Which of the following alkali metals has the biggest tendency of the half reaction `M_((g))rarr M_((aq))^(+) + e^(-)`

Options

A. Sodium
B. Lithium
C. Potassium
D. Cesium

Answer

To determine which alkali metal has the biggest tendency for the half-reaction \( M_{(g)} \rightarrow M_{(aq)}^{+} + e^{-} \), we need to analyze the standard reduction potentials of the given alkali metals: sodium (Na), lithium (Li), potassium (K), and cesium (Cs).

### Step 1: Understand the half-reaction
The half-reaction \( M_{(g)} \rightarrow M_{(aq)}^{+} + e^{-} \) represents the process where a gaseous metal (M) loses an electron to form a cation in aqueous solution. The tendency of this reaction is influenced by the standard reduction potential of the metal.

### Step 2: Identify standard reduction potentials
The standard reduction potential values for the alkali metals are as follows:
- Lithium (Li): -3.04 V
- Sodium (Na): -2.71 V
- Potassium (K): -2.93 V
- Cesium (Cs): -2.92 V

### Step 3: Analyze the values
The more negative the standard reduction potential, the greater the tendency for the metal to undergo oxidation (lose electrons). Therefore, we need to look for the metal with the most negative standard reduction potential.

### Step 4: Compare the potentials
From the values we have:
- Lithium has the most negative standard reduction potential of -3.04 V.
- Sodium has -2.71 V.
- Potassium has -2.93 V.
- Cesium has -2.92 V.

### Step 5: Conclusion
Since lithium has the most negative standard reduction potential, it has the biggest tendency to undergo oxidation in the half-reaction \( M_{(g)} \rightarrow M_{(aq)}^{+} + e^{-} \). Therefore, the answer is lithium (Li).

### Final Answer
The alkali metal with the biggest tendency for the half-reaction is **lithium (Li)**.