Even though the toxicity of cadmium has become a concern, nickel-cadmium (nicad) batteries are still used commonly in many devices. The overall cell reaction is $$\mathrm{Cd}(s)+2 \mathrm{NiO}(\mathrm{OH})(s)+2 \mathrm{H}_{2} \mathrm{O}(I) \longrightarrow 2 \mathrm{Ni}(\mathrm{OH})(s)+\mathrm{Cd}(\mathrm{OH})_{2}(s)$$ A certain nicad battery weighs \(18.3 \mathrm{~g}\) and has a capacity of 300\. mA \(h\) (that is, the cell can store charge equivalent to a current of \(300 .\) mA flowing for \(1 \mathrm{~h}\) ). (a) What is the capacity of this cell in coulombs? (b) What mass of reactants is needed to deliver \(300 . \mathrm{mA} \cdot \mathrm{h} ?\) (c) What percentage of the cell mass consists of reactants?

Electrochemistry is the branch of chemistry that studies the relationship between electricity and chemical reactions. In a nickel-cadmium (NiCad) battery, the chemical reaction allows the storage and release of electrical energy. The battery includes two electrodes: a cadmium anode (negative electrode) and a nickel oxide hydroxide cathode (positive electrode), with an electrolyte solution between them. During discharge, cadmium reacts with water and nickel oxide hydroxide to form cadmium hydroxide and nickel hydroxide, while releasing electrons. These electrons flow through the external circuit, providing electrical power to a connected device. Understanding electrochemistry is crucial for improving battery performance, including increasing capacity and lifespan.

Stoichiometry involves calculating the quantities of reactants and products in chemical reactions. For a NiCad battery, the overall cell reaction is:
$$\text{Cd}(s) + 2 \text{NiO}(\text{OH})(s) + 2 \text{H}_2 \text{O}(l) \longrightarrow 2 \text{Ni}(\text{OH})_2(s) + \text{Cd}(\text{OH})_2(s)$$
This equation shows that one mole of cadmium reacts with two moles of nickel oxide hydroxide and two moles of water to produce two moles of nickel hydroxide and one mole of cadmium hydroxide. By using stoichiometry, we can determine the mass of each reactant needed for the reaction. For example, to find the mass of cadmium required, we use the molar mass of Cd (112.41 g/mol) and the fact that it takes 0.0056 moles of Cd to produce 1080 coulombs of charge. Applying stoichiometric principles ensures we measure the correct proportions of each chemical involved.

The Faraday constant (F) is a fundamental factor in electrochemistry, representing the amount of electric charge carried by one mole of electrons. It has a value of 96485 coulombs per mole. In a NiCad battery, knowing the Faraday constant allows us to relate the amount of charge (in coulombs) to the number of moles of electrons transferred in the reaction. The formula:
$$ Q = n \times F $$
where Q is the total charge in coulombs and n is the number of moles of electrons. For instance, to find the moles of electrons necessary for the NiCad battery reaction given a charge of 1080 coulombs, we use:
$$ n = \frac{Q}{F} = \frac{1080 \text{ C}}{96485 \text{ C/mol}} \approx 0.0112 \text{ mol} $$
This calculation shows that 0.0112 moles of electrons are involved, and using further stoichiometric relationships, we can find how much of each reactant is required.

Battery capacity indicates how much charge a battery can store and deliver. It is usually measured in milliamp-hours (mA h). For the NiCad battery in question, the capacity is 300 mA h. This means the battery can provide a current of 300 milliamperes for one hour. To convert this to coulombs (C), we use the conversion factor:
1 mA h = 3.6 coulombs
Thus, the battery's capacity in coulombs is:
$$ 300 \text{ mA h} \times 3.6 \text{ C}/\text{mA h} = 1080 \text{ C} $$
Knowing this allows us to understand the total amount of electric charge the battery can store and helps in designing circuits and predicting battery life.

The specific chemical reactions inside a NiCad battery involve the transformation of reactants during discharge and recharge cycles. The key reaction is:
$$ \text{Cd}(s) + 2 \text{NiO}(\text{OH})(s) + 2 \text{H}_2\text{O}(l) \longrightarrow 2 \text{Ni}(\text{OH})_2(s) + \text{Cd}(\text{OH})_2(s) $$
During discharge, cadmium (Cd) forms cadmium hydroxide (Cd(OH)₂) and nickel oxide hydroxide (NiO(OH)) gets reduced to nickel hydroxide (Ni(OH)₂). Each of these transformations involves the transfer of electrons, which creates a flow of electricity. Understanding these reactions is important not only for predicting how much energy can be extracted but also for knowing how to recharge the battery effectively, reversing the chemical changes.