Question

The wastewater solution from a factory containing high levels of salts needs to be diluted before it can be released into the environment. Therefore, two containers of waste solution are separated by a semipermeable membrane and pressure is applied to one container, forcing only water molecules through the membrane and diluting the waste solution in the other container. As dilution continues, higher and higher pressures are needed to counteract the natural tendency for the water molecules to have a net flow back toward the more concentrated solution.

What was the applied pressure at the end of this process if the final concentrations of the solutions were 0.048 M and 0.190 M at a temperature of 23 C?

Answer 1

3.5 atm

Step-by-step explanation:

As stated in the question pressure is required to counteract the natural tendency for water to dilute the more concentrated solution. The difference in concentrations will give us the answer using the osmotic pressure equation.

π = ( n/v) RT where n/v is the molarity (mol/L), R is the gas constant and T is the temperature.

The difference in osmotic pressure of the solutions is:

Δπ = Δ c RT where c is the difference in molar concentrations.

pressure required = Δπ = (0.190 - 0.048) M x 0.821 Latm/Kmol x 298 K

= 3.47 atm