Two elements, R and Q, combine to form two binary compounds....

Two elements, $\mathrm{R}$ and $\mathrm{Q}$, combine to form two binary compounds. In the first compound, $14.0 \mathrm{~g}$ of $\mathrm{R}$ combines with $3.00 \mathrm{~g}$ of $\mathrm{Q}$. In the second compound, $7.00 \mathrm{~g}$ of $\mathrm{R}$ combines with $4.50 \mathrm{~g}$ of $\mathrm{Q}$. Show that these data are in accord with the law of multiple proportions. If the formula of the second compound is $\mathrm{RQ}$, what is the formula of the first compound?

Key Concepts

Law_of_Multiple_Proportions

This law states that when two elements form more than one compound, the masses of one element that combine with a fixed mass of the other element are in ratios of small whole numbers. It is foundational to understanding how elements combine in fixed integer ratios and provides evidence for the atomic theory of matter.

Stoichiometry

Stoichiometry involves the quantitative relationships between the amounts of reactants and products in a chemical reaction, and, in the context of compound formation, it refers to determining the ratios in which elements combine. It is used to calculate the empirical formulas of compounds from mass data.

Determination_of_Empirical_Formulas

This concept involves using the mass of each element in a compound to determine the simplest whole number ratio of atoms. By converting mass ratios to mole ratios, one can deduce the empirical formula, which is crucial in validating laws such as the law of multiple proportions.

Transcript

00:01 All right, so we know we have two compounds and they're both made of r and q's.

00:04 I just wrote down right here compound one r and q compound two r and q.

00:08 We just don't know what ratios they are so we could have something like r1 q2 or we could have you know r2 we have no idea or oops that's a 7 so we're gonna try to figure that out right now we have some doubt about these we know that the first compound has let's see has 14 grams of r and it also has has 3 grams of q.

00:33 But you know the second compound has 7 grams of r and 4 .5 grams of q.

00:43 Alright, so we have one last piece of information that's going to help us figure this out.

00:49 We know that when r and q combined in the second compound, repeat in the second compound, that is going to be rq.

01:01 So right here, when these two combine it's going to make rq.

01:08 That's nice because based on that, we know that we have the same proportion of r and q.

01:16 So, for example, i could have one mole of r and one mole of q.

01:20 Two moles of r and two moles of q.

01:23 Now, we don't know anything about this one right here.

01:26 If you notice, r is different and q is different.

01:28 So here's what we're going to do.

01:29 We're going to actually solve for q and then solve for q on both of them.

01:37 So i'm going to go ahead and solve for q on the second one right here.