Answer
(a) $V$ = $\frac{5.3}{P}$
(b)
$\frac{dV}{dP}$ = $-0.00212$
The derivative is the instantaneous rate of change of the volume with respect to the pressure at 25 °C.
Its units are $m^3
/kPa$
Work Step by Step
(a)
$P$ = $\frac{k}{V}$
$P$ = $50$
$k$ = $0.106$
so
$k$ = $50(0.106)$ = $5.3$
Thus
$P$ = $\frac{5.3}{V}$
$V$ = $\frac{5.3}{P}$
(b)
$V$ = $\frac{5.3}{P}$
$\frac{dV}{dP}$ = $-\frac{5.3}{P^{2}}$
$\frac{dV}{dP}$ = $-\frac{5.3}{50^{2}}$ = $-0.00212$
The derivative is the instantaneous rate of change of the volume with respect to the pressure at 25 °C. Its units are $m^3
/kPa$
