Question

During the decomposition of a binary compound two simple substances were formed: 44.8 grams of metal and 47.04 liters of a non-flammable gas (conditions are normal). Find chemical formula of the reagent. Dear community, of course I tried to solve it myself, so I think I did put some effort. Firstly, I calculated the quantity of substance of the escaped gas:

ν(gas) = V(gas) : Vm(gases) = 47.04 l : 22.4 l/mol = 2.1 mol. I have a strong hypothesis that the escaped gas must have diatomic molecules. We know noble gases have monoatomic molecules, but they can hardly be products of any reaction. So I tried writing my equation as: kMₐXb -----> akM + (bk/2)X₂↑ (Sorry, I have no ideas about how to write a subscript letter b.) After this step, it became more like a game of guessing. I tried to divide the number 44.8 by different quotients of 2.1 over multiple natural numbers: 44.8 : 2.1 = 21.333 — apparently no such element in sign; 44.8 : (2.1 : 2) = 2.666; 44.8 : (2.1 : 3) = 64 — here is at least something good, 64 is copper. However, copper cannot have a valence of six. 44.8 : (2.1 : 4) = 85.333 — rubidium? I am not sure at all if I must continue. May rubidium be the correct M? No clear ideas how to find X though. What am I missing and how to solve my problem? Help really needed.

Answer 1

The calculation suggests that the metal is scandium, as dividing 44.8 grams by 2.1 moles gives an approximate molar mass of 21.33 g/mol. The likely diatomic non-flammable gas is oxygen, and the binary compound from the decomposition could be scandium(III) oxide, Sc₂O₃.

Step-by-step explanation:

To determine the chemical formula of the reagent, you have correctly identified the quantity of substance of the gas produced during the decomposition as 2.1 moles. Now, let's focus on the metal. Since you have 44.8 grams of it, we need to calculate which metal corresponds to that mass when combined with 2.1 moles of gas. The gas has a diatomic molecular structure which is not flammable, suggesting it's likely an element such as oxygen (O₂).

Suppose the gas is indeed O₂, then every 2 moles of gas (O₂) released comes from 2 moles of metal oxide decomposing. Hence, for 2.1 moles of O₂, we'd expect 2.1 moles of metal. Now divide 44.8 grams by 2.1 moles to calculate the molar mass of the metal, which gives you approximately 21.33 g/mol. Looking at the periodic table, the element closest to this atomic mass is scandium (Sc) with an atomic mass around 44.96 g/mol. Therefore, you would expect that the result would be twice the atomic mass of scandium (since the amount of substance of metal would be half the moles of oxygen).

The binary compound could be ScO₂, but since scandium typically forms Sc₂O₃, the actual compound likely decomposing is Sc₂O₃. However, if additional data or context points to a metal with a different mass, you would need to adjust your hypothesis accordingly.