Answer :
Final answer:
The molar mass of the gas was calculated using the Ideal Gas Law and found to be approximately 3.92 g/mol. However, there might be a mistake in the calculations as this does not match any of the given options.
Explanation:
To find the molar mass of the gas in question, we can use the Ideal Gas Law equation, PV = nRT, where P is pressure, V is volume, n is the number of moles of the gas, R is the ideal gas constant, and T is temperature. However, we need to rearrange the equation to solve for molar mass (M), which is mass (m) divided by number of moles (n), M = m/n.
In these calculations, we need to stick to a common set of units. Here, we convert the give mass, volume, temperature, and pressure to gram, litre, Kelvin and atm, respectively.
T in Kelvin = 56°C + 273.15 = 329.15 K. Volume in liter = 226 mL / 1000 = 0.226 L. Pressure in atm = 860 torr / 760 = 1.132 atm. Mass in gram = 38.8 mg / 1000 = 0.0388 g.
First, let's find the number of moles (n) using the rearranged ideal gas law equation: n = PV/RT. Substituting P = 1.132 atm, V = 0.226 L, R = 0.08206 L.atm/mol.K (standard gas constant), and T = 329.15 K: n = (1.132 atm * 0.226 L) / (0.08206 L.atm/mol.K * 329.15 K) = 0.0099 mol.
Now, we can calculate the molar mass, M = m/n = 0.0388 g / 0.0099 mol = 3.92 g/mol. However, we have likely made an error in our calculations as none of the given options match this result.
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