Final answer:
To calculate the molar mass of the unknown gas, we used the ideal gas law and the given values to determine the number of moles, and then divided the mass of the sample by the number of moles, yielding a molar mass of 28.93 g/mol.
Step-by-step explanation:
To calculate the molar mass of the diatomic gas, we can apply the ideal gas law formula, which is PV = nRT. In this formula, P is the pressure of the gas in atmospheres, V is the volume in liters, n is the number of moles of the gas, R is the universal gas constant (0.0821 L·atm/K·mol), and T is the absolute temperature in Kelvin.
First, we will need to convert the units given in the problem: convert the pressure from torr to atmospheres and the volume from mL to L, and convert the temperature from Celsius to Kelvin.
Pressure in atmospheres: 560 torr x (1 atm / 760 torr) = 0.7368 atm
Volume in liters: 125 mL x (1 L / 1000 mL) = 0.125 L
Temperature in Kelvin: 23 C + 273 = 296 K
Using the ideal gas law and rearranging for n (number of moles): n = PV / RT
n = (0.7368 atm * 0.125 L) / (0.0821 L·atm/K·mol * 296 K)
n = 0.00363 moles
Now we can find the molar mass by dividing the mass of the sample by the number of moles:
Molar mass = mass / n = 0.105 g / 0.00363 moles = 28.93 g/mol