A transition metal compound contains a cobalt ion, chloride...

A transition metal compound contains a cobalt ion, chloride ions, and water molecules. The $\mathrm{H}_{2} \mathrm{O}$ molecules are the ligands in the complex ion and the $\mathrm{Cl}^{-}$ ions are the counterions. $\mathrm{A}$ $0.256-\mathrm{g}$ 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 $0.145 \mathrm{~g}$. What is the oxidation state of cobalt in the complex ion and what is the formula of the compound?

Key Concepts

Coordination Compound Structure

Coordination compounds consist of a central metal ion surrounded by a set of bound molecules or ions called ligands, along with counterions to balance the overall charge. Understanding the separation between the coordination sphere (inner?sphere ligands) and the counterions is crucial for analyzing the compound’s chemical behavior and reactivity.

Ligand Behavior and Types

Ligands are molecules or ions that donate electron pairs to the metal center, forming coordinate bonds. In many complexes, neutral molecules (like water) act as ligands while other ions (such as chloride) can remain outside the coordination sphere as counterions, which affects both the compound’s charge and its reactivity in subsequent chemical analyses.

Precipitation Analysis for Ion Determination

Precipitation analysis is an analytical technique used to identify and quantify specific ions in a compound. By reacting the compound with a reagent that forms an insoluble precipitate with one of the ions (like chloride forming silver chloride), one can determine the amount of that ion present and thus deduce aspects of the compound’s stoichiometry.

Stoichiometric Calculations

Stoichiometry involves using mass and mole relationships from experimental data to deduce the ratios of components in a compound. By measuring the masses of precipitates or products and converting these to moles, one can establish the empirical formula and deduce the number of ions or ligands per metal center in the coordination compound.

Oxidation State Determination in Complexes

Determining the oxidation state of the central metal ion in a coordination compound requires balancing the charges of all components — the metal ion and its attached ligands and counterions. By using both the known charges of the ligand units and the overall charge neutrality of the compound, one can deduce the oxidation state of the metal, which is key to predicting its chemical behavior.

Transcript

00:01 Okay, so in this problem we are given a mystery compound, but we know that compound is made of cobalt, we're going to just say x, chloride ions, y, and we also know that we have water molecules of hydration, so we're just going to use z for the water.

00:20 And we're asked to find the oxidation state of cobalt and the formula of the compound.

00:27 So what we're going to do here is simply use the experiments to get the relative masses of each one of the compounds, and with that we're going to do an empirical formula calculation.

00:39 Okay, so let's start with writing some useful information that we're going to use.

00:44 I'm going to write here the molar mass of silver chloride.

00:50 The molar mass of silver chloride is 143 .32 grams per mole.

00:58 I'm going to also write the molar mass of cobalt 3 oxide, which is 165 .86 grams per mole.

01:09 The molar mass of water, which is 18 grams per mole.

01:19 We're going to be using these for the problem, so that's why i'm writing those.

01:23 Okay, so we have the first experiment where 0 .256 grams of the compound is reacted with silver nitrate and we form silver chloride.

01:34 We obtain a mass of 0 .308 grams of silver chloride.

01:38 Now looking at the silver chloride formula, we know that in one mole of silver chloride we have one mole of chlorine.

01:52 Now one mole of silver chloride, given the molar mass, is 133 .32 grams of silver chloride, and in one mole of silver chloride we have one mole of chlorine, which is 35 .5 grams.

02:06 That is the molar mass of chlorine.

02:08 Now we can use proportionality and say that in 0 .308 grams of silver chloride, which is the amount that we get in the first experiment, we can obtain the amount of chlorine corresponding to that amount.

02:23 And that's going to be 0 .076 grams of chlorine.

02:29 Now these are going to be the grams of chlorine present in the silver chloride of my first experiment, and we can also infer that all of the chlorine coming in that silver chloride is the chlorine that was originally present in my mystery compound.

02:46 So i also know that i start with 0 .256 grams of my compound, and i know that this is the chlorine present in that compound.

02:59 So we can calculate the percentage of chlorine in the compound to be 0 .076 grams of chlorine in 0 .256 grams of the compound times 100, and we're going to get that the percentage of chlorine in my compound is 29 .7%.

03:20 So that's the percentage of chlorine in my original.

03:23 Now we're going to do the same for the cobalt.

03:28 We are told that we do a second experiment, and in that second experiment we react 0 .416 of the compound, and we form 0 .145 grams of cobalt oxide.

03:44 So in one mole of cobalt oxide i have two moles of cobalt.

03:56 One mole of cobalt oxide i have two moles of cobalt.

04:01 So the molar mass of cobalt oxide is 165 .86.

04:12 In 165 .86 grams of cobalt oxide, which is one mole, i have two times the molar mass of cobalt, which is 117 .86 grams of cobalt, and this is of cobalt oxide.

04:31 Now with proportionality i know that in 0 .145 grams of cobalt oxide, which is what i form in the experiment, i can calculate x to be 0 .103 grams of cobalt...

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