Chapter 19: Problem 48
How many faradays of electricity are required to produce (a) \(0.84 \mathrm{~L}\) of \(\mathrm{O}_{2}\) at exactly 1 atm and \(25^{\circ} \mathrm{C}\) from aqueous \(\mathrm{H}_{2} \mathrm{SO}_{4}\) solution, (b) \(1.50 \mathrm{~L}\) of \(\mathrm{Cl}_{2}\) at \(750 \mathrm{mmHg}\) and \(20^{\circ} \mathrm{C}\) from molten \(\mathrm{NaCl}\), and (c) \(6.0 \mathrm{~g}\) of Sn from molten \(\mathrm{SnCl}_{2}\) ?
Short Answer
Expert verified
(a) 0.1368 faradays, (b) 0.12374 faradays, (c) 0.10108 faradays.
Step by step solution
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Electrochemistry
Electrochemistry is a branch of chemistry dealing with reactions involving electrical currents and chemical changes. The main idea is the conversion of chemical energy to electrical energy and vice versa. This involves redox reactions where oxidation and reduction processes occur at electrodes. The electrical energy can cause chemical reactions, like splitting water into oxygen and hydrogen gas.
Faraday’s Law of Electrolysis is an essential principle within electrochemistry, stating that the mass of a substance altered at an electrode during electrolysis is directly proportional to the amount of electricity passed through the cell. This law leads us to understand how substances are deposited or dissolved during electrochemical reactions.
The unit of electricity used in this context is the "faraday," equivalent to one mole of electrons or approximately 96485 coulombs. This measurement helps calculate the amount of a substance produced or consumed during an electrolytic process by determining the number of moles of electrons involved.
Faraday’s Law of Electrolysis is an essential principle within electrochemistry, stating that the mass of a substance altered at an electrode during electrolysis is directly proportional to the amount of electricity passed through the cell. This law leads us to understand how substances are deposited or dissolved during electrochemical reactions.
The unit of electricity used in this context is the "faraday," equivalent to one mole of electrons or approximately 96485 coulombs. This measurement helps calculate the amount of a substance produced or consumed during an electrolytic process by determining the number of moles of electrons involved.
Ideal Gas Law
The ideal gas law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of an ideal gas. The formula is given by \(PV = nRT\), where:
It’s particularly useful when dealing with gases produced in electrochemical reactions, as it allows for the computation of the number of moles needed for further reactions or processes. This is critical when calculating the required faradays for producing certain quantities of gases like \(O_2\) or \(Cl_2\).
- \(P\) is the pressure of the gas
- \(V\) is the volume of the gas
- \(n\) is the number of moles
- \(R\) is the ideal gas constant (0.0821 L·atm/mol·K)
- \(T\) is the temperature in Kelvin
It’s particularly useful when dealing with gases produced in electrochemical reactions, as it allows for the computation of the number of moles needed for further reactions or processes. This is critical when calculating the required faradays for producing certain quantities of gases like \(O_2\) or \(Cl_2\).
Electrode Reactions
Electrode reactions are chemical reactions that occur at the interface of an electrode and an electrolyte. They involve the transfer of electrons between substances. Two main types of electrode reactions are oxidation, which occurs at the anode, and reduction, occurring at the cathode.
In the context of electrolysis:
In the context of electrolysis:
- An anode reaction might involve the oxidation of water to produce oxygen gas \( (2H_2O \rightarrow O_2 + 4H^+ + 4e^-) \).
- A cathode reaction could involve the reduction of metallic ions to pure metal, like \( Sn^{2+} + 2e^- \rightarrow Sn \).
Moles Calculation
Calculating moles is fundamental in chemistry to quantify the amount of substance involved in a reaction. A mole represents Avogadro's number of particles (usually atoms or molecules), which is approximately \(6.022 \times 10^{23}\).
In electrolysis problems, such as the ones we've examined, calculating the moles of a gas or a metal is an initial crucial step before determining the number of faradays required. For gases, we often use the ideal gas law, while for metals or solids, we often use the mass and molar mass.
For instance, to find moles of tin \( (\text{Sn}) \), you divide the mass by its molar mass: \( n = \frac{m}{M} \). Similarly, for a gas like \( O_2 \), as we've seen, we rearrange the ideal gas law: \( n = \frac{PV}{RT} \). Once the number of moles is known, you can calculate how many moles of electrons (faradays) the reaction will require based on the stoichiometry of the electrode reactions.
In electrolysis problems, such as the ones we've examined, calculating the moles of a gas or a metal is an initial crucial step before determining the number of faradays required. For gases, we often use the ideal gas law, while for metals or solids, we often use the mass and molar mass.
For instance, to find moles of tin \( (\text{Sn}) \), you divide the mass by its molar mass: \( n = \frac{m}{M} \). Similarly, for a gas like \( O_2 \), as we've seen, we rearrange the ideal gas law: \( n = \frac{PV}{RT} \). Once the number of moles is known, you can calculate how many moles of electrons (faradays) the reaction will require based on the stoichiometry of the electrode reactions.
