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Chapter 13: Problem 78

A dilute aqueous solution of an organic compound soluble in water is formed by dissolving \(2.35 \mathrm{~g}\) of the compound in water to form \(0.250 \mathrm{~L}\) solution. The resulting solution has an osmotic pressure of \(0.605 \mathrm{~atm}\) 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 \(38.3\mathrm{~g/mol}\).

Step by step solution

01

Calculate Temperature in Kelvin

Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius value: \(T = 25 + 273.15 = 298.15\mathrm{~K}\)
02

Calculate Molarity of the Solution

Use the osmotic pressure formula (蟺 = MRT) to calculate the molarity (M) by rearranging it: \(M = \frac{蟺}{RT}\) Substitute the given values of 蟺, R, and T into the formula to calculate the molarity: \(M = \frac{0.605\mathrm{~atm}}{(0.0821\mathrm{~L~atm/mol~K}) (298.15\mathrm{~K})} = 0.0247 \mathrm{~mol/L}\)
03

Calculate Grams per Mole

Use the formula to calculate grams per mole: \[M鈧� = \frac{m}{MV}\] Substitute the mass (m), molarity (M), and volume (V) into the formula to calculate the molar mass: \(M鈧� = \frac{2.35\mathrm{~g}}{(0.0247\mathrm{~mol/L})(0.250\mathrm{~L})} = 38.3\mathrm{~g/mol}\) Therefore, the molar mass of the organic compound is 38.3 g/mol.

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Most popular questions from this chapter

Show that the vapor-pressure reduction, \(\Delta P_{\text {solvent }}\), associated with the addition of a nonvolatile solute to a volatile solvent is given by the equation \(\Delta P_{\text {solvent }}=\) \(X_{\text {solute }} \times P_{\text {solvent }}^{\circ}\)

Two beakers are placed in a sealed box at \(25^{\circ} \mathrm{C}\). One beaker contains \(30.0 \mathrm{~mL}\) of a \(0.050 \mathrm{M}\) aqueous solution of a nonvolatile nonelectrolyte. The other beaker contains \(30.0 \mathrm{~mL}\) of a \(0.035 \mathrm{M}\) aqueous solution of \(\mathrm{NaCl}\). The water vapor from the two solutions reaches equilibrium. (a) In which beaker does the solution level rise, and in which one does it fall? (b) What are the volumes in the two beakers when equilibrium is attained, assuming ideal behavior?

Explain how (a) a soap such as sodium stearate stabilizes a colloidal dispersion of oil droplets in water; (b) milk curdles upon addition of an acid.

A solution contains \(0.115 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) and an unknown number of moles of sodium chloride. The vapor pressure of the solution at \(30^{\circ} \mathrm{C}\) is \(25.7\) torr. The vapor pressure of pure water at this temperature is \(31.8\) torr. Calculate the number of moles of sodium chloride in the solution. (Hint: remember that sodium chloride is a strong electrolyte.)

Calculate the number of moles of solute present in each of the following solutions: (a) \(185 \mathrm{~mL}\) of \(1.50 \mathrm{M}\) \(\mathrm{HNO}_{3}(a q)\), (b) \(50.0 \mathrm{mg}\) of an aqueous solution that is \(1.25 \mathrm{~m} \mathrm{NaCl}\), (c) \(75.0 \mathrm{~g}\) of an aqueous solution that is \(1.50 \%\) sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) by mass.
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