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Chapter 12: Problem 88

A 262-mL sample of a sugar solution containing \(1.22 \mathrm{~g}\) of the sugar has an osmotic pressure of \(30.3 \mathrm{mmHg}\) at \(35^{\circ} \mathrm{C}\). What is the molar mass of the sugar?

Short Answer

Expert verified
The molar mass of the sugar is approximately 778 g/mol.

Step by step solution

01

Convert All Measurements To Appropriate Units

Before applying the formula, ensure that all the given measurements are in appropriate units. The 262 mL of the solution should be expressed in liters, which equals 0.262 L. The 30.3 mmHg pressure should be converted to atmospheres, which is approximately 0.0398 atm. The temperature in Celsius must be converted to the Kelvin scale by adding 273 to 35°C, yielding 308K.
02

Apply the Osmotic Pressure Formula

The osmotic pressure formula is rearranged to calculate molar concentration (C): \(C = \Pi / RT\), which gives a result equal to 0.0398 atm / (0.0821 L.atm/mol.K * 308 K) = 0.00157 mol/L.
03

Calculate the Molecular Weight of Sugar

Now that we have the molar concentration (C) and we know the mass of the sugar in grams (1.22 g), we can determine the molecular weight by dividing the mass of the sugar by the amount in moles. That is \(Molecular Weight = 1.22 g / 0.00157 mol\). This results in a molar mass of approximately 778 g/mol.

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