Three electrochemical cells were connected in series so that...

Three electrochemical cells were connected in series so that the same quantity of electrical current passes through all three cells. In the first cell, $1.15 \mathrm{~g}$ chromium metal was deposited from a chromium(III) nitrate solution. In the second cell, $3.15 \mathrm{~g}$ osmium was deposited from a solution made of $\mathrm{Os}^{n+}$ and nitrate ions. What is the name of the salt? In the third cell, the electrical charge passed through a solution containing $\mathrm{X}^{2+}$ ions caused deposition of $2.11 \mathrm{~g}$ metallic $\mathrm{X}$. What is the electron configuration of $\mathrm{X}$ ?

Key Concepts

Electron Configuration of Transition Metals

Transition metals exhibit characteristic electron configurations, and sometimes these configurations deviate from the expected order due to subtle energetic considerations. In the case of an element that forms a divalent ion and whose atomic mass and deposition data correspond to copper, its actual electron configuration is [Ar] 3d10 4s1, reflecting the unique stability provided by a completely filled d subshell.

Faraday's Law of Electrolysis

This principle states that the amount of chemical change produced by an electric current is directly proportional to the total charge passed through the substance. In electrolysis, the mass of a substance deposited or dissolved at an electrode depends on the number of electrons transferred, which provides the basis for relating deposited mass, molar mass, and the number of electrons involved in the process.

Stoichiometry in Electroplating

In electroplating, the mass of metal deposited is linked to the number of moles of electrons transferred in the reduction of its ions. By converting the given mass of metal into moles and considering the number of electrons required per ion, one can determine not only the electron count but also infer properties such as the oxidation state of the metal in the salt from which it was deposited.

Determination of Oxidation State

The oxidation state of a metal in a compound can be deduced by calculating how many electrons are needed to reduce one mole of its ions to the metallic form. When the same amount of charge is passed through different cells, comparing the moles of metal deposited and the corresponding electrons per metal ion reveals the oxidation number, which in turn affects the formulation of the salt.

Naming of Metal Nitrate Salts

For salts formed with nitrate ions, the overall charge neutrality requires that the metal’s oxidation state is balanced by an appropriate number of nitrate anions. For example, a metal ion that requires the gain of four electrons for reduction would correspond to a salt formula combining one metal ion with four nitrate ions, leading to a name that reflects the specific oxidation state of the metal.

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