To find the molar mass of the gas, we can use the ideal gas law:
PV = nRT
where P is the pressure in Pa, V is the volume in m^3, n is the number of moles of gas, R is the ideal gas constant (8.31 J/(mol·K)), and T is the temperature in K.
First, we need to convert the given values to the appropriate units:
12.0 g -> 0.0120 kg
2.8 dm^3 -> 0.0028 m^3
27°C -> 300 K (adding 273 to convert from Celsius to Kelvin)
100 kPa -> 100,000 Pa
Now we can rearrange the ideal gas law to solve for n:
n = PV/RT
n = (100,000 Pa) x (0.0028 m^3) / [(8.31 J/(mol·K)) x (300 K)]
n = 0.001214 mol
Finally, we can calculate the molar mass (M) using the formula:
M = m/n
where m is the mass of the gas (in grams). Since we have the mass in kilograms, we need to multiply by 1000 to convert to grams:
M = (0.0120 kg x 1000 g/kg) / 0.001214 mol
M = 9906.2 g/mol
Therefore, the molar mass of the gas is approximately 9906 g/mol.