Question

In an acidic solution, permanganate ion reacts with tin(II) ion to give manganese(II) ion and tin(IV) ion. (a) Write a balanced net ionic equation for the reaction. (b) How many milliliters of \(0.230 M\) potassium permanganate solution are needed to react completely with \(40.0 \mathrm{~mL}\) of \(0.250 \mathrm{M}\) tin(II) chloride solution?

Short answer

The balanced net ionic equation is 5 Sn2+ + 2 MnO4- + 16 H+ -> 5 Sn4+ + 2 Mn2+ + 8 H2O. To react with 40.0 mL of 0.250 M SnCl2, 34.8 mL of 0.230 M KMnO4 solution is needed.

Step-by-step solution

Write the half-reactions

To balance the net ionic equation in acidic solution, write the two half-reactions, first for the reduction of permanganate to manganese(II), and second for the oxidation of tin(II) to tin(IV).

Balance the half-reactions for atoms other than Hydrogen and Oxygen

Ensure that the atoms other than H and O are balanced in each half-reaction. The reduction half-reaction does not need balancing for Mn but the oxidation half-reaction needs to be balanced for Sn. The balanced half-reactions (excluding H and O) are: Reduction: MnO4- -> Mn2+ Oxidation: Sn2+ -> Sn4+

Balance the half-reactions for Oxygen by adding water

Balance the oxygen atoms by adding H2O molecules to the side that needs oxygen. For the reduction half-reaction, add 4 H2O to the right side.

Balance the half-reactions for Hydrogen by adding H+

Balance the hydrogen atoms by adding H+ ions to the side that needs hydrogen. For the reduction half-reaction, add 8 H+ to the left side.

Balance the charges by adding electrons

For the half-reactions to balance, the charge must be equal on both sides. This is done by adding electrons (e-). Add 5 e- to the left side of the reduction half-reaction to balance the charge, and add 2 e- to the right side of the oxidation half-reaction.

Combine the half-reactions

Make the number of electrons lost equal to the number gained by multiplying the half-reactions by appropriate coefficients. Multiply the oxidation half-reaction by 5 and the reduction half-reaction by 2, then combine them to cancel out the electrons and form the balanced net ionic equation.

Confirm the net ionic equation

The final balanced net ionic equation is: 5 Sn2+ + 2 MnO4- + 16 H+ -> 5 Sn4+ + 2 Mn2+ + 8 H2O

Determine the molar ratio of reactants

Use the coefficients of the balanced net ionic equation to find the molar ratio of tin(II) to permanganate. The reaction shows a 5:2 ratio of Sn2+ to MnO4-.

Calculate the moles of tin(II) ion

Calculate the moles of tin(II) ion present in the 40.0 mL of 0.250 M SnCl2 solution using the formula Moles = Molarity x Volume (in liters).

Use the molar ratio to calculate the moles of permanganate needed

Multiply the moles of tin(II) by the molar ratio from step 8 to find the moles of permanganate required.

Calculate the volume of permanganate solution required

Use the moles of permanganate ion needed and its molarity to calculate the volume that contains these moles using the formula Volume (L) = Moles / Molarity. Convert the volume to milliliters by multiplying by 1000.

Key concepts

Balancing Redox Reactions Using the Net Ionic Equation

Understanding the concept of a net ionic equation is essential for solving redox reactions in chemistry. It represents the ions directly involved in the chemical reaction, excluding the spectator ions which do not partake in the reaction.

When writing a net ionic equation, it's useful to start with the full ionic equation and then eliminate the ions that appear unchanged on both sides of the equation. This simplifies the equation to show only the species that change during the reaction, making it much clearer which components are being oxidized and reduced.

In the case of the permanganate ion reacting with the tin(II) ion, the net ionic equation isolates the redox process, focusing on the permanganate and tin ions that undergo a change in oxidation state.

The Half-Reaction Method Simplified

The half-reaction method is a systematic approach for balancing redox equations, particularly useful when dealing with complex reactions in aqueous solutions. It involves breaking down the overall redox reaction into two separate half-reactions—one for oxidation and one for reduction.

Each half-reaction is balanced independently for mass and charge. Afterward, they are recombined, adjusting coefficients to ensure that the number of electrons lost in oxidation is equal to those gained in reduction. This method not only helps maintain order and prevents mistakes in balancing complicated equations but also provides a clear illustration of the electron transfer process that defines redox reactions.

Applying this technique to our example, the permanganate ions are reduced while the tin(II) ions are oxidized, resulting in a clear representation of the electron exchange between the two half-reactions.

Oxidation-Reduction Titration

Oxidation-reduction titration is a powerful analytical method used to determine the concentration of an unknown solution. It relies on the reaction between an oxidizing agent and a reducing agent to reach an equivalence point, which can be monitored using an indicator or an electrode.

The equivalence point signifies that the oxidizing and reducing agents have completely reacted with one another. Knowing the molarity of the titrant—typically a strong oxidizer or reductor—enables the calculation of the molarity of the unknown solution by relating the volume used at the equivalence point to the reaction stoichiometry established though a balanced net ionic equation.

For instance, in the reaction between potassium permanganate and tin(II) chloride, titration helps in determining the precise amount of the permanganate solution necessary to completely react with a known volume of the tin(II) chloride solution.

Understanding Molarity and Volume Relation in Solutions

The relationship between molarity and volume is instrumental in the field of chemistry, especially when preparing solutions or performing titrations. Molarity, defined as moles of solute per liter of solution, indicates the concentration of a solution.

To find the volume of solution required for a reaction, the concept of 'moles = molarity x volume' is applied. To achieve a stoichiometrically correct mixture, you can rearrange the formula to 'volume = moles / molarity'. This is highly significant in titrations where you need to know the exact volume of one reactant to completely react with a given amount of the other.

In our textbook problem, by using the balanced net ionic equation, which tells us the molar ratio of reactants, we can apply this principle to find out how many milliliters of potassium permanganate solution are needed to react with the tin(II) ion.