Question

Balance each of the following redox reactions and classify it as a combination, decomposition, or displacement reaction: (a) \(\mathrm{Mg}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{Mg}(\mathrm{OH})_{2}(s)+\mathrm{H}_{2}(g)\) (b) \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}(a q)+\mathrm{Al}(s) \longrightarrow \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}(a q)+\mathrm{Cr}(s)\) (c) \(\mathrm{PF}_{3}(g)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{PF}_{5}(g)\)

Short answer

(a) Balanced: \(\mathrm{Mg} + 2\mathrm{H}_2\mathrm{O} \rightarrow \mathrm{Mg}(\mathrm{OH})_2 + \mathrm{H}_2\). Type: Single Displacement(b) Balanced: \(\mathrm{Cr}(\mathrm{NO}_3)_3 + 2\mathrm{Al} \rightarrow 2\mathrm{Al}(\mathrm{NO}_3)_3 + 3\mathrm{Cr}\). Type: Single Displacement(c) Balanced: \(\mathrm{PF}_3 + 2\mathrm{F}_2 \rightarrow \mathrm{PF}_5\). Type: Combination

Step-by-step solution

Identify Oxidation States - Reaction (a)

Identify the oxidation states of each element in \(\mathrm{Mg}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{Mg}(\mathrm{OH})_{2}(s)+\mathrm{H}_{2}(g)\). Magnesium (Mg) starts as 0 and turns into +2 in \( \mathrm{Mg}(\mathrm{OH})_{2} \). Hydrogen (H) starts as +1 in \(\mathrm{H}_2 \mathrm{O}\) and ends as 0 in \(\mathrm{H}_2\). Oxygen remains -2.

Write Half Reactions - Reaction (a)

Write the oxidation and reduction half-reactions for reaction (a):\[\text{Oxidation: } \mathrm{Mg} \rightarrow \mathrm{Mg}^{2+} + 2e^-\]\[\text{Reduction: } 2\mathrm{H}^{+} + 2e^- \rightarrow \mathrm{H}_2\]

Balance Half Reactions - Reaction (a)

Ensure the number of electrons lost in oxidation equals the number of electrons gained in reduction. Already balanced since each half-reaction has 2 electrons.

Combine Half Reactions - Reaction (a)

Combine the half-reactions for the balanced redox reaction: \[ \mathrm{Mg} + 2\mathrm{H}_2\mathrm{O} \rightarrow \mathrm{Mg}(\mathrm{OH})_2 + \mathrm{H}_2 \]

Classify the Reaction - Reaction (a)

This reaction is a Single Displacement reaction because magnesium displaces hydrogen from water.

Identify Oxidation States - Reaction (b)

Identify the oxidation states in \(\mathrm{Cr}(\mathrm{NO}_3)_3(\mathrm{aq}) + \mathrm{Al}(s) \longrightarrow \mathrm{Al}(\mathrm{NO}_3)_3(\mathrm{aq}) + \mathrm{Cr}(s)\): Chromium (Cr) in \(\mathrm{Cr}(\mathrm{NO}_3)_3\) is +3, Aluminum (Al) starts as 0 and turns into +3 in \(\mathrm{Al}(\mathrm{NO}_3)_3\).

Write Half Reactions - Reaction (b)

Write the oxidation and reduction half-reactions for reaction (b):\[\text{Oxidation: } \mathrm{Al} \rightarrow \mathrm{Al}^{3+} + 3e^-\]\[\text{Reduction: } \mathrm{Cr}^{3+} + 3e^- \rightarrow \mathrm{Cr}\]

Balance Half Reactions - Reaction (b)

Ensure the balance of electrons in oxidation and reduction. Combine them: \[ \mathrm{Al} + \mathrm{Cr}^{3+} \rightarrow \mathrm{Al}^{3+} + \mathrm{Cr}\].

Combine Half Reactions - Reaction (b)

Combine the half-reactions for the balanced redox reaction (observing coefficients):\[\mathrm{Cr}(\mathrm{NO}_3)_3(\mathrm{aq}) + 2\mathrm{Al}(s) \longrightarrow 2\mathrm{Al}(\mathrm{NO}_3)_3(\mathrm{aq}) + 3\mathrm{Cr}(s)\]

Classify the Reaction - Reaction (b)

This reaction is a Single Displacement reaction because aluminum displaces chromium.

Identify Oxidation States - Reaction (c)

Identify the oxidation states in \(\mathrm{PF}_3(\mathrm{g}) + \mathrm{F}_2(\mathrm{g}) \rightarrow \mathrm{PF}_5(\mathrm{g})\): Phosphorus (P) in \(\mathrm{PF}_3\) is +3 and turns into +5 in \(\mathrm{PF}_5\); Fluorine (F) stays -1.

Write Overall Reaction - Reaction (c)

Combine the integer balanced reaction to confirm all atoms are balanced: \[\mathrm{PF}_3 + 2F_2 \rightarrow \mathrm{PF}_5\].

Classify the Reaction - Reaction (c)

This reaction is a Combination reaction because two reactants combine to form one product.

Key concepts

Oxidation States

Understanding oxidation states is crucial for balancing redox reactions. An oxidation state (or number) indicates the degree of oxidation of an atom in a substance. It's a hypothetical charge that an atom would have if all bonds to atoms of different elements were completely ionic.

In reaction (a) \(\text{Mg}(s) + \text{H}_2 \text{O}(g) \rightarrow \text{Mg}(\text{OH})_2(s) + \text{H}_2(g)\), we need to determine the oxidation states of \(\text{Mg}\), \(\text{H}\), and \(\text{O}\). Magnesium starts with an oxidation state of 0 and becomes +2 in \(\text{Mg}(\text{OH})_2\). Hydrogen starts as +1 in \(\text{H}_2 \text{O}\) and ends as 0 in \(\text{H}_2\). Oxygen remains -2.

Knowing these states allows us to identify which elements are oxidized and reduced. This process is repeated for reactions (b) and (c) to identify changes in oxidation states.

Half-Reactions

Balancing redox reactions often involves separating them into half-reactions—one that shows oxidation and one that shows reduction. This method helps to clearly see the electron transfer.

In reaction (a), we split the reaction:
- Oxidation half-reaction: \(\text{Mg} \rightarrow \text{Mg}^2+ + 2e^-\)
- Reduction half-reaction: \(\text{2H}^+ + 2e^- \rightarrow \text{H}_2\)

Both parts show how electrons are transferred. We then balance each to ensure that the electrons lost in oxidation are equal to those gained in reduction.

The half-reactions for reaction (b) are:
- Oxidation: \(\text{Al} \rightarrow \text{Al}^{3+} + 3e^-\)
- Reduction: \(\text{Cr}^{3+} + 3e^- \rightarrow \text{Cr}\)

After balancing, these half-reactions are combined to give us the overall balanced reaction.

Reaction Classification

Classifying redox reactions helps us understand the process better. The main types of reactions include:

• Combination reactions
• Decomposition reactions
• Single displacement reactions

Reaction (a) is a Single Displacement reaction where magnesium displaces hydrogen from water.

In reaction (b), \(\text{Cr}(\text{NO}_3)_3(aq) + \text{Al}(s) \rightarrow \text{Al}(\text{NO}_3)_3(aq) + \text{Cr}(s)\), aluminum displaces chromium, classifying it as another Single Displacement reaction.

Reaction (c), \(\text{PF}_3(g) + \text{F}_2(g) \rightarrow \text{PF}_5(g)\), is a Combination reaction where two substances combine to form a single product.

Understanding these classifications helps us predict the types of products and balance the equations efficiently.