Question

Since salt water at 25°C contains 3.0% NaCl with a density of 1.025 g/mL, what is the minimum pressure required to maintain the flow of pure water through the membrane of a reverse osmosis water purifier?

Answer 1

we have formula P = i x C x R x T

i = vantoff factor = 2 for NaCl since NaCl gives 2 ions ( Na+ and Cl-) when dissolved in water per 1 molecule

R = gas constant = 0.08206 liter atm/molK , T = 25C = 25+273 = 298 K

given 3% NaCl which means 3 g NaCl in 100 g solution

moles of NaCl = mass of NaCl / Molar mass of NaCl = 3 / 58.44 = 0.0513347

volume fo solution = mass of solution / density of solution = ( 100/1.025) = 97.56 ml = 0.09756 L

concentration of NaCl = ( 0.0513347 /0.09756) = 0.5262 mol/L = 0.5262 M

Now we calculate pressure

P = ( 2 x 0.5262 x 0.08206 x 298) = 25.735 atm

this is minimum pressure required to maintain flow of pure water