Question

A sample of an unknown compound is vaporized at 160. °C. The gas produced has a volume of 1210. mL at a pressure of 1.00 atm, and it weighs 3.23g. 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.

Answer 1

The molar mass of the unknown compound is calculated using the ideal gas law formula and the provided temperature, pressure, and volume, with the result being 95.0 g/mol after rounding to three significant digits.

Step-by-step explanation:

To calculate the molar mass of the unknown compound, the ideal gas law can be used: PV = nRT, where P is pressure, V is volume, n is number of moles, R is the ideal gas constant, and T is temperature in Kelvins.

First, convert the temperature from Celsius to Kelvin (160 °C + 273.15 = 433.15 K), and use the volume in liters (1210 mL = 1.210 L).

The ideal gas constant (R) is 0.0821 L·atm·K⁻¹·mol⁻¹. Solving for n (moles) gives: n = PV / (RT).

Substituting the known values, n = (1.00 atm)(1.210 L) / (0.0821 L·atm·K⁻¹·mol⁻¹)(433.15 K) = 0.0340 moles.

Finally, the molar mass (MM) is mass (g) divided by moles (mol): MM = 3.23 g / 0.0340 mol = 95.0 g/mol (rounded to three significant digits).