Answer
$-8.83 k Pa$
Work Step by Step
The differential form can be evaluated as follows:
$dP=\dfrac{\partial P}{\partial V} dV + \dfrac{\partial P}{\partial T} dT$
Take the partial derivatives.
$dP=\dfrac{-8.31 T}{V^2} dV + \dfrac{8.31}{V} dT$
Re-arrange as: $\triangle P \approx \dfrac{-8.31 T}{V^2} \triangle V + \dfrac{8.31 T}{V} \triangle T$
Plug in the given data and we have
$\triangle P \approx \dfrac{-8.31 \times 310}{(12)^2} \cdot (0.3) + \dfrac{8.31}{12} \cdot (-5)$
Hence, we have $\triangle P \approx -8.83 k Pa$