Let's analyze the given reaction and its associated half-reactions:
The overall oxidation-reduction reaction is:
[tex]\[ Mg + 2 HCl \rightarrow MgCl_2 + H_2 \][/tex]
First, we need to identify the oxidation states of the elements involved in the reaction:
- In [tex]\( Mg \)[/tex], magnesium starts with an oxidation state of 0.
- In [tex]\( MgCl_2 \)[/tex], magnesium has an oxidation state of +2.
- In [tex]\( HCl \)[/tex], hydrogen has an oxidation state of +1 and chlorine has an oxidation state of -1.
- In [tex]\( H_2 \)[/tex], hydrogen has an oxidation state of 0.
Now let's break down the half-reactions:
1. Magnesium Reaction:
[tex]\[ Mg \rightarrow MgCl_2 + 2e^- \][/tex]
- Magnesium (Mg) goes from an oxidation state of 0 to an oxidation state of +2 (in [tex]\( MgCl_2 \)[/tex]).
- This means magnesium is losing two electrons.
- This is an oxidation half-reaction. (O)
2. Hydrogen Reaction:
[tex]\[ 2H^+ + 2e^- \rightarrow H_2 \][/tex]
- In [tex]\( 2HCl \)[/tex], hydrogen is present as [tex]\( H^+ \)[/tex] (with an oxidation state of +1).
- Hydrogen then gains electrons to form [tex]\( H_2 \)[/tex] (with an oxidation state of 0).
- This is a reduction half-reaction. (R)
3. Combined Reaction that is Neither:
[tex]\[ HCl \rightarrow MgCl_2 \][/tex]
- This is not a valid half-reaction, as it involves multiple species and does not represent a clear oxidation or reduction process on its own.
- This reaction is neither. (N)
To summarize:
- [tex]\( HCl \rightarrow MgCl_2 \)[/tex]: N
- [tex]\( Mg \rightarrow MgCl_2 + 2e^- \)[/tex]: O
- [tex]\( 2H^+ + 2e^- \rightarrow H_2 \)[/tex]: R
