Question

In some regions of the southwest United States, the water is very hard. For example, in Las Cruces, New Mexico, tap water contains about 560 mg of dissolved solids per milliliter. Reverse osmosis units are marketed in this area to soften water. A typical unit exerts a pressure of 8.0 atm and can produce 45 L of water per day. a. Assuming that all the dissolved solids are MgCO3, and assuming a temperature of 278C, what total volume of water must be processed to produce 45 L of pure water? b. Would the same system work for purifying seawater? (Assume that seawater is 0.60 M .

Short answer

(a)$v=46.9L$

(b) No

Step-by-step solution

Subpart (a):Step 1:

Calculate the molarity of the purified water from the osmotic pressure equation.

$$\begin{gathered} M=\frac{8.0atm}{2\times 0.08206Latm{K}^{1}mo{l}^1\times 300K} \\ M=0.1625mol/L \end{gathered}$$

Step 2:

Molarity in tap water.

$$\begin{gathered} M=\frac{560\times {10}^{-6}}{84.31g/mol\times 1\times {10}^{-3}L} \\ M=6.642\times {10}^{-3}mol/L \end{gathered}$$

Step 3:

The volume of tap water required to get 45L of purified water.

$$\begin{gathered} V_2=0.595\times V_1 \\ {V}_1=\frac{V_2}{0.595} \\ {V}_1==46.9L \end{gathered}$$

Subpart (b):

Sea water cannot be purified using the same technology since a reverse osmosis system operating at 8 atm pressure can only do so for water with a molarity of less than 0.1625 mol/L.