The temperature dependence of the ion-product constant of water can be represented by…

CHEMISTRY · Multi-part · A Level · Chemistry · Acids and bases · Acids and bases

Problem

The temperature dependence of the ion-product constant of water can be represented by the empirical expression

\displaystyle \ln K_w = A - \tfrac{B}{T}

where

T

is the absolute temperature in kelvin and

A

and

B

are constants. A set of measurements yields

A = 14.94

and

B = 1.50 \times 10^{4}

K. (a) Derive an explicit formula that gives the pH of neutral water as a function of temperature in kelvin, expressed only in terms of

A

B

, and

T

. Show each algebraic step. (b) Use your formula to calculate the neutral pH at 298 K, and compare it to the commonly cited value of 7.00. Discuss the agreement or discrepancy. (c) Calculate the neutral pH at 373 K (the normal boiling point of water). Comment on the practical implications of your result for acid–base indicators used at high temperatures. (d) The constants

A

and

B

are obtained by fitting data over a limited temperature range. Identify one potential source of systematic error that could arise when extrapolating the expression to temperatures far outside the fitted range.

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