In most of its ionic compounds, cobalt is either Co(II) or...

In most of its ionic compounds, cobalt is either $\mathrm{Co}(\mathrm{II})$ or $\mathrm{Co}(\mathrm{III})$. One such compound, containing chloride ion and waters of hydration, was analyzed, and the following results were obtained. A $0.256-\mathrm{g}$ sample of the compound was dissolved in water, and excess silver nitrate was added. The silver chloride was filtered, dried, and weighed, and it had a mass of $0.308 \mathrm{~g}$. A second sample of $0.416 \mathrm{~g}$ of the compound was dissolved in water, and an excess of sodium hydroxide was added. The hydroxide salt was filtered and heated in a flame, forming cobalt(III) oxide. The mass of cobalt(III) oxide formed was $0.145 \mathrm{~g}$. a. What is the percent composition, by mass, of the compound? b. Assuming the compound contains one cobalt atom per formula unit, what is the molecular formula? c. Write balanced equations for the three reactions described.

In most of its ionic compounds, cobalt is either $\mathrm{Co}(\mathrm{II})$ or $\mathrm{Co}(\mathrm{III})$. One such compound, containing chloride ion and waters of hydration, was analyzed, and the following results were obtained. A $0.256-\mathrm{g}$ sample of the compound was dissolved in water, and excess silver nitrate was added. The silver chloride was filtered, dried, and weighed, and it had a mass of $0.308 \mathrm{~g}$. A second sample of $0.416 \mathrm{~g}$ of the compound was dissolved in water, and an excess of sodium hydroxide was added. The hydroxide salt was filtered and heated in a flame, forming cobalt(III) oxide. The mass of cobalt(III) oxide formed was $0.145 \mathrm{~g}$.
a. What is the percent composition, by mass, of the compound?
b. Assuming the compound contains one cobalt atom per formula unit, what is the molecular formula?
c. Write balanced equations for the three reactions described.

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is the process of ensuring that the number of atoms for each element is equal on both the reactant and product sides of a reaction. This principle reflects the law of conservation of mass and is crucial for accurately applying stoichiometric relationships in chemical reactions, which in turn is essential for quantitative analyses and determining compositions.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions using the conservation of mass and mole ratios derived from balanced chemical equations. By relating measured masses to moles and using known molecular weights, one can deduce the composition and relationships between different species in a reaction.

Molecular Formula Determination

Molecular formula determination involves using the percent composition or relative mass data of the elements in a compound to deduce the simplest whole-number ratio of atoms in the molecule. This often requires combining experimental data from different analyses, such as gravimetric measurements, to establish both the empirical formula and the actual molecular formula.

Percent Composition Analysis

This concept involves determining the mass percentage of each element in a compound by comparing the mass of an individual element (or a derivative compound containing that element) to the total mass of the sample. It is a fundamental method in analytical chemistry used for characterizing unknown compounds and verifying the elemental composition by experimental means.

Gravimetric Analysis

Gravimetric analysis is a quantitative method in analytical chemistry where the amount of an analyte is determined by converting it to a compound of known composition that can be isolated and weighed. In this process, reactions are carried out to yield precipitates or other solid products whose masses are used to infer the moles and hence the mass of the target element in the original sample.

Transcript

00:01 Okay, so in this problem we are given a mystery compound that we know is made of cobalt, chlorine, and waters of hydration.

00:11 Now i used x, y, and z now to indicate generic numbers because we do not know these numbers yet and we're going to use the experiments to obtain those numbers.

00:20 So in my first experiment, i know that i start with 0 .256 grams of my compound and that i precipitate 0 .308 grams of silver chloride.

00:38 Now i know that all of the chloride in this silver chloride is going to correspond that all of the chlorine or chloride ions in my original compound.

00:49 So we can just use stoichiometry for this.

00:52 Now, the molar mass of silver chloride is 143 .32 grams per mole.

01:07 Now i know that in 143 .32 grams of silver chloride, which is the molar mass, i have exactly one mole of chlorine, which is 35 .5 grams of chlorine.

01:23 Now in 0 .308 grams of silver chloride, by proportionality, we can obtain the amount of chlorine that i'm going to have, which is 0 .076 grams of chlorine.

01:41 This is then all of the chlorine that i'm going to have in my original compound.

01:45 Now if i have 0 .076 grams of chlorine in a total compound mass of 0 .256 grams, then i can obtain the percentage mass for chlorine, which is 29 .7 % chlorine.

02:05 So we already know the percentage of chlorine in my compound from the first experiment.

02:10 Now from the second experiment, we're going to form cobalt oxide.

02:20 Now in this case it's cobalt 3 oxide.

02:26 And again, i know that all of the cobalt in my cobalt oxide is going to correspond to the original cobalt in my compound.

02:35 Now in this case, i am starting with 0 .416 grams of my original compound.

02:42 And i'm going to be forming 0 .145 grams of the cobalt oxide.

02:53 The molar mass of cobalt oxide is 165 .86 grams per mole.

03:07 So in 166 .86 grams of cobalt oxide, i know that i have 2 moles of cobalt, which is the equivalent in mass to 117 .86 grams of cobalt.

03:25 Again, this is the mass of 2 moles of cobalt, which i have for every 1 mole of cobalt oxide.

03:31 In 0 .145 grams of cobalt oxide, which is what i form in this experiment, then i can obtain by proportionality 0 .103 grams of cobalt.

03:48 And i know that all of this cobalt corresponds to my original compound.

03:55 So in 0 .103 grams, sorry, i have 0 .103 grams of cobalt in 0 .416 grams of my total compound, which gives me 24 .8 percentage of cobalt.

04:12 So now i know the percentage of chlorine from the previous experiment, and i also know the percentage of cobalt in my compound.

04:22 I know that my compound is made of chlorine, cobalt, and water.

04:27 So all of the remaining percentage is basically going to be water.

04:32 So i know that 100%, which is my total compound, minus 24 .8 minus 29 .7 is going to be equal to the percentage of water in my compound, which is 54 .5%.

04:50 This is going to be the percentage of water in my compound.

04:56 Now if i know, sorry, i made a mistake here, so let me correct.

05:04 The calculation is actually 45 .5%.

05:10 This is the percentage of water in my compound.

05:15 Now we can use the original, the first experiment.

05:19 Remember that in my first experiment, i had a total amount of compound of 0 .256 grams.

05:26 And i know that 0 .455, or 45 .5%, of those 0 .256 grams is going to be water.

05:38 So we just multiply 0 .455 times 0 .256 to get the grams of water.

05:49 And in this case, i get 0 .116 grams of water.

05:54 This is for, again, the first experiment.

05:57 So in the first experiment, i have 0 .116 grams of water coming from my compound.

06:05 Now i know that in 18 grams of water, the molar mass of water is 18 grams per mole.

06:15 I know that in 18 grams of water, i have 2 grams of hydrogen...

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