Question

What is the molar mass of a gas if 0.281 g of the gas occupies a volume of 125 mL at a temperature 126 °C and a pressure of 777 torr?

a) 32.06 g/mol
b) 40.28 g/mol
c) 54.62 g/mol
d) 68.94 g/mol

Answer 1

To find the molar mass of a gas at non-standard conditions, you must first calculate the number of moles using the Ideal Gas Law with converted units (pressure in atm, volume in L, temperature in K). Then, you can determine the molar mass by dividing the mass of the gas by the calculated number of moles.

Step-by-step explanation:

To determine the molar mass of a gas based on the given conditions, we can use the Ideal Gas Law, which is PV = nRT. Here, P is the pressure in atmospheres (atm), V is the volume in liters (L), n is the number of moles, R is the universal gas constant (0.0821 L·atm/K·mol), and T is the temperature in kelvins (K).

First, we need to convert the given pressure from torr to atm and the volume from milliliters (mL) to liters (L). Then, convert the temperature from degrees Celsius (°C) to kelvins (K) by adding 273.15.

Conversions: 777 torr / 760 = 1.0224 atm, 125 mL = 0.125 L, 126 °C = 399.15 K

Calculations: Using the Ideal Gas Law, we calculate the number of moles (n):

n = PV / RT = (1.0224 atm * 0.125 L) / (0.0821 L·atm/K·mol * 399.15 K)

The number of moles of the gas can then be used to find the molar mass by dividing the mass of the gas by the number of moles:

Molar mass (MM) = mass / n

Rearranging and inserting the given mass of the gas, we can find the molar mass.