Question

Because osmotic pressures can be quite large, you may wonder whether the approximation made in $equation5.74$is valid in practice: Is ${\mu }_0$really a linear function of $P$to the required accuracy? Answer this question by discussing whether the derivative of this function changes significantly, over the relevant pressure range, in realistic examples.

${\mu }_0\left(T,P_2\right)\approx {\mu }_0\left(T,P_1\right)+\left(P_2-P_1\right)\frac{\partial {\mu }_0}{\partial P}......equation(5.74)$

Short answer

If a solution has high density then it will produces more pressure than the solution of low density.

Step-by-step solution

Given information

We have been given the difference between pressures

Explanation

It does not matter how large the osmotic pressure is ${\mu }_0\left(T,P_2\right)\approx {\mu }_0\left(T,P_1\right)+\left(P_2-P_1\right)\frac{\partial {\mu }_0}{\partial P}\dots \dots \text{equation}(5.74)$,

If the pressure in two parts of the system does not change significantly,

So we can say that the derivative of the function does not change significantly.

Therefore, we can say that an approximation is good enough.