Problem

A laboratory reference book lists the following values of the ion-product constant for water. Temperature (

^{\circ}\!\text{C}

)

K_w

6.8 \times 10^{\! -15}

1.5 \times 10^{\! -14}

2.9 \times 10^{\! -14}

A student needs the neutral pH of water at 35

^{\circ}\!\text{C}

for a simulation, but the value is not tabulated. (a) Using an appropriate numerical method, estimate

K_w

at 35

^{\circ}\!\text{C}

. Clearly outline your reasoning and any assumptions. (b) From the value obtained in part (a), determine the pH of neutral water at 35

^{\circ}\!\text{C}

. (c) Suppose the student mistakenly used the 30

^{\circ}\!\text{C}

value of

K_w

instead of the estimated 35

^{\circ}\!\text{C}

value. Calculate the resulting percent error in the neutral pH and comment on whether the approximation would be acceptable in routine laboratory work.

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