[12%] Studtite is a mineral that contains only hydrogen, oxygen, and a metal M. Its empirical formul — Stoichiometry and Gas Laws Chemistry Question
Problem Context
[12%] Studtite is a mineral that contains only hydrogen, oxygen, and a metal M. Its empirical formula is MOx(H2O)y, where x and y are integers.
A 1.0000 g sample of studtite is heated at 520 ºC, which causes it to decompose to molecular oxygen, water vapor, and the solid metal trioxide MO3. The gases from this reaction are collected in a rigid container with a volume of 1.000 L. When this container is maintained at 200.0 ºC, the pressure is 355.0 mm Hg. When the container is cooled to 25.0 ºC, some of the water vapor condenses to the liquid, and the pressure in the container falls to 48.65 mm Hg. The vapor pressure of water at 25.0 ºC is 23.80 mm Hg.
Calculate the number of moles of O2 produced in this reaction.
Model Answer
At 25 ºC, some liquid water is present, so the pressure of water is equal to the vapor pressure, 23.80 mm Hg. Thus the partial pressure of O2 is 48.65 mm Hg – 23.80 mm Hg = 24.85 mm Hg. From the ideal gas law,
n = PV/RT
n = (24.85 mm Hg)(1.000 L)/(62.36 L mol-1 K-1)(298.15 K)
n = 1.337 × 10-3 mol
Calculate the number of moles of H2O produced in this reaction.
Model Answer
At 200 ºC, the total moles of gas are given by
n = (355.0 mm Hg)(1.000 L)/(62.36 L mol-1 K-1)(473.15 K)
n = 0.01203 mol
The number of moles of water vapor = (0.01203 mol total gases) – (1.337 × 10-3 mol O2) = 0.01069 mol.
Calculate the mass of solid MO3 produced in this reaction.
Model Answer
The total mass of gaseous products = (18.032 g mol-1)(0.01069 mol H2O) + (32.00 g mol-1)(1.337 × 10-3 mol O2) = 0.2355 g. Thus 0.7645 g MO3 remains.
What is the identity of the metal M? Support your answer.
Model Answer
The balanced equation for this reaction is:
MOx(H2O)y → y H2O + (x–3)/2 O2 + MO3
Since x is an integer, the smallest amount of O2 that can be produced per mol MO3 is 0.5, or any integer multiple of this could be produced. If x = 4, then 2(1.337 × 10-3 mol) mol MO3 is present, and the molar mass of MO3 is (0.7645 g)/(2.674 × 10-3 mol MO3) = 285.9 g mol-1. This would imply that the atomic mass of M is 285.9 – 3(16.00) = 237.9 g mol-1. This is the atomic mass of U.
If x = 5, then only 1.337 × 10-3 mol of MO3 would be present, and the molar mass of MO3 would be twice as high, and the atomic mass of M would be over twice that of uranium. This is impossible. (Higher values of x would give even higher values of the atomic mass of M.) Therefore M = U. Since x = 4, the 8:1 mol ratio of H2O to O2 produced implies that y = 4 as well.
What is the oxidation state of the metal M in the mineral studtite? Explain your answer.
Model Answer
Naively, one would expect that UO4(H2O)4 would have U(VIII). But this is impossible: since U has only 6 valence electrons, it cannot possibly have an oxidation state greater than +6! The only reasonable formulation is that some of the oxygens in studtite are in the form of peroxide, O2 2–, with an oxidation state of –1 for oxygen (not the –2 of oxide). Since it is unlikely that a strongly oxidizing species such as peroxide would coexist with a reduced oxidation state of uranium, uranium must be in its highest oxidation state, +6. Studtite should then be formulated as UO2(O2)(H2O)4. This mineral and its partially dehydrated form metastudtite, UO2(O2)(H2O)2, are the only known peroxide-containing minerals.