^{- 5}$ (M1)

$6.31 \times 10^{- 5}$ A1

[2 marks]

b.ii.

Examiners’ report

[N/A]

b.i.

[N/A]

b.ii.