Question

a sample of an unknown compound is vaporized at 110. °c. the gas produced has a volume of 1090. ml at a pressure of 1.00 atm, and it weighs 1.75 g. assuming the gas behaves as an ideal gas under these conditions, calculate the molar mass of the compound. round your answer to 3 significant digits.

Explanation:

Step1: Convert units

Convert volume to liters ($V = 1090\ mL=1.090\ L$), temperature to Kelvin ($T=(110 + 273.15)\ K = 383.15\ K$), and use the ideal - gas constant $R = 0.0821\ L\cdot atm/(mol\cdot K)$ and pressure $P = 1.00\ atm$.

Step2: Use the ideal - gas law $PV=nRT$ to find the number of moles $n$.

$n=\frac{PV}{RT}=\frac{1.00\ atm\times1.090\ L}{0.0821\ L\cdot atm/(mol\cdot K)\times383.15\ K}$
$n=\frac{1.090}{0.0821\times383.15}\ mol$
$n=\frac{1.090}{31.456615}\ mol\approx0.03465\ mol$

Step3: Calculate the molar mass $M$.

The mass of the sample $m = 1.75\ g$. Molar mass $M=\frac{m}{n}$.
$M=\frac{1.75\ g}{0.03465\ mol}\approx50.5\ g/mol$

Answer:

$50.5\ g/mol$