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Chapter 13: Problem 63

What is the osmotic pressure (in atmospheres) of a \(12.36 M\) aqueous urea solution at \(22.0^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
The osmotic pressure of the urea solution is \( 301 \, \mathrm{atm} \).

Step by step solution

01

Conversion of temperature to Kelvin

Temperature must be in Kelvin for the calculation of osmotic pressure. So we convert the given temperature from Celsius \( T = 22.0^{\circ}C \) to Kelvin. In Kelvin, temperature \( T = 22.0 + 273.15 = 295.15K \).
02

Insert values into formula

The osmotic pressure \( \pi \) is calculated using the formula for osmotic pressure \( \pi = i M R T \). Since urea is a nonelectrolyte, the van't Hoff factor \( i \) is equal to 1. The value of the ideal gas constant \( R = 0.0821 \frac{\mathrm{L} \cdot \mathrm{atm}}{\mathrm{mol} \cdot \mathrm{K}} \) is known. The molarity \( M = 12.36 M \) is given in the problem. So, substituting these values into the osmotic pressure formula, we find: \( \pi = 1 \times 12.36 \times 0.0821 \times 295.15 \).
03

Calculate osmotic pressure

Multiplying out, we get \( \pi = 301.03747 \, \mathrm{atm} \). However, to match significant figures with the given data, we should round the result to three significant figures: \( \pi = 301 \, \mathrm{atm} \).

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