Question

question when 1.87 g of a certain molecular compound x are dissolved in 45.0 g of cyclohexane (c6h12), the freezing - point of the solution is measured to be 4.7 °c. calculate the molar mass of x. if you need any additional information on cyclohexane, use only what you find in the aleks data resource. also, be sure your answer has a unit symbol, and is rounded to 2 significant digits.

Explanation:

Step1: Recall freezing - point depression formula

$\Delta T = K_f\times m$, where $\Delta T$ is the freezing - point depression, $K_f$ is the cryoscopic constant, and $m$ is the molality of the solution. For cyclohexane, $K_f=20.0\ ^{\circ}C/m$. The freezing - point depression $\Delta T$ is given as $4.7\ ^{\circ}C$. First, find the molality $m$.
$m=\frac{\Delta T}{K_f}$
$m = \frac{4.7\ ^{\circ}C}{20.0\ ^{\circ}C/m}=0.235\ m$

Step2: Define molality formula

Molality $m=\frac{n}{m_{solvent}(kg)}$, where $n$ is the number of moles of solute and $m_{solvent}$ is the mass of the solvent in kilograms. The mass of cyclohexane $m_{solvent}=45.0\ g = 0.0450\ kg$. We know $m = 0.235\ m$, so we can find the number of moles of solute $n$.
$n=m\times m_{solvent}$
$n=0.235\ mol/kg\times0.0450\ kg = 0.010575\ mol$

Step3: Calculate molar mass

The molar mass $M=\frac{m_{solute}}{n}$, where $m_{solute} = 1.87\ g$ and $n = 0.010575\ mol$.
$M=\frac{1.87\ g}{0.010575\ mol}\approx177\ g/mol$

Answer:

$180\ g/mol$ (rounded to 2 significant digits)