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 \(0.308 \mathrm{~g}\). 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 ion per formula unit, what is the formula? c. Write balanced equations for the three reactions described.

Step by step solution

01

Calculate the moles of silver chloride and chloride ions

Given that the mass of silver chloride formed is \(0.308g\). We have to convert this mass into moles using the molar mass of silver chloride (AgCl), which is \(143.32 g/mol\). Moles of AgCl = \(\frac{0.308g}{143.32g/mol}\) Moles of AgCl = \(0.00215mol\) Since the ratio of AgCl to Cl in the compound is 1:1, the moles of chloride ions (Cl) = Moles of AgCl = \(0.00215mol\)

02

Calculate the moles of cobalt ions from cobalt(III) oxide

Given that the mass of cobalt(III) oxide (Co_2O_3) formed is \(0.145g\). We have to convert this mass into moles using the molar mass of cobalt(III) oxide, which is \(240.80g/mol\). Moles of Co_2O_3 = \(\frac{0.145g}{240.80g/mol}\) Moles of Co_2O_3 = \(0.000602mol\) Since there are 2 Co ions in 1 mole of Co_2O_3, the moles of cobalt ions (Co) = 2 * Moles of Co_2O_3 = \(0.00120mol\)

03

Determine the ratio of cobalt ions to chloride ions

We have moles of cobalt ions (Co) = \(0.00120mol\) and moles of chloride ions (Cl) = \(0.00215mol\). To find the ratio, we need to divide the moles of each ion by the smallest value to get whole numbers. Ratio of Co:Cl = \(\frac{0.00120}{0.00120}\) : \(\frac{0.00215}{0.00120}\) = 1 : 1.79 ≈ 1 : 1.8 Since we cannot have a fraction in the ratio, we will multiply it by 10 to get whole numbers. So, Ratio = 10 : 18

04

Find the percent composition by mass

We will now find the percent composition of the compound by calculating the percentage by mass of Co and Cl. The mass of Co in the second sample = moles of Co * molar mass of Co = \(0.00120mol * 58.93g/mol = 0.0707g\) The mass of Cl in the first sample = moles of Cl * molar mass of Cl = \(0.00215mol * 35.45g/mol = 0.0762g\) The total mass = \(0.416g\) Percent of Co = \(\frac{0.0707}{0.416}\) * 100 = 17.0% Percent of Cl = \(\frac{0.0762}{0.416}\) * 100 = 18.3% Percent of waters of hydration = 100 - (Percent of Co + Percent of Cl) = 100 - (17.0% + 18.3%) = 64.7%

05

Determine the formula of the compound

We now know the empirical formula of Co(x)Cl(y).(z)H_2O, where x:y = 1:1.8, which means CoCl_1(0.8) and the percent composition is 17.0% Co, 18.3% Cl, 64.7% H_2O. Multiplying the ratio by 10, we get CoCl_18.6H_2O as the empirical formula.

06

Write balanced equations for the three reactions

a. Precipitation of silver chloride: CoCl_(1.8)(H_2O)_6 + 1.8AgNO3 → Co(H_2O)_6^(3+) + 1.8[AgCl ↓ + NO3^-] b. Formation of cobalt(III) oxide: 2CoCl_(1.8)(H_2O)_6 + 12NaOH → 2Co(OH)_3 + 12NaCl + 12H2O 2Co(OH)_3 → Co_2O_3↓ + 3H2O c. Overall equation: CoCl_(1.8)(H_2O)_6 + 1.8AgNO3 → Co_2O_3 + 1.8AgCl↓ + 6H2O

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