Chapter 20, Problem 31P

Environmental engineers dealing with the impacts of acid rain must determine the value of the ion product of water $K_w$ as a function of temperature. Scientists have suggested the following equation to model this relationship:

$-{\log }_{10}{K}_w=\frac{a}{T_a}+b{\log }_{10}{T}_a+c{T}_a+d$

where $T_a=$ absolute temperature (K), and a, b, c, and d are parameters. Employ the following data and regression to estimate the parameters:

$T_a\left(K\right)$	273.15	283.15	293.15	303.15	313.15
$K_w$	$1.164\times {10}^{-15}$	$2.950\times {10}^{-15}$	$6.846\times {10}^{-15}$	$1.467\times {10}^{-14}$	$2.929\times {10}^{-14}$