Answer :
The molar mass of the gas is 4.31 g/mol
The Ideal Gas Law equation: PV = nRT. This equation relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of a gas.
We can rearrange this equation to solve for the number of moles of gas (n) using the formula:
n = PV/RT
where P is the pressure in atm, V is the volume in liters, R is the gas constant (0.08206 Latm/molK), and T is the temperature in Kelvin.
Once we have calculated the number of moles of gas, we can find the molar mass of the gas using the formula:
molar mass = mass / moles
where mass is the mass of the gas in grams and moles is the number of moles of gas.
First, we need to convert the given values to the appropriate units:
mass = 38.8 mg = 0.0388 g
volume = 224 mL = 0.224 L
temperature = 54°C = 327.15 K (add 273.15 to convert from Celsius to Kelvin)
pressure = 884 torr = 1.16 atm (divide by 760 to convert from torr to atm)
Next, we can plug in the values into the Ideal Gas Law equation:
n = (1.16 atm) x (0.224 L) / (0.08206 Latm/molK x 327.15 K)
n = 0.009 mol
Finally, we can calculate the molar mass of the gas:
molar mass = 0.0388 g / 0.009 mol
molar mass = 4.31 g/mol
Therefore, the molar mass of the gas is approximately 4.31 g/mol.
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