In most of its ionic compounds, cobalt is either Co(II) or Co(III). One such compound, containing chloride ion and waters of hydration, was analyzed, and the following results were obtained. A 0.256-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 g. A second sample of 0.416 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 g. a. What is the percent composition, by mass, of the compound? b. Assuming the compound contains one cobalt ion per formula unit, what is the formula? c. Write balanced equations for the three reactions described.

Step by step solution

01

1. Finding moles of Chloride ions (Cl-)

To find the moles of Cl- ions, we first need to find the moles of Silver Chloride (AgCl). Given the mass of AgCl formed is 0.308g, we can use the molar mass of AgCl (143.32 g/mol) to find the moles. Moles of AgCl = Mass / Molar Mass Moles of AgCl = \(\dfrac{0.308 g}{143.32 g/mol}\) Now, since the mole ratio of AgCl to Cl- is 1:1, we can assume that the moles of Cl- ions are equal to the moles of AgCl. Moles of Cl- = Moles of AgCl

02

2. Mass of Cl- in the sample

We can now find the mass of Cl- in the 0.256 g sample by multiplying the moles of Cl- with the molar mass of Cl (35.45 g/mol). Mass of Cl- = Moles of Cl- × Molar Mass of Cl

03

3. Mass of waters of hydration

We can find the mass of waters of hydration by subtracting the masses of Co and Cl from the total mass of the compound. Mass of waters of hydration = Total mass of the compound - Mass of Co - Mass of Cl

04

4. Moles of waters of hydration

Now, we will find the moles of waters of hydration by dividing the mass of waters of hydration with the molar mass of water (H2O, 18.02 g/mol). Moles of waters of hydration = Mass of waters of hydration / Molar Mass of H2O

05

5. Percent composition

Now we can find the percent composition by mass of the compound by dividing the mass of each component by the total mass of the compound and multiplying by 100. Percent composition of Cl = (Mass of Cl / Total mass of the compound) × 100 Percent composition of waters of hydration = (Mass of waters of hydration / Total mass of the compound) × 100 Now, we have the percent composition of the ionic compound. #b. Finding the empirical formula#

06

1. Finding moles of Co & Ratio of Co, Cl, H2O

Given the mass of Cobalt(III) oxide (Co2O3) formed in the second sample is 0.145g and its molar mass is 221.11 g/mol. We can find the moles and use the mole ratio to find the moles of Co. Moles Co2O3 = Mass of Co2O3 / Molar Mass of Co2O3. Moles Co = 2 × Moles Co2O3. Now, we can find the ratio of Co to Cl to H2O. Ratio of Co:Cl:H2O = Moles of Co : Moles of Cl- : Moles of waters of hydration

07

2. Simplifying the ratio

We will divide the Co:Cl:H₂O ratio by the smallest value among them to get the empirical formula. Empirical formula of the ionic compound: Co(Cl)_a(Hₒₒ)_b Now, we have found the empirical formula of the compound. #c. Writing the balanced equations#

08

1. First Reaction: Formation of AgCl

The reaction between ionic compound and excess silver nitrate can be written as: Co(Cl)_a(H₂O)_b + a AgNO₃ → a AgCl + Co(NO₃)_a(H₂O)_b

09

2. Second Reaction: Formation of Co(III) oxide

The reaction between ionic compound and excess sodium hydroxide can be written as: Co(Cl)_a(H₂O)_b + a NaOH → Co(OH)_a + a NaCl + b H₂O Upon heating, Cobalt(III) hydroxide decomposes into Cobalt(III) oxide: 2 Co(OH)_a → Co₂O₃ + 3 H₂O

10

3. Third Reaction: Formation of ionic compound

Now, the formation of the ionic compound can be considered as a combination of cobalt ions (Co³⁺), chloride ions (Cl⁻), and water molecules. Co³⁺ + a Cl⁻ + b H₂O → Co(Cl)_a(H₂O)_b

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