Answer :
Final Answer:
The molar mass of the gas is approximately 40.06 g/mol.
Explanation:
To find the molar mass of the gas, we can use the ideal gas law, which relates the pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, we need to convert the given values to the appropriate units. The pressure is given in torr, so we convert it to atm:
931 torr * (1 atm / 760 torr) = 1.225 atm
The volume is given in milliliters, so we convert it to liters:
220 mL * (1 L / 1000 mL) = 0.220 L
The temperature is given in Celsius, so we convert it to Kelvin:
57 °C + 273.15 = 330.15 K
Now, we can rearrange the ideal gas law to solve for the number of moles (n):
n = (PV) / (RT)
Plugging in the values:
n = (1.225 atm * 0.220 L) / (0.0821 L·atm/(mol·K) * 330.15 K) ≈ 0.0142 moles
Finally, we can calculate the molar mass by dividing the mass of the gas (38.8 mg) by the number of moles:
Molar mass = (38.8 mg / 0.0142 moles) ≈ 40.06 g/mol
So, the molar mass of the gas is approximately 40.06 g/mol.
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