Question

Wastewater discharged into a stream by a sugar refinery contains 3.40 g of sucrose (C12H22O11) per liter. A government-industry project is designed to test the feasibility of removing the sugar by reverse osmosis. What pressure must be applied to the apparatus at 20.°C to produce pure water?

Answer 1

Answer: The pressure that must be applied to the apparatus is 0.239 atm

Explanation:

To calculate the osmotic pressure, we use the equation for osmotic pressure, which is:

$\pi=iMRT$

or,

$\pi=i\times \frac{m_{solute}}{M_{solute}\times V_{solution}\text{ (in L)}}}\times RT$

where,

$\pi$ = osmotic pressure of the solution

i = Van't hoff factor = 1 (for non-electrolytes)

$m_{solute}$ = mass of sucrose = 3.40 g

$M_{solute}$ = molar mass of sucrose = 342.3 g/mol

$V_{solution}$ = Volume of solution = 1 L

R = Gas constant = $0.0821\text{ L atm }mol^{-1}K^{-1}$

T = temperature of the solution = $20^oC=[20+273]K=293K$

Putting values in above equation, we get:

$\pi =1\times \frac{3.40g}{342.3g/mol\times 1}\times 0.0821\text{ L. atm }mol^{-1}K^{-1}\times 293K\\\\\pi =0.239atm$

Hence, the pressure that must be applied to the apparatus is 0.239 atm