The wastewater solution from a factory containing high levels of salts needs to

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 0.056 M and 0.190 M at a temperature of 23 C?

Explanation / Answer

The difference of osmotic pressure() of two different concentration solutions is known as applied pressure

We know that, = CRT

where R is gas constant and its value is 0.0821 (atm *L)/(mol* K)

T = 23 +273 = 296 K

C for the solution in first container = 0.056M and C for the solution in second container = 0.190 M

for first container, = 0.056 mol L-1 x 0.0821 atm x L x mol-1 x K-1 x 296 K = 1.36 atm

for second container, = 0.190 mol L-1 x 0.0821 atm x L x mol-1 x K-1 x 296 K = 4.62 atm

Since the applied pressure would be the difference of these two pressures,

So, 4.62 atm - 1.36 atm = 3.26 atm

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