#### A reverse osmosis plant is designed to produce $10 \ \text{m}^3/\text{day}$ of drinking water from seawater containing 35,000 ppm of dissolved salts. The membrane has a rejection coefficient of 0.98 for salt, and the applied pressure is 20 bar. What is the concentration of dissolved salts in the permeate?Option: 1  700 ppm Option: 2 1,400 ppmOption: 3  2,100 ppm  Option: 4  2,800 ppm

The permeate flow rate can be calculated using the water recovery rate, which is defined as the ratio of the permeate flow rate to the feed flow rate: $\text{Water recovery rate }= \frac{\text{Permeate flow rate}}{\text{Feed flow rate}} \times 100%$

Given,

$\\\text{feed flow rate} = 10 \ \text{m}^3/\text{day}, \\ \text{salt concentration in feed }= 35,000 \text{ ppm}, \\ \text{rejection coefficient }= 0.98, \\ \text{and applied pressure = 20 bar.}$

We can calculate the permeate flow rate as:

$\text{Permeate flow rate} = \text{Feed flow rate} \times \text{Water recovery rate}$

$= 10 \times \frac{1 - \text{Rejection coefficient}}{\text{Applied pressure}}$

$= 0.1 \ \text{m}^3/\text{h}$

Using the rejection coefficient, we can calculate the concentration of salts in the permeate as:

$\\\mathrm{C_\text{permeate} = C_\text{feed} \times (1 - \text{Rejection coefficient})}\\\\ \mathrm{C_\text{permeate} = 35,000 \times (1 - 0.98) = 700 \ \text{ppm}}$