Question

Assuming that seawater has a total ion concentration (also known as colligative molarity) of 1.10 M c, calculate how many liters of seawater are needed to produce 56.2 L of fresh water at 20°C with an applied pressure of 44.0 bar.

Answer 1

Answer:

140.89 L

Explanation:

P = Pressure = 44 bar

R = Gas constant = 0.082 L atm/K mol

T = Temperature = 273.15+20 = 293.15 K

W = Volume of water

$c_i$ = Initial ion concentration = 1.1 M

Final concentration is given by

$c_f=\frac{P}{RT}\\\Rightarrow c_f=\frac{44}{0.082\times 293.15}\\\Rightarrow c_f=1.83M$

For 1 L of sea water we have

$c_f=\frac{c_i}{1-W}\\\Rightarrow W=1-\frac{c_i}{c_f}\\\Rightarrow W=1-\frac{1.1}{1.83}\\\Rightarrow W=0.3989\ L$

In sea water

$\frac{56.2}{0.3989}=140.89L$

The amount of water needed to produce the freshwater is 140.89 L