The lanthanide elements react with oxygen to give,...

The lanthanide elements react with oxygen to give, generally, compounds of the type $\mathrm{Ln}_{2} \mathrm{O}_{3}$ (where Ln stands for a lanthanide element). However, there are interesting exceptions, such as a common oxide of terbium, $\mathrm{Tb}_{\mathrm{x}} \mathrm{O}_{y}$ Given that the compound is $73.945 \%$ Tb, what is its formula? What is the oxidation number of terbium in this compound? Write a balanced equation for the reaction of terbium and oxygen to give this oxide.

Key Concepts

Balancing Chemical Equations

Balancing chemical equations ensures that the law of conservation of mass is satisfied by having equal numbers of each type of atom on both sides of the reaction. This process often requires finding the correct stoichiometric coefficients that balance atoms and charge. Mastery of this technique is essential for accurately representing chemical reactions and for further quantitative analysis in chemistry.

Lanthanide Chemistry

Lanthanide chemistry deals with the properties and reactions of lanthanide elements, which often show typical oxidation states and form oxides with unique stoichiometries. The behavior of lanthanides in oxygen reactions, as well as the variable oxidation states they can adopt, are of particular interest, reflecting the subtle electronic effects and coordination chemistry inherent to these f-block elements.

Empirical Formula Determination from Percent Composition

This concept involves calculating the simplest whole number ratio of atoms in a compound using the mass percentages of its constituents. By converting the percentage of each element to moles (using their respective atomic masses) and then finding the lowest whole number ratio, one can deduce the empirical formula of the compound. This method is fundamental for analyzing unknown compounds in chemistry.

Oxidation Number Assignment

Oxidation numbers indicate the degree of oxidation of an element within a compound, serving as a bookkeeping tool for electrons in redox reactions. Determining the oxidation state in a compound involves applying rules such as the sum of oxidation numbers equaling the overall charge of the compound. This concept is crucial for understanding electron transfer, bonding, and reactivity in chemical systems.

Transcript

00:01 Hello everyone.

00:02 Thanks for joining as i'm going to check, make sure my screen is on, as we talk about empirical formulas and reactions.

00:11 Okay, let's begin.

00:14 I have a problem, and we are given this information.

00:20 We have a substance called it's an oxide of terbium, and i don't know what my subscripts are.

00:27 But i have some information.

00:29 I am told that my terbium.

00:32 Has 73 .945.

00:41 That's the percent of terbium in the oxide.

00:43 Now since there's only two elements in here, 100 minus 73 .945 equals 26 .055 percent oxygen.

01:03 Now let's review really quickly.

01:06 We are going to change our percent to mass, then we're going to use molar mass to go from mass to mole.

01:16 We are going to divide, in this case two, by the smaller of the two moles, divide by the small moles, and if necessary, we will multiply until we have a whole number.

01:33 Let's begin.

01:34 Percent to mass is so easy.

01:37 Change that to a g.

01:38 We now have 100 gram sample.

01:40 Now we're going to divide each of these.

01:43 Let's go to a blue.

01:45 We're going to divide by the molar mass.

01:47 Terbium is 158 .925355.

01:57 And that's grams per mole...