Answer :
Final answer:
To find the molar mass of the gas, first convert all the given parameters into SI units. Then, use the ideal gas equation to find the number of moles in the sample. Lastly, calculate molar mass by dividing the mass of the sample by the number of moles.
Explanation:
To calculate the molar mass of the gas, we first need to convert the given parameters into SI units. Thus, we can consider the mass as 38.6 x 10-3 g, volume as 228 x 10-6 m3, the temperature as 55 + 273.15 = 328.15 K (converting from Celsius to Kelvin), and pressure 866 Torr = 1.138 atm (using the conversion 1 Torr = 0.001316 atm).
Now, we can use the ideal gas equation PV = nRT, where P stands for pressure, V for volume, n for number of moles, R for gas constant (0.0821 L.atm.K-1.mol-1), and T for temperature. We know all the variables except the number of moles, so we can rearrange and solve for n as n = PV/RT.
Substituting the given values we find: n = 1.138 * 0.228 / (0.0821 * 328.15). This will give us the number of moles of the gas present in the sample.
To find molar mass, we divide mass by the number of moles (Molar mass = Mass/n). The result of the calculation is the molar mass of the gas in g/mol.
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