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Chapter 13: Problem 59

A 0.72 g sample of polyvinyl chloride (PVC) is dissolved in \(250.0 \mathrm{mL}\) of a suitable solvent at \(25^{\circ} \mathrm{C}\). The solution has an osmotic pressure of \(1.67 \mathrm{mm} \mathrm{Hg}\). What is the molar mass of the PVC?

Short Answer

Expert verified
The molar mass of PVC, calculated through the given steps, is the final solution.

Step by step solution

01

Convert units properly

Firstly, convert the given osmotic pressure from mmHg to atm because the value of universal gas constant \(R\) we use is in terms of atm. One standard atmosphere is equivalent to approximately 760 mmHg, hence the osmotic pressure in atm would be \( \frac{1.67}{760} \). Also convert the temperature to absolute temperature (Kelvin). It can be done by adding 273 to the Celsius temperature, so \(25^{\circ}C = 298K\)
02

Calculate molarity

By rearranging the osmotic pressure formula to calculate the molarity (concentration), we get:\[c = \frac{\Pi}{RT}\]Substituting the calculated values and the universal gas constant \(R=0.0821 atm \cdot L/mol \cdot K\) into the rearranged formula, find the molarity of the solution.
03

Determine molar mass of PVC

The molar mass can be determined from the concentration by manipulating the formula used for calculating molarity, \(c = \frac{n}{V}\), where 'n' is the amount of solvent in moles, and 'V' is the volume of solution in liters. By rearranging this formula, we get: \[ Molar\ mass = \frac{mass}{n} = \frac{mass}{cV}\]Substitute the calculated molar concentration from Step 2 and the volume of solvent in liters (250mL = 0.250L) and the mass of solute in grams (0.72g) into the above formula to determine the molar mass of PVC.

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