Question

Which of the following reactions is/are spontaneous at standard conditions? (a) \(\mathrm{Ba}(s)+2 \mathrm{Cr}^{3+}(a q) \longrightarrow 2 \mathrm{Cr}^{2+}(a q)+\mathrm{Ba}^{2+}(a q)\) (b) \(\mathrm{Co}^{2+}(a q)+\mathrm{Cu}(s) \longrightarrow \mathrm{Co}(s)+\mathrm{Cu}^{2+}(a q)\) (c) \(2 \mathrm{~S}(s)+4 \mathrm{OH}^{-}(a q) \longrightarrow\) \(\mathrm{O}_{2}(g)+2 \mathrm{~S}^{2-}(a q)+2 \mathrm{H}_{2} \mathrm{O} \quad\) (basic)

Short answer

(a) Ba(s) + 2Cr³⁺(aq) -> 2Cr²⁺(aq) + Ba²⁺(aq) (b) *Provide the second reaction* (c) *Provide the third reaction* Answer: Based on the calculations, the spontaneous reaction(s) under standard conditions is/are reaction (a). Remember to analyze reactions (b) and (c) following the steps provided in the solution to complete the answer.

Step-by-step solution

Identify the oxidation states and half-reactions

We need to determine the oxidation states of the elements involved in each reaction, and then identify the corresponding half-reactions. Let's take reaction (a) as an example: \(\mathrm{Ba}(s)+2 \mathrm{Cr}^{3+}(a q) \longrightarrow 2 \mathrm{Cr}^{2+}(a q)+\mathrm{Ba}^{2+}(a q)\) We see that Ba changes from 0 to +2 (loses 2 electrons), and Cr changes from +3 to +2 (gains one electron). The half-reactions are: Ba: Ba(s) -> Ba²⁺(aq) + 2e⁻ (Oxidation) Cr: 2Cr³⁺(aq) + 2e⁻ -> 2Cr²⁺(aq) (Reduction) Do the same for reactions (b) and (c).

Calculate the standard cell potential (E°) of each reaction

To determine whether a reaction is spontaneous or not, we need to calculate the standard cell potential (E°) of the reactions using the standard reduction potentials of the half-reactions involved. Remember that we need to reverse the sign of the standard potential of the oxidation half-reaction. Look up these values in a standard reduction potentials table. Example for reaction (a) for the half-reactions: Ba: E°(Ba/Ba²⁺) = -2.92 V Cr: E°(Cr³⁺/Cr²⁺) = -0.41 V E°(cell) = E°(reduction) + E°(oxidation) = -0.41 + (-(-2.92)) = 2.51 V Do the same for reactions (b) and (c).

Determine the spontaneity of each reaction

A positive E°(cell) implies that a reaction is spontaneous, while a negative E°(cell) implies that the reaction is not spontaneous. According to our calculations in step 2, the E°(cell) of reaction (a) is positive (2.51 V). This means the reaction is spontaneous. Calculate the cell potential and determine the spontaneity of reactions (b) and (c) using the same approach.

Answer the given problem

Finally, using the results from step 3, determine which of the given reactions are spontaneous at standard conditions. If there are multiple reactions that are spontaneous, list all of them.

Key concepts

Standard Cell Potential

The standard cell potential, abbreviated as E°(cell), is a measure of the voltage that a galvanic cell can produce under standard conditions. Standard conditions imply a temperature of 298 K, all solutes at a concentration of 1 M, and gases at a pressure of 1 atm. The standard cell potential is calculated by taking the difference between the standard reduction potentials of the cathode (reduction half-reaction) and the anode (oxidation half-reaction).
When dealing with a spontaneous redox reaction, the E°(cell) is positive, signifying that the electrical energy can be obtained from the chemical reaction. On the other hand, a negative E°(cell) implies that the reaction requires an input of electrical energy to proceed and is not spontaneous under standard conditions. The E°(cell) provides valuable insight into the reactivity of the substances involved and is central to the study of electrochemistry.
Understanding how to calculate the standard cell potential involves identifying each half-reaction, determining their standard reduction potentials, and applying the proper sign convention. Reversing the sign for the oxidation half-reaction before summing it with the reduction potential is a critical step often overlooked. By clearly identifying oxidation and reduction half-reactions, students can achieve a more accurate calculation and better conceptual understanding.

Redox Reactions

Redox reactions are a type of chemical reaction involving the transfer of electrons between two species. These reactions consist of two parts: oxidation, where electrons are lost, and reduction, where electrons are gained. It's vital to remember the mnemonic 'LEO says GER' - Lose Electrons in Oxidation and Gain Electrons in Reduction.
In each reaction, the substance being oxidized becomes more positive in its oxidation state, while the substance being reduced becomes more negative. Redox reactions are the foundation of various processes such as rusting, combustion, photosynthesis, and even the production of energy in batteries.

• Oxidation is the loss of electrons, and involves the increase of the oxidation number.
• Reduction is the gain of electrons, and involves the decrease of the oxidation number.
• Electrons move from the reducing agent to the oxidizing agent.

Understanding the flow of electrons is crucial for predicting the spontaneity and direction of the redox reactions which in turn helps in numerous practical applications.

Standard Reduction Potentials

Standard reduction potentials, often represented as E°, are the voltages associated with reduction half-reactions under standard conditions. These values are benchmarks that allow chemists to predict the likelihood of a half-reaction to proceed as reduction in comparison with the standard hydrogen electrode, which has an assigned potential of 0.00 volts.
These potentials are fundamental in determining the standard cell potential by providing the necessary values to compute E°(cell). For oxidation half-reactions, their E° values must be inverted as the process is the reverse of reduction. This is a critical concept to understand because it is the differential in potential, the 'voltage', that drives the flow of electrons.
When using standard reduction potentials to solve problems, it's important to:

• Reference values from a standard reduction potential table.
• Change the sign of the oxidation half-reaction's standard potential.
• Sum the potentials to get the overall cell potential.

The higher the standard reduction potential, the greater the substance's tendency to gain electrons and undergo reduction.

Oxidation States

Oxidation states, also known as oxidation numbers, are an indicator of the degree of oxidation (electron loss) or reduction (electron gain) a substance has undergone. They are conceptual charges on atoms in molecules or ions, assuming that the bond is ionic and all the electrons are assigned to the more electronegative atom.
Oxidation states help in balancing redox reactions and in identifying which atoms are oxidized and which are reduced. The rules for assigning oxidation states include:

• The oxidation state of an element in its standard state is zero.
• For monoatomic ions, the oxidation state is equal to the ion's charge.
• Oxygen typically has an oxidation state of -2, while hydrogen is usually +1 (except when bonded to metals where it is -1).
• The sum of oxidation states in a neutral compound is zero, and in an ion, it is equal to the ion's charge.

Many students struggle with oxidation states when they involve unusual bonding or when elements have multiple common oxidation states. Therefore, it's crucial to practice determining oxidation states across different compounds to build confidence and accuracy.