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Chapter 13: Problem 82

A dilute aqueous solution of fructose in water is formed by dissolving $1.25 \mathrm{~g}\( of the compound in water to form \)0.150 \mathrm{~L}$ of solution. The resulting solution has an osmotic pressure of \(112.8 \mathrm{kPa}\) at \(20^{\circ} \mathrm{C}\). Assuming that the organic compound is a nonelectrolyte, what is its molar mass?

Short Answer

Expert verified
The molar mass of fructose is approximately \(186.9 \, \text{g/mol}\), calculated using the given mass, volume, osmotic pressure, and temperature with the osmotic pressure equation.

Step by step solution

01

Convert given values to appropriate units

We need to make sure that all given values have the appropriate units. Mass of fructose: 1.25 g Volume of solution: 0.150 L Osmotic pressure: 112.8 kPa Temperature: 20°C 1. Convert kPa to atm: 1 atm = 101.325 kPa Osmotic pressure in atm: \(112.8 \,\text{kPa} × \frac{1 \,\text{atm}}{101.325 \,\text{kPa}} \approx 1.113 \,\text{atm}\) 2. Convert Celsius to Kelvin: \(T = 20°C + 273.15 = 293.15 \,\text{K}\) Values in appropriate units: Osmotic pressure: 1.113 atm Temperature: 293.15 K
02

Use the osmotic pressure equation to find molar concentration

We will use the osmotic pressure equation to solve for the molar concentration (c): \(Π = cRT\) where: Π = 1.113 atm R = 0.0821 L atm / K mol T = 293.15 K Rearrange the equation to solve for c: \(c = \frac{Π}{RT}\) Now substitute the values: \(c = \frac{1.113 \,\text{atm}}{(0.0821 \,\text{(L atm)}/\text{(K mol})) \times 293.15 \,\text{K}} \approx 0.0446 \frac{\text{mol}}{\text{L}}\) Molar concentration: 0.0446 mol/L
03

Find the molar mass of fructose using the molar concentration

We can calculate the moles of fructose using the molar concentration and the volume of the solution: Moles of fructose = Concentration × Volume Moles of fructose = (0.0446 mol/L) × (0.150 L) ≈ 0.00669 mol Now we will use the mass and moles of fructose to find its molar mass: Molar mass = Mass / Moles Molar mass = (1.25 g) / (0.00669 mol) ≈ 186.9 g/mol Molar mass of fructose: 186.9 g/mol

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