To solve this problem, we can use the ideal gas law:
PV = nRT
where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the volume to liters and the temperature to Kelvin:
V = 50 cc = 0.05 L
T = 27 + 273 = 300 K
Next, we can rearrange the ideal gas law to solve for the number of moles:
n = PV/RT
where P is pressure in atm, V is volume in liters, R is the gas constant in L·atm/mol·K, and T is temperature in Kelvin.
We need to convert the pressure from cm Hg to atm:
P = 76 cm Hg × 1 atm/76 cm Hg = 1 atm
Plugging in the values:
n = (1 atm) × (0.05 L) / [(0.0821 L·atm/mol·K) × (300 K)]
n = 0.0021 mol
Finally, we can calculate the molar mass using the mass and the number of moles:
molar mass = mass / moles
molar mass = 0.05 g / 0.0021 mol
molar mass = 23.81 g/mol
Therefore, the molar mass of the gas is 23.81 g/mol.