Calculate the number of cations and anions in each of the...

Calculate the number of cations and anions in each of the following compounds: (a) $8.38 \mathrm{g}$ of $\mathrm{KBr}$, (b) $5.40 \mathrm{g}$ of $\mathrm{Na}_{2} \mathrm{SO}_{4}$
(c) $7.45 \mathrm{g}$ of $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$.

Key Concepts

Molar Mass and Mole Calculation

This concept involves using the molar mass of a compound to convert a given mass into moles. The number of moles is calculated by dividing the mass of the substance by its molar mass. This step is essential for bridging the gap between the macroscopic measurement of mass and the microscopic count of chemical formula units or ions.

Stoichiometry of Ionic Compounds

Understanding the stoichiometry of ionic compounds is crucial because it determines the ratio in which cations and anions appear in a compound's formula unit. By interpreting the chemical formula, one identifies how many cations and anions are present in each formula unit. This concept allows for the calculation of the total number of each type of ion once the number of formula units is known.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is used to convert the number of moles of a substance to the actual number of particles, such as ions, molecules, or atoms. This fundamental constant bridges the mole concept and the counting of discrete particles, making it possible to determine the number of ions present in a given sample of an ionic compound.

Transcript

00:01 So for this problem, we want to find the number of cations and anions in each of these compounds.

00:06 And for part a, we have 8 .38 grams of kbr.

00:16 The first thing that we want to do is we want to find the molar mass of that kbr.

00:20 So we have one potassium atom, or 1k, which is 39 .10.

00:30 And then finally, a bromine, which has an atomic mass of 79.

00:36 We add those things together, we get 119 .00 grams per mole.

00:44 So now we can then find our overall number of cations and anions and kbr.

00:51 We have 8 .38 grams of kbr.

00:56 We can then multiply this into moles, kbr, by dividing by the molar mass.

01:06 And now is our multiple conversion.

01:08 So let's first do cat ions.

01:11 So the cation in this compound is k plus.

01:17 And so the multiple ratio of k plus to kbr is one to one because there's only one potassium ion and kbr.

01:25 So we get this as our multiple ratio.

01:34 And then finally we just multiply by avogadra's number to get the number of actual molecules.

01:40 So one mole of k plus corresponds to 6 .02 times 10 to the 23 molecules.

01:49 Or ions of k plus.

01:51 And when we multiply that out, we will get 4 .24 times 10 to be 22 k plus ions or cations.

02:05 Now for anions.

02:07 Well, we just did the exact same setup as we did for the cations.

02:11 We have 8 .38 grams of kvr.

02:17 And we divide by the molar mass.

02:25 Now for the multiple ratio.

02:27 Well, our anion is br myons.

02:29 And there's only 1 br minus per every mole of kbr, so the multiple ratio is 1 to 1.

02:40 Then finally we multiply by avogadro's number, as before, and we'll get that same as part, the first part for the cat ions, there's 4 .24 times 10 to the 22 br minus ions or n ions.

03:07 So now we move on to part b.

03:10 And for part b, we are given 5 .40 grams of na2 s -o -4.

03:22 So the first step is going to be finding the molar mass with sodium sulfate.

03:27 So we have two moles of sodium, the two atoms of sodium, each of which are 22 .99.

03:35 Sulfur, which is 32 .07.

03:39 And finally, four oxygens, each of which are 16 .00.

03:43 So when we multiply these two together, we'll get that the molar mass is 142 .04 grams per mole.

03:56 So now that we have the molar mass, we can then do some conversions to find first cations.

04:02 And the cations here is the n -a -plus ion.

04:06 So we'll keep that in mind...

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