Which Of The Following Reactions Will Occur Spontaneously As Written

The spontaneity of a chemical reaction, whether it will occur naturally without external influence, is a fundamental concept in thermodynamics. Predicting spontaneity involves understanding Gibbs Free Energy, electrochemical series, and standard reduction potentials. This article delves into the criteria for determining spontaneity, providing practical examples and explanations to help you confidently predict whether a reaction will proceed as written.

Understanding Spontaneity: The Basics

A spontaneous reaction is one that favors product formation under the conditions in which the reaction is occurring. In thermodynamics, spontaneity is determined by the change in Gibbs Free Energy (ΔG). The Gibbs Free Energy combines enthalpy (ΔH), which relates to the heat absorbed or released, and entropy (ΔS), which measures disorder or randomness.

• ΔG < 0: Reaction is spontaneous (favors product formation).
• ΔG > 0: Reaction is non-spontaneous (requires energy input).
• ΔG = 0: Reaction is at equilibrium.

The equation that relates these variables is:

ΔG = ΔH - TΔS

Where:

• T is the temperature in Kelvin.

However, calculating ΔG isn't always practical. In electrochemistry, we often use electrochemical series and standard reduction potentials to determine spontaneity, especially for redox reactions.

Electrochemical Series and Standard Reduction Potentials

The electrochemical series is a list of elements arranged in order of their standard reduction potentials (E°). The standard reduction potential measures the tendency of a chemical species to be reduced (gain electrons). These potentials are measured under standard conditions: 298 K (25°C), 1 atm pressure, and 1 M concentration.

A more positive E° indicates a greater tendency to be reduced, while a more negative E° indicates a greater tendency to be oxidized (lose electrons).

How to Use Standard Reduction Potentials to Determine Spontaneity

1. Identify the Oxidation and Reduction Half-Reactions: Break the overall reaction into its oxidation and reduction half-reactions.

2. Find the Standard Reduction Potentials (E°): Look up the standard reduction potentials for each half-reaction in a standard reduction potential table. Remember that the reduction potential is for the reduction half-reaction as written in the table.

3. Calculate the Standard Cell Potential (E°cell): Use the following equation:

   E°cell = E°reduction (cathode) - E°oxidation (anode)

   Where:

   • E°reduction (cathode) is the standard reduction potential of the reduction half-reaction.
   • E°oxidation (anode) is the standard reduction potential of the oxidation half-reaction. However, since oxidation is the reverse of reduction, you'll need to change the sign of the reduction potential found in the table.

4. Determine Spontaneity:

   • E°cell > 0: The reaction is spontaneous as written.
   • E°cell < 0: The reaction is non-spontaneous as written. The reverse reaction is spontaneous.
   • E°cell = 0: The reaction is at equilibrium.

Practical Examples: Determining Spontaneity

Let's work through several examples to illustrate how to determine whether a reaction will occur spontaneously as written using standard reduction potentials.

Example 1: Reaction of Zinc with Copper(II) Ions

Consider the reaction:

Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s)

1. Identify Half-Reactions:

   • Oxidation: Zn(s) → Zn2+(aq) + 2e-
   • Reduction: Cu2+(aq) + 2e- → Cu(s)

2. Find Standard Reduction Potentials:

   • Cu2+(aq) + 2e- → Cu(s) E° = +0.34 V
   • Zn2+(aq) + 2e- → Zn(s) E° = -0.76 V

3. Calculate E°cell:

   E°cell = E°reduction (Cu2+/Cu) - E°oxidation (Zn2+/Zn)

   E°cell = (+0.34 V) - (-0.76 V) = +1.10 V

4. Determine Spontaneity:

   Since E°cell = +1.10 V > 0, the reaction is spontaneous as written. Zinc will spontaneously react with copper(II) ions to form zinc ions and copper metal.

Example 2: Reaction of Silver with Copper(II) Ions

Consider the reaction:

2Ag(s) + Cu2+(aq) → 2Ag+(aq) + Cu(s)

1. Identify Half-Reactions:

   • Oxidation: 2Ag(s) → 2Ag+(aq) + 2e-
   • Reduction: Cu2+(aq) + 2e- → Cu(s)

2. Find Standard Reduction Potentials:

   • Cu2+(aq) + 2e- → Cu(s) E° = +0.34 V
   • Ag+(aq) + e- → Ag(s) E° = +0.80 V

3. Calculate E°cell:

   E°cell = E°reduction (Cu2+/Cu) - E°oxidation (Ag+/Ag)

   E°cell = (+0.34 V) - (+0.80 V) = -0.46 V

4. Determine Spontaneity:

   Since E°cell = -0.46 V < 0, the reaction is non-spontaneous as written. Silver will not spontaneously react with copper(II) ions to form silver ions and copper metal. The reverse reaction (Cu(s) + 2Ag+(aq) → Cu2+(aq) + 2Ag(s)) is spontaneous.

Example 3: Reaction of Iron with Hydrogen Ions (Acid)

Consider the reaction:

Fe(s) + 2H+(aq) → Fe2+(aq) + H2(g)

1. Identify Half-Reactions:

   • Oxidation: Fe(s) → Fe2+(aq) + 2e-
   • Reduction: 2H+(aq) + 2e- → H2(g)

2. Find Standard Reduction Potentials:

   • 2H+(aq) + 2e- → H2(g) E° = 0.00 V (By definition, the standard hydrogen electrode has E° = 0 V)
   • Fe2+(aq) + 2e- → Fe(s) E° = -0.44 V

3. Calculate E°cell:

   E°cell = E°reduction (H+/H2) - E°oxidation (Fe2+/Fe)

   E°cell = (0.00 V) - (-0.44 V) = +0.44 V

4. Determine Spontaneity:

   Since E°cell = +0.44 V > 0, the reaction is spontaneous as written. Iron will spontaneously react with acid (H+ ions) to form iron(II) ions and hydrogen gas. This is why iron corrodes in acidic environments.

Example 4: Reaction of Magnesium with Water

Consider the reaction:

Mg(s) + 2H2O(l) → Mg(OH)2(s) + H2(g)

While water isn't directly listed in standard reduction potential tables in its molecular form, we can consider the reduction of water to hydrogen gas in a basic solution:

2H2O(l) + 2e- → H2(g) + 2OH-(aq)

1. Identify Half-Reactions:

   • Oxidation: Mg(s) → Mg2+(aq) + 2e- (We'll adjust for the OH- later)
   • Reduction: 2H2O(l) + 2e- → H2(g) + 2OH-(aq)

2. Find Standard Reduction Potentials (Approximate):

   • 2H2O(l) + 2e- → H2(g) + 2OH-(aq) E° ≈ -0.83 V (This is pH dependent and approximate. A value close to -0.83 V is often used at pH 14)
   • Mg2+(aq) + 2e- → Mg(s) E° = -2.37 V

3. Calculate E°cell:

   E°cell = E°reduction (H2O/H2) - E°oxidation (Mg2+/Mg)

   E°cell = (-0.83 V) - (-2.37 V) = +1.54 V

   Note: This is a simplified calculation. The actual reaction involves the formation of Mg(OH)2(s), and the potential is pH-dependent. However, this approximation gives us a good indication.

4. Determine Spontaneity:

   Since E°cell ≈ +1.54 V > 0, the reaction is generally considered spontaneous, although the rate can be slow at room temperature. Magnesium reacts with water to form magnesium hydroxide and hydrogen gas, though often not vigorously unless the water is hot.

Example 5: Predicting Non-Spontaneity - Electrolysis

Electrolysis involves using an external voltage to drive a non-spontaneous reaction. Consider the electrolysis of water:

2H2O(l) → 2H2(g) + O2(g)

1. Identify Half-Reactions:

   • Oxidation: 2H2O(l) → O2(g) + 4H+(aq) + 4e-
   • Reduction: 4H+(aq) + 4e- → 2H2(g)

2. Find Standard Reduction Potentials:

   • O2(g) + 4H+(aq) + 4e- → 2H2O(l) E° = +1.23 V
   • 4H+(aq) + 4e- → 2H2(g) E° = 0.00 V

3. Calculate E°cell:

   E°cell = E°reduction (H+/H2) - E°oxidation (O2/H2O)

   E°cell = (0.00 V) - (+1.23 V) = -1.23 V

4. Determine Spontaneity:

   Since E°cell = -1.23 V < 0, the reaction is non-spontaneous as written. This means that water will not spontaneously decompose into hydrogen and oxygen gas. Instead, we need to apply an external voltage of at least 1.23 V to force the reaction to occur (electrolysis).

Factors Affecting Spontaneity Beyond Standard Conditions

While standard reduction potentials provide a good starting point, it's important to remember that reaction conditions can significantly affect spontaneity. Here are some key factors:

• Temperature: As seen in the Gibbs Free Energy equation (ΔG = ΔH - TΔS), temperature plays a crucial role. Reactions that are non-spontaneous at low temperatures might become spontaneous at higher temperatures if the entropy change (ΔS) is positive.

• Concentration (or Partial Pressure for Gases): The Nernst equation describes how changes in concentration affect the cell potential (Ecell).

  Ecell = E°cell - (RT/nF) lnQ

  Where:

  • R is the ideal gas constant (8.314 J/mol·K)
  • T is the temperature in Kelvin
  • n is the number of moles of electrons transferred in the balanced reaction
  • F is Faraday's constant (96,485 C/mol)
  • Q is the reaction quotient, which is a measure of the relative amounts of reactants and products present in a reaction at any given time.

  The Nernst equation shows that increasing the concentration of reactants or decreasing the concentration of products will generally make the reaction more spontaneous (increase Ecell).

• Pressure: For reactions involving gases, pressure changes can also affect spontaneity. The effect is similar to concentration changes, as described by the Nernst equation when applied to partial pressures of gases.

• pH: For reactions involving H+ or OH- ions, pH has a significant impact on spontaneity. The standard reduction potential of half-reactions involving H+ ions is pH-dependent.

Common Mistakes to Avoid

• Forgetting to Flip the Sign of E° for Oxidation: When calculating E°cell, remember that the standard reduction potential table lists reduction potentials. If a half-reaction is an oxidation, you must change the sign of its E° value.
• Incorrectly Identifying Oxidation and Reduction: Carefully determine which species is being oxidized (losing electrons) and which is being reduced (gaining electrons).
• Not Considering Stoichiometry: While multiplying a half-reaction by a coefficient to balance the overall equation does not change the standard reduction potential (E°), it does affect the number of moles of electrons transferred (n) in the Nernst equation and the Gibbs Free Energy change (ΔG = -nFE).
• Assuming Standard Conditions: Remember that standard reduction potentials are measured under standard conditions. Real-world conditions may differ, affecting spontaneity. Use the Nernst equation to adjust for non-standard conditions.
• Confusing Spontaneity with Rate: A spontaneous reaction will occur without external energy input, but it doesn't tell you how fast the reaction will occur. A spontaneous reaction can be very slow. Reaction rate is governed by kinetics, not thermodynamics.
• Ignoring the Role of Entropy: While standard reduction potentials are useful for redox reactions, remember that the overall spontaneity is determined by the Gibbs Free Energy (ΔG = ΔH - TΔS). In some cases, a large entropy change (ΔS) can make a reaction spontaneous even if the enthalpy change (ΔH) is unfavorable.

Advanced Concepts: Pourbaix Diagrams

For systems involving metal ions in aqueous solutions, Pourbaix diagrams (also known as potential/pH diagrams) provide a graphical representation of the thermodynamically stable phases as a function of potential (E) and pH. These diagrams are invaluable for understanding corrosion behavior and predicting the stability of different metal species under various conditions. They are based on the principles of electrochemistry and thermodynamics and take into account the effects of both redox reactions and acid-base equilibria.

Conclusion

Determining whether a reaction will occur spontaneously as written is a crucial skill in chemistry. By understanding the principles of Gibbs Free Energy, electrochemical series, standard reduction potentials, and the factors that affect spontaneity, you can confidently predict the direction of chemical reactions. Remember to carefully identify oxidation and reduction half-reactions, use standard reduction potential tables correctly, and consider the influence of temperature, concentration, pressure, and pH. While standard reduction potentials provide a valuable starting point, keep in mind the broader thermodynamic context and the potential impact of non-standard conditions. With a solid grasp of these concepts, you will be well-equipped to analyze and predict chemical behavior in a wide range of scenarios.