Equations, balancing half reactions

Balancing the chemical equation for a redox reaction by inspection can be a real challenge, especially for one taking place in aqueous solution, when water may participate and we must include HzO and either H+ or OH. In such cases, it is easier to simplify the equation by separating it into its reduction and oxidation half-reactions, balance the half-reactions separately, and then add them together to obtain the balanced equation for the overall reaction. When adding the equations for half-reactions, we match the number of electrons released by oxidation with the number used in reduction, because electrons are neither created nor destroyed in chemical reactions. The procedure is outlined in Toolbox 12.1 and illustrated in Examples 12.1 and 12.2. 

The first step In balancing a redox reaction is to divide the unbalanced equation into half-reactions. Identify the participants in each half-reaction by noting that each half-reaction must be balanced. That Is, each element In each half-reaction must be conserved. Consequently, any element that appears as a reactant In a half-reaction must also appear among the products. Hydrogen and oxygen frequently appear in both half-reactions, but other elements usually appear In just one of the half-reactions. Water, hydronium ions, and hydroxide ions often play roles In the overall stoichiometry of redox reactions occurring in aqueous solution. Chemists frequently omit these species in preliminary descriptions of such redox reactions. 

The balanced half-reactions appear in Example. Balance the overall equation by combining the half-reactions in such a way that electrons cancel. 

Remember that the number of electrons transferred is not explicitly stated in a net redox equation. This means that any overall redox reaction must be broken down into its balanced half-reactions to determine n, the ratio between the number of electrons transferred and the stoichiometric coefficients for the chemical reagents. 

The coefficients of any balanced redox equation describe the stoichiometric ratios between chemical species, just as for other balanced chemical equations. Additionally, in redox reactions we can relate moles of chemical change to moles of electrons. Because electrons always cancel in a balanced redox equation, however, we need to look at half-reactions to determine the stoichiometric coefficients for the electrons. A balanced half-reaction provides the stoichiometric coefficients needed to compute the number of moles of electrons transferred for every mole of reagent. 

There are 250 g of Pb02, and the headlights draw 5.9 A of current. Equation links current with moles of electrons. Moles of electrons and moles of Pb02 are related as described by the balanced half-reaction, determined in Example ... 

This equation provides the link between electrical measurements and amount of electrons, and the balanced half-reactions for the electrolytic process provide the link between the amount of electrons and amounts of chemical substances. Example shows a calculation regarding electrolytic stoichiometry. 

Write balanced half-reactions from the net ionic equation for the reaction between solid aluminum and aqueous iron(in) sulfate. The sulfate ions are spectator ions, and are not included. 

Write balanced half-reactions from the following net ionic equations. 

Predict whether each of the following single displacement reactions will occur. If so, write a balanced chemical equation, a balanced net ionic equation, and two balanced half-reactions. Include the physical states of the reactants and products in each case. 

For the reaction of magnesium metal with aluminum ions, the two balanced half-reactions include different numbers of electrons, 2 and 3. The least common multiple of 2 and 3 is 6. To combine the half-reactions and give a balanced net ionic equation, multiply the balanced halfreactions by different numbers so that the results both include six electrons, as shown below. 

Balance each of the following redox equations by inspection. Write the balanced half-reactions in each case. 

O A silver utensil is said to tarnish when its surface corrodes to form a brown or black layer of silver sulfide. Research and describe a chemical procedure that can be used to remove this layer. Write balanced half-reactions and a chemical equation for the process. 

BALANCING EQUATIONS, WITH HALF-REACTIONS GIVEN... 

Write a balanced half-reaction equation for the oxidation of Mo3+ t0 MoO in acid solution... 

Step 6. Add the two balanced half-reactions together, and cancel electrons and other species that appear on both sides of the equation. 

Half-reactions can be added to produce a net reaction, which is the oxidation-reduction reaction. However, this summation cannot be performed unless the electron numbers are the same on both sides of the reaction by agreement among chemists, electrons are not written into summation reactions. The way in which adjustments are made is to preserve the ratio of coefficients in the individual balanced half-reaction by multiplying all of the participants in an equation by the same number. The goal is to have the same number of electrons on opposite sides of the half-reactions. The electrons will then algebraically cancel when the half-reactions are added. Since the summation equation should not have coefficients divisible by a common factor, it is customary to choose numbers that will yield the least number of electrons for cancellation. 

Balanced equations for half-reactions always include electrons balanced equations for overall reactions never include electrons. 

The general procedure is to balance the equations for the half-reactions separately and then to add them to obtain the overall balanced equation. The half-reaction method for balancing oxidation-reduction equations differs slightly depending on whether the reaction takes place in acidic or basic solution. 

You will learn more about the importance of half-reactions when you study electrochemistry in Chapter 21. For now, however, you can learn to use halfreactions to balance a redox equation. First, look at an unbalanced equation taken from Table 20-3 to see how to separate a redox equation into half-reactions. For example, the following unbalanced equation represents the reaction that occurs when you put an iron nail into a solution of copper(II) sulfate, as shown in Figure 20-8. Iron atoms are oxidized as they lose electrons to the copper(ll) ions. 

Step 5. Add the balanced half-reactions and simplify by canceling or reducing like terms on both sides of the equation. 

Two methods are commonly used to balance redox equations the half-reaction method and the oxidation number method. 

The rules for balancing half-reactions (see Feature 18-1) are the same as those for other reaction types that is, the number of atoms of each element as well as the net charge on each side of the equation must be the same. Thus, for the oxidation of Fe- by MnOj, the half-reactions are... 

The Nernst equation lets us calculate potentials for concentrations other than one molar. The tabulation of standard reduction potentials gives us the value of for the reduction halfreaction. We use the balanced half-reaction and the given concentration ratio to calculate the value of Q. Then we substitute this into the Nernst equation with n equal to the number of moles of electrons involved in the half-reaction. 

The balanced half-reaction shows one mole of electrons, or w = 1. Putting values into the Nernst equation. 

Write a balanced half reaction involving the species/solids of a redox-sensitive element and write the Eh equation that corresponds to that reaction. Define the terms in the Eh equation and know how to plot it on an Eh-pH diagram. 

You can answer these questions by writing the complete, balanced half-reactions for each case. Then, analyse each half-reaction if either H or OH" appear on any side of reaction, the potential of the half-reaction is going to depend on the pH of the solution. Once you have determined this, write down the Nemst equation and see how the potential changes with change in acidity of your solution. If you have problems writing the balanced halfreactions, consult Section 5.1 and worked Example 5.1. 

Again H" ions show up in the balanced half-reaction. Thus, this reaction s potential is going to depend on H" concentration. Writing the Nemst equation ... 

Write balanced half-reactions and Nemst equations for the reduction NO3 to N2 and for N2 to NH3. 

The half-reaction method for balancing redox reactions divides the overall redox reaction into oxidation and reduction half-reactions. Each half-reaction is balanced for atoms and charge. Then, one or both are multiplied by some integer to make electrons gained equal electrons lost, and the half-reactions are recombined to give the balanced redox equation. The half-reaction method is commonly used for studying electrochemistry because... 

To iearn to balance oxidation-reduction equations using half reactions... 

Reduction Equations The Half-Reaction Method for Balancing Oxidation-Reduction Reactions in Aqueous Solutions... 

Balancing Redox Equations Using Half-Reactions... 

Before we combine the equations, the electrons need to be balanced out. So multiplying the balanced half-reaction (I) by 4, we get... 

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