Q 13.106P - Chemistry: Molecular Nature Of Matter And Change

Question

Question: wastewater discharged into a stream by a sugar refinery contains 3.55g of sucrose (${\mathbf{C}}_{\mathbf{12}}{\mathbf{H}}_{\mathbf{22}}{\mathbf{O}}_{\mathbf{11}}$) 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  to produce pure water?

Step-by-Step Solution

Answer

Answer

 

Pressure which is greater than the osmotic pressure 0.2498 atm applied to apparatus to produce pure water.

Step 1: Reverse osmosis

 

Reverse osmosis is a method of water filtration that removes impurities from drinking water by using a semi-permeable membrane to trap big impurities and contaminants including chlorine, salt, and sediments.

Step 2: Calculation of molarity

Molarity is defined as the number of moles per liter solution. 

$$\begin{gathered} \mathbf{molarity}\mathbf{=}\frac{\mathbf{moles}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{sucrose}}{\mathbf{volume}\mathbf{ }\mathbf{of}\mathbf{solution}\mathbf{\left(}\mathbf{L}\mathbf{\right)}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\frac{\left(\frac{\mathrm{mass} \mathrm{of} \mathrm{sucrose}}{\mathrm{molar} \mathrm{mass} \mathrm{of} \mathrm{sucrose}}\right)}{\mathbf{volume}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{solution}\mathbf{\left(}\mathbf{L}\mathbf{\right)}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\frac{\left(\frac{3.55g}{342.30g/mol}\right)}{\mathbf{1}\mathbf{L}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0104}\mathit{m}\mathit{o}\mathit{l}\mathbf{/}\mathit{L} \end{gathered}$$

Step 3: calculation of pressure

 

Calculate the reverse osmosis by using equation $\Pi =MRT$. 

Where$\Pi$  is osmotic pressure, M is molarity of solution, R gas constant and T temperature.

The value of R is$0.082 L.atm/mol.K$ .

Temperature can be converted into kelvin

 $$\begin{gathered} T=20+273 \\ =293K \end{gathered}$$

Hence,

 $$\begin{gathered} \Pi =0.0104mol/L\times 0.082L.atm/mol.K\times 293K \\ =0.2498 \end{gathered}$$

 

Thus, when the pressure is greater than the osmotic pressure  is applied to the apparatus, water goes out of solution.