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Chapter 13: Problem 82

A dilute aqueous solution of an organic compound soluble in water is formed by dissolving 2.35 g of the compound in water to form 0.250 L of solution. The resulting solution has an osmotic pressure of 0.605 atm at \(25^{\circ} \mathrm{C}\) . Assuming that the organic compound is a nonelectrolyte, what is its molar mass?

Short Answer

Expert verified
The molar mass of the organic compound is approximately 378.71 g/mol.

Step by step solution

01

List the given information

We are given the following information: - Mass of organic compound = 2.35 g - Volume of solution = 0.250 L - Osmotic pressure = 0.605 atm - Temperature = 25°C (298.15 K)
02

Write the osmotic pressure formula

The osmotic pressure (π) can be related to the concentration of the solute (moles of solute per liter of solution) using the formula: \(π = MiRT\) where: - π = osmotic pressure (atm) - M = molarity (moles of solute / L of solution) - i = van't Hoff factor (unitless), which is 1 for a nonelectrolyte - R = ideal gas constant = 0.0821 L atm K⁻¹ mol⁻¹ - T = temperature in Kelvin
03

Calculate the molarity M of the solution

By rearranging the formula from step 2, we can calculate the molarity (M) of the solution: \( M = \frac{π}{iRT} \) Since the compound is a nonelectrolyte, the van't Hoff factor i will be 1. Now, we can plug in the given values: \( M = \frac{0.605 \text{ atm}}{1 \times 0.0821 \frac{\text{L atm}}{\text{K mol}} \times 298.15 \text{ K}} \) M = 0.0248 mol/L
04

Calculate the moles of organic compound in the solution

Now that we know the molarity of the solution, we can calculate the number of moles of organic compound present in the solution using the formula: moles of solute = M × volume of solution moles of solute = 0.0248 mol/L × 0.250 L = 0.0062 mol
05

Calculate the molar mass of the organic compound

Finally, we can determine the molar mass of the organic compound using the formula: molar mass = mass of solute / moles of solute molar mass = 2.35 g / 0.0062 mol = 378.71 g/mol So, the molar mass of the organic compound is approximately 378.71 g/mol.

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Most popular questions from this chapter

\(\mathrm{KBr}\) is relatively soluble in water, yet its enthalpy of solution is \(+19.8 \mathrm{kJ} / \mathrm{mol} .\) Which of the following statements provides the best explanation for this behavior? (a) Potassium salts are always soluble in water. (b) The entropy of mixing must be unfavorable. (c) The enthalpy of mixing must be small compared to the enthalpies for breaking up water-water interactions and K-Brionic interactions. (d) KBr has a high molar mass compared to other salts like NaCl.

(a) Would you expect stearic acid, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{16} \mathrm{COOH},\) to be more soluble in water or in carbon tetrachloride? (b) Which would you expect to be more soluble in water, cyclohexane or dioxane?

At \(35^{\circ} \mathrm{C}\) the vapor pressure of acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO},\) is 360 torr, and that of chloroform, \(\mathrm{CHCl}_{3},\) is 300 torr. Acetone and chloroform can form very weak hydrogen bonds between one another; the chlorines on the carbon give the carbon a sufficient partial positive charge to enable this behavior: A solution composed of an equal number of moles of acetone and chloroform has a vapor pressure of 250 torr at \(35^{\circ} \mathrm{C}\) (a) What would be the vapor pressure of the solution if it exhibited ideal behavior? (b) Based on the behavior of the solution, predict whether the mixing of acetone and chloroform is an exothermic \(\left(\Delta H_{\text { soln }}<0\right)\) or endothermic \(\left(\Delta H_{\text { soln }}>0\right)\) process.

Adrenaline is the hormone that triggers the release of extra glucose molecules in times of stress or emergency. A solution of 0.64 g of adrenaline in 36.0 g of \(\mathrm{CCl}_{4}\) elevates the boiling point by \(0.49^{\circ} \mathrm{C}\) Calculate the approximate molar mass of adrenaline from this data.

Calculate the molality of each of the following solutions: (a) 8.66 g of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) dissolved in 23.6 \(\mathrm{g}\) of carbon tetrachloride \(\left(\mathrm{CCl}_{4}\right),(\mathbf{b}) 4.80 \mathrm{g}\) of NaCl dissolved in 0.350 \(\mathrm{L}\) of water.
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