1. Given overall reaction

We need the galvanic cell in which the net reaction is

$\frac{1}{2}H_2(g) + AgCl(s) \rightleftharpoons H^+(aq) + Cl^-(aq) + Ag(s)$

So we should identify the two half-cells that combine to give this reaction.

---

2. Write the relevant half-reactions

(i) Hydrogen electrode

Oxidation of hydrogen is:

$\frac{1}{2}H_2(g) \rightarrow H^+(aq) + e^-$

This requires a hydrogen electrode:

$\text{Pt} | H_2(g) | H^+(aq)$

(ii) Silver-silver chloride electrode

Reduction of silver chloride is:

$AgCl(s) + e^- \rightarrow Ag(s) + Cl^-(aq)$

This requires the electrode:

$Ag | AgCl(s) | Cl^-(aq)$

---

3. Add the half-reactions

Adding

$\frac{1}{2}H_2(g) \rightarrow H^+(aq) + e^-$

and

$AgCl(s) + e^- \rightarrow Ag(s) + Cl^-(aq)$

we get

$\frac{1}{2}H_2(g) + AgCl(s) \rightarrow H^+(aq) + Cl^-(aq) + Ag(s)$

This matches the given reaction exactly.

So the cell must contain:

• a hydrogen electrode in acidic medium,
• a silver-silver chloride electrode in chloride-containing medium.

---

4. Check each option

Option A

$Ag|AgCl(s)|KCl(\text{soln})|AgNO_3|Ag$

This has:

• one $Ag/AgCl$ electrode,
• one $Ag^+/Ag$ electrode,
• no hydrogen electrode.

So it cannot produce the required reaction involving $\frac{1}{2}H_2$ and $H^+$.

❌ A is incorrect.

---

Option B

$Pt|H_2(g)|HCl(\text{soln})|AgCl(s)|Ag$

Left electrode:

$Pt|H_2(g)|H^+(aq)$

since $HCl$ provides $H^+$.

Right electrode:

$AgCl(s)|Ag$

in chloride medium (again supplied by $HCl$), so the half-reaction is

$AgCl(s)+e^-\rightarrow Ag(s)+Cl^-(aq)$

Combining with hydrogen oxidation gives exactly the required net reaction.

✅ B is correct.

---

Option C

$Pt|H_2(g)|HCl(\text{soln})|AgNO_3(\text{soln})|Ag$

Here the silver electrode is $Ag^+/Ag$, whose half-reaction is

$Ag^+(aq)+e^-\rightarrow Ag(s)$

Combining with hydrogen oxidation would give

$\frac{1}{2}H_2(g)+Ag^+(aq)\rightarrow H^+(aq)+Ag(s)$

This does not involve $AgCl(s)$ and $Cl^-$ as in the given reaction.

❌ C is incorrect.

---

Option D

$Pt|H_2(g)|KCl(\text{soln})|AgCl(s)|Ag$

Here the solution is $KCl$, which provides $Cl^-$ but no $H^+$ for a hydrogen electrode. A hydrogen electrode requires acidic medium containing $H^+$.

So this does not represent the required half-cell for

$\frac{1}{2}H_2(g)\rightarrow H^+(aq)+e^-$

❌ D is incorrect.

---

5. Final answer

The correct galvanic cell is:

$\boxed{Pt|H_2(g)|HCl(\text{soln})|AgCl(s)|Ag}$

So the correct option is B.