A binary oxide XmOn is a white, slightly volatile solid that reacts with saturated aqueous Ba(OH)2 t — Stoichiometry and Thermodynamics Chemistry Question
Problem Context
A binary oxide XmOn is a white, slightly volatile solid that reacts with saturated aqueous Ba(OH)2 to give a white precipitate.
A 69.5 mg sample of this oxide is placed in an evacuated 1.00 L container, which is then heated slowly until the solid just vaporizes completely. At this point, the pressure in the container is 20.0 mm Hg and the temperature is 239.7 °C. What is the molar mass of the oxide in the gas phase?
Model Answer
P = [(20.0 mm Hg)/(760 mm Hg/atm)](1.013 bar/atm) = 0.0267 bar
n = PV/RT = (0.0267 bar)(1.00 L)/(0.08314 L bar mol-1 K-1)(512.8 K) = 6.26 × 10-4 mol
M = 0.0695 g/6.26 × 10-4 mol = 111 g mol-1
A 1.00 g sample of the oxide is dissolved in aqueous acid and electrolytically reduced, with elemental X depositing on the cathode. Complete electrolysis requires 58 minutes with a current of 1.00 A. What is the value of n in the formula XmOn?
Model Answer
1.00 g/(111 g mol-1) = 9.01 × 10-3 mol of the oxide
Electrolysis requires (58 min)(60 s/min)(1.00 A) = 3480 C
3480 C/(96500 C/mol) = 0.0361 mol electrons/9.01 × 10-3 mol of the oxide = 4.0
It thus requires 4 mol electrons per mol compound to reduce m X to its elemental form, which corresponds to 2 O atoms per formula unit.
What is the chemical formula of the oxide?
Model Answer
If the oxide has n = 1, then the atomic mass of X = (111 – 32) = 79, X = Se. SeO2 is indeed a white, slightly volatile, acidic oxide, so this is reasonable. If the oxide has n = 2, then the atomic mass of X = 79/2 = 39.5. This is not especially close to any atomic mass, but the closest would be K and Ca. K2O2 is not an oxide (it is a peroxide), and Ca2O2 is not plausible as a volatile molecule and would be a basic oxide, not an acidic one. If n = 3, then the atomic mass of X would be 79/3 = 26.3. Close to Al, but Al3O2 is not a stable oxide, and higher values of n are even worse. So the oxide is SeO2.
Write a balanced net ionic equation for the reaction of the oxide with a saturated aqueous solution of Ba(OH)2.
Model Answer
Ba2+(aq) + 2 OH–(aq) + SeO2(s) → BaSeO3(s) + H2O(l)
or
Ba2+(aq) + 2 OH–(aq) + H2SeO3(aq) → BaSeO3(s) + 2 H2O(l)
The experiment described in part (a) is repeated with a 415.7 mg sample of the oxide, which requires heating to 280.0 °C to just vaporize the solid. What is the standard enthalpy of sublimation of the oxide?
Model Answer
In part (a), a smaller amount of SeO2 was used, and we found the equilibrium vapor pressure at T1 = 512.8 K. Here, using more SeO2 will require a higher temperature to achieve a higher vapor pressure so that a larger mass will fill the same volume:
0.4157 g SeO2/(111.0 g mol-1) = 3.745 × 10-3 mol
P = nRT/V = (3.745 × 10-3 mol)(0.08314 L bar mol-1 K-1)(553.2 K)/(1.00 L) = 0.172 bar
ln(P2/P1) = (–∆H°subl/R)(1/T2 – 1/T1)
∆H°subl = –(8.314 J mol-1 K-1)ln(0.172 bar/0.0267 bar)([1/553.2 K] – [1/512.8 K])–1
∆H°subl = 10900 J mol-1 = 109 kJ mol-1