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A sample of sulfur weighing 0.210 $\mathrm{g}$ was dissolved in 17.8 $\mathrm{g}$ of carbon disulfide, $\mathrm{CS}_{2}\left(K_{\mathrm{b}}=2.43^{\circ} \mathrm{C} / m\right) .$ If the boiling point elevation was $0.107^{\circ} \mathrm{C}$ , what is the formula of a sulfur molecule in carbon disulfide?
$\begin{aligned} \text { Number of atoms present } &=\frac{\text { Molecular mass }}{\text { Molar mass }} \\ &=\frac{256 \mathrm{g} \mathrm{mol}^{-1}}{32.066 \mathrm{g} \mathrm{mol}^{-1}} \\ &=8 \end{aligned}$
02:42
Aadit S.
Chemistry 102
Chapter 11
Solutions and Colloids
Solutions
University of Maryland - University College
Brown University
University of Toronto
Lectures
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to determine this formula for the sulfur molecule, we need to know the molar mass associated with this solar, this sulfur molecule. To calculate the molar mass, we need to know the mass of sulfur that was added. This is provided at 0.210 g and we need to know the moles of sulfur that correspond to that mass. To calculate the moles of sulfur that correspond to that mass, we need to use the boiling point elevation equation. Rearrangement of this equation will allow us to solve for the morality of the sulfur in the solution producing the boiling point. The change in boiling point Change in boiling point is .107°C.. They tell us that the solvent carbon di sulfide has a K. B value of 2.43 degrees Celsius per mole al. So we get a morality of 0.440 Mueller. Then what we can do is we can use this morality which has units of moles sulfur per kilogram solvent. to calculate the moles of sulfur. We'll start with the mass of the solvent 17.8 g converted into kilograms by dividing by 1000. Then use morality to convert the kilograms of the solvent into moles of the solute. Then we recognize molar masses to find as grams per mole. So we simply take the grams of the solute divided by the moles of the solute to get the molar mass of the salute, We get to 68 g per mole Because Sulfur has a molar mass of a little bit over 32, this would correspond to a little bit over eight sulfur atoms per sulfur molecule.
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