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Question:
An unknown organic compound weighing 29.28 g was placed in a Dumas apparatus and volatized at 312 K. The volume of the gas was found to be 13.4 L. What is the molecular weight of the compound?
Answer:
We need to use Charles's Law to find the volume this amount of gas will occupy at STP:
V1 / T1 = V2 / T2
For our problem:
V1 = volume gas occupies at initial conditions
T1 = temperature of gas at initial conditions
V2 = volume gas occupies at STP
T2 = temperature of gas at STP
Rearrange the equation to solve for V2:
V2 = (13.4 L * 273.15 K) / 312 K
V2 = 11.73 L
Now, determine what fraction of a mole this volume represents:
mol fraction = V2 / Vn
Where:
Vn = volume occupied by 1 mole of gas at STP
mol fraction = 11.73 L / 22.4 L
mol fraction = 0.524
Now, determine the molecular weight of the compound:
MW = 29.28 g / 0.524 mol
MW = 55.88 g/mol
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