Phosgene, a chemical warfare agent used in World War I, consists of 12.41% C, 16.17% O, and 71.69% Cl. 1.00 L of this gas at STP has a mass of 4.42 g. What is the molecular formula of phosgene

Question

Quizplus · Accepted Answer

1 mol of a gas at STP occupies 22.4 L and has a mass of its molar mass in grams. We can use this information to calculate the molar mass of phosgene.
1 L of phosgene at STP has a mass of 4.42 g/1000 mL = 0.00442 g/mL
The density of phosgene at STP is therefore 0.00442 g/mL / 1.25 g/L = 0.00354 g/mL
1 mol of phosgene at STP would occupy 22.4 L and have a mass of 0.00354 g/mL x 22.4 L = 0.079 g
Since the percentages given add up to 100%, the mass of each element can be converted directly to moles:
C: 0.1241 g / 12.01 g/mol = 0.01033 mol
O: 0.1617 g / 16.00 g/mol = 0.01011 mol
Cl: 0.7169 g / 35.45 g/mol = 0.02020 mol
Dividing each element's mole value by the smallest of those values yields a ratio of approximately 1:1:2 (the actual ratio is 1:0.98:1.97 due to rounding errors). This gives the empirical formula COCl2. The molar mass of COCl2 is approximately 98 g/mol which is not the same as the molar mass calculated above for phosgene (0.079 g/mol). We can obtain the molecular formula from the empirical formula by multiplying its subscripts by the smallest integer that gives a molar mass close to the experimental molar mass. This turns out to be approximately 1/0.079 = 12.66. Multiplied by the empirical formula, this gives the molecular formula COCl12.66 which can be rounded to COCl13. Dividing by the smallest integer (13), we get COCl. Therefore, the molecular formula of phosgene is COCl.

Phosgene, a Chemical Warfare Agent Used in World War I