Question

A quantity of $0.300\mathrm{g}$ of copper was deposited from a ${\mathrm{CuSO}}_4$ solution by passing a current of $3.00\mathrm{A}$ through the solution for 304 s. Calculate the value of the Faraday constant.

Short answer

The Faraday constant is approximately 96500 C/mol.

Step-by-step solution

Calculate Moles of Copper Deposited

The molar mass of copper (Cu) is approximately $63.55\text{g/mol}$. We can calculate the moles of copper deposited using the formula: $\text{moles}=\frac{\text{mass}}{\text{molar mass}}$. Thus, $\text{moles of Cu}=\frac{0.300\text{g}}{63.55\text{g/mol}}\approx 0.00472\text{mol}$.

Determine the Charge Required to Deposit Copper

For copper, ${\mathrm{Cu}}^{2+}+2e^{-}\to \mathrm{Cu}$, meaning 2 moles of electrons are needed to reduce 1 mole of copper ions. Thus, the charge required is $0.00472\text{mol}\times 2=0.00944\text{mol of electrons}$.

Calculate the Total Charge Flow in Coulombs

The total charge $Q$ that flowed through the solution is calculated using the formula $Q=I\times t$, where $I$ is the current in amperes and $t$ is the time in seconds. Therefore, $Q=3.00\text{A}\times 304\text{s}=912\text{C}$.

Calculate the Faraday Constant

The Faraday constant $F$ is the total charge required to deposit one mole of electrons. Thus, the Faraday constant is calculated as $F=\frac{Q}{n}$, where $Q$ is the total charge and $n$ is the moles of electrons. Therefore, $F=\frac{912\text{C}}{0.00944\text{mol}}\approx 96500\text{C/mol}$.

Key concepts

Electrochemistry Basics

Electrochemistry is the study of chemical reactions that involve the movement of electrons, which leads to the conversion between chemical energy and electrical energy. It plays a crucial role in processes like electroplating, batteries, and fuel cells. In electrochemical reactions, there are two distinct sites where reactions occur: the anode, where oxidation happens, and the cathode, where reduction takes place.

Understanding these processes is vital for calculating how elements, like copper, can be deposited or removed from solutions. In electroplating, for example, ions from a solution are reduced and deposited onto a surface, forming a thin layer of metal.

The efficiency and rate of these reactions depend on several factors, including the type of metal, the current applied, and the duration of the reaction.

Copper Deposition

Copper deposition is a specific application of electrochemistry where copper ions (${\text{Cu}}^{2+}$) in a solution gain electrons and are transformed into solid copper metal. This process is represented by the equation: ${\text{Cu}}^{2+}+2e^{-}\to \text{Cu}$.

During this reaction, electrons are transferred to the copper ions, reducing them to form solid copper. This process is crucial not only in electroplating but also in processes like copper refining.

The quality of the deposited copper layer depends on the precise control of several factors, including current density, temperature, and solution composition.

Understanding Coulombs

Coulombs measure the quantity of charge in electrical circuits. One coulomb is equivalent to the charge of approximately 6.242 x 10^18 electrons. In electrochemistry, coulombs help quantify the amount of electric charge used in reactions.

To find out how much charge is used during electroplating, the formula $Q=I\times t$ is used, where $Q$ is the charge in coulombs, $I$ is the current in amperes, and $t$ is the time in seconds.

For example, if you pass a current of $3.00\text{A}$ for $304\text{s}$, you calculate the total charge as: $Q=3.00\text{A}\times 304\text{s}=912\text{C}$.

Molar Mass Explained

Molar mass is a fundamental concept that refers to the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It allows chemists to convert between the mass of a substance and the moles of the substance, which is crucial for balancing chemical equations and calculating reactant and product masses.

For copper, the molar mass is approximately $63.55\text{g/mol}$. This means that one mole of copper atoms weighs 63.55 grams.

In the context of copper deposition, calculating the moles from a given mass helps determine how much copper can be deposited from a solution and how many electrons are involved in the process.

Basics of Mole Calculation

Mole calculations allow us to quantify the amount of substance used or produced in a chemical reaction, using the concept of moles, which are based on Avogadro's number (approximately 6.022 x 10^23).

To calculate moles, you use the formula: $\text{moles}=\frac{\text{mass}}{\text{molar mass}}$. For example, if you have $0.300\text{g}$ of copper, you use copper's molar mass (63.55 g/mol) to find the moles: $\text{moles of Cu}=\frac{0.300\text{g}}{63.55\text{g/mol}}\approx 0.00472\text{mol}$.

Knowing the number of moles is essential for determining how much of other substances will interact with it, and for calculating the Faraday constant, which represents the charge per mole of electrons.