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

140.89 L

Step-by-step 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=(P)/(RT)\\\Rightarrow c_f=(44)/(0.082* 293.15)\\\Rightarrow c_f=1.83M`

For 1 L of sea water we have

`c_f=(c_i)/(1-W)\\\Rightarrow W=1-(c_i)/(c_f)\\\Rightarrow W=1-(1.1)/(1.83)\\\Rightarrow W=0.3989\ L`

In sea water

`(56.2)/(0.3989)=140.89L`

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