Heating 2.40 g of the oxide of metal X (molar mass of X=55.9 g / mol ) in carbon monoxide (CO)

Heating 2.40 g of the oxide of metal X (molar mass of...

Heating $2.40 \mathrm{~g}$ of the oxide of metal $\mathrm{X}$ (molar mass of $\mathrm{X}=55.9 \mathrm{~g} / \mathrm{mol}$ ) in carbon monoxide (CO) yields the pure metal and carbon dioxide. The mass of the metal product is $1.68 \mathrm{~g}$. From the data given, show that the simplest formula of the oxide is $\mathrm{X}_{2} \mathrm{O}_{3}$ and write a balanced equation for the reaction.

Key Concepts

Mole Concept

The mole concept is fundamental in chemistry, as it provides a means to convert between the mass of a substance and the number of particles (atoms, molecules, etc.) it contains, using its molar mass. It is crucial when relating mass measurements to the actual quantities involved in chemical reactions.

Stoichiometry

Stoichiometry involves using the quantitative relationships between reactants and products in a chemical reaction. This includes converting masses to moles and using molar ratios derived from a balanced equation to determine how much product is formed or how much reactant is needed.

Empirical Formula Determination

Empirical formula determination is the process of finding the simplest whole-number ratio of elements in a compound. This is achieved by converting the masses of each element in the compound to moles and then simplifying the ratio to the smallest integers.

Chemical Reaction Balancing

Chemical reaction balancing is the practice of ensuring that the number of atoms for each element is the same on both sides of the equation. This is important for upholding the law of conservation of mass, meaning that matter is neither created nor destroyed during a reaction.

Redox Reactions

Redox (reduction-oxidation) reactions involve the transfer of electrons between chemical species, where one substance is reduced and another is oxidized. In many processes, a reducing agent (often carbon monoxide) is used to convert a metal oxide to its pure metal form while producing another byproduct.

Transcript

00:01 So for this problem, we have some unknown metal x that has a molar mass of 55 .9 grams per mole.

00:09 And we want to prove that when this reacts with carbon monoxide, that it forms x203.

00:15 And we are given that the oxide mass is 2 .4 grams.

00:24 And that the mass of the metal is 1 .68 grams.

00:33 So the first thing that we want to do is want to find the moles of metal.

00:37 Do that because we have the mass of the metal and we can divide by the molar mass which we are given as 55 .9 grams per one mole of x and then you multiply this through you get 0 .03 moles of x.

01:00 Now we want to find moles of o.

01:03 Well we first need to find the mass of oxygen if you want to do that and we can find that because we know that the mass of the entire oxide which includes both the metal and the oxygen can be subtracted and we can take out the mass of metal to just get the oxygen.

01:16 So the mass of the oxygen is just 2 .4 minus 1 .68 which gives us a mass of 0 .72 grams of oxygen.

01:30 Now if we just divide by the molar mass of oxygen which is 16 grams per mole, we get 0 .045 woxygen.

01:47 So now that we have the moles of each, we can then find a positive integer ratio that divides these two and can thus find the empirical formula.

01:55 So we have 0 .3 000 .0 moles of x and 0 .045 moles of 0.

02:06 And if we divide these both by 0 .015, then we get two positive integers.

02:17 We get two moles of x and three moles of o so this then proves that the empirical formula must contain two moles of x or x2 and three moles of o or o3 so that is a proof and now we want to balance the equation that represents this entire process well we know as given to us in the problem that the two reactants are x2 or o3 as well as c o you know that our products include just x as well as co2...

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