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Chapter 11: Problem 88

A water desalination plant is set up near a salt marsh containing water that is 0.10\(M \mathrm{NaCl}\) . Calculate the minimum pressure that must be applied at \(20 .^{\circ} \mathrm{C}\) to purify the water by reverse osmosis. Assume NaCl is completely dissociated.

Short Answer

Expert verified
The minimum pressure that must be applied at 20°C to purify the water by reverse osmosis is approximately 2.395 atm.

Step by step solution

01

Convert temperature to Kelvin

First, we need to convert the given temperature from Celsius to Kelvin. The conversion formula is: \[K = °C + 273.15\] Given the temperature in Celsius, 20°C, we can calculate the temperature in Kelvin: \[K = 20 + 273.15 = 293.15\]
02

Calculate the osmotic pressure

Now, using the formula for osmotic pressure (\(π = CRT\)), we can calculate the osmotic pressure required to purify the water: - \(C = 0.10 \: M\) - \(R = 0.0821 \: \frac{L \cdot atm}{mol \cdot K} \) - \(T = 293.15 \: K\) \[π = (0.10 \: M)(0.0821 \: \frac{L \cdot atm}{mol \cdot K})(293.15 \: K)\]
03

Calculate the minimum pressure

Now, we just need to perform the multiplication: \[π = 2.395 \: atm\] The minimum pressure that must be applied at 20°C to purify the water by reverse osmosis is approximately 2.395 atm.

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