A sample of an unknown compound is vaporized at 200.°C. The gas produced has a volume of 2230.mL at a pressure of 1.00atm, and it weighs 5.98g.Assuming the gas behaves as an ideal gas under these conditions, calculate the molar mass of the compound. Be sure your answer has the correct number of significant digits.
Question
A sample of an unknown compound is vaporized at 200.°C. The gas produced has a volume of 2230.mL at a pressure of 1.00atm, and it weighs 5.98g.Assuming the gas behaves as an ideal gas under these conditions, calculate the molar mass of the compound. Be sure your answer has the correct number of significant digits.
Solution
To calculate the molar mass of the compound, we can use the ideal gas law equation, which is PV = nRT.
Here, P = pressure = 1.00 atm V = volume = 2230 mL = 2.230 L (since 1L = 1000mL) R = ideal gas constant = 0.0821 L.atm/K.mol T = temperature = 200°C = 473.15 K (since Kelvin = Celsius + 273.15)
First, we need to solve for n, which represents the number of moles. We can rearrange the ideal gas law equation to solve for n:
n = PV/RT
Substituting the given values into the equation:
n = (1.00 atm * 2.230 L) / (0.0821 L.atm/K.mol * 473.15 K) = 0.057 moles
The molar mass of a substance is the mass of one mole of that substance. So, we can calculate the molar mass (M) using the formula:
M = mass / n
Substituting the given mass and the calculated number of moles into the equation:
M = 5.98 g / 0.057 moles = 105 g/mol
So, the molar mass of the compound is 105 g/mol.
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