---
title: "Standard hydrogen electrode; Mg/Ag cell emf"
subject: "Engineering Chemistry"
chapter: 1
key: "semester_2/engineering_chemistry:she-mg-ag-cell"
source: https://www.bctengineer.com/q/semester_2/engineering_chemistry/she-mg-ag-cell
site: BCT Engineering
---

# Standard hydrogen electrode; Mg/Ag cell emf

Engineering Chemistry · Chapter 1: Electro-chemistry and Buffer

- Asked in: 2072 Asoj, 3+2 marks
- Video: [Cell Potential Problems - Electrochemistry](https://www.youtube.com/watch?v=UzkLP8segcs) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/engineering_chemistry/she-mg-ag-cell
- Whole chapter: https://www.bctengineer.com/md/semester_2/engineering_chemistry/chapter-1

## Question

What is meant by standard hydrogen electrode? Explain briefly with diagram. Calculate the emf of the following cell at 25°C Mg/Mg²⁺ (0.1M)//Ag⁺(1M)/Ag. Given E°Mg²⁺/Mg = −2.37 V, E°Ag⁺/Ag = +0.80 V

## Short answer

The standard hydrogen electrode is the primary reference (E°=0) with Pt in 1 M H⁺ and H₂ at 1 atm. In Mg|Mg²⁺(0.1M)||Ag⁺(1M)|Ag, Mg is anode, Ag cathode; E°cell = 3.17 V. Using Nernst equation with Q=0.1, EMF = 3.20 V.

## Answer

#### Standard hydrogen electrode (SHE)
The SHE is the primary reference electrode, whose potential is arbitrarily taken as zero. It is a platinum foil coated with platinum black, dipped in 1 M H⁺ (1 M HCl), with pure H₂ gas at 1 atm bubbled over it at 25°C.

```text
   H₂ gas (1 atm)
        |
   ┌────┴────┐
   │ glass   │
   │ tube    │
   │  Pt foil│  (coated with
   │  (black)│   Pt black)
 ──┴─────────┴──
   1 M HCl (H⁺ = 1 M)
```
- Notation: Pt, H₂ (1 atm) | H⁺ (1 M)
- Reaction: H₂ ⇌ 2H⁺ + 2e⁻ (as anode) or 2H⁺ + 2e⁻ → H₂ (as cathode)
- Pt black adsorbs H₂ and acts as an inert conductor; E°(SHE) = 0.00 V. It is used to find the potential of other electrodes by coupling.

#### EMF of Mg | Mg²⁺ (0.1 M) || Ag⁺ (1 M) | Ag
```text
Anode  : Mg → Mg²⁺ + 2e⁻
Cathode: 2Ag⁺ + 2e⁻ → 2Ag
Cell   : Mg + 2Ag⁺ → Mg²⁺ + 2Ag     (n = 2)

E°cell = 0.80 − (−2.37) = 3.17 V
Q = [Mg²⁺]/[Ag⁺]² = 0.1/1² = 0.1,  log Q = −1
E = 3.17 − (0.0591/2)(−1)
  = 3.17 + 0.0296 = 3.1996 V
```
**Answer: EMF ≈ 3.20 V.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the role of platinum black in the SHE?
   A. It reacts with H+
   B. It adsorbs H2 and acts as an inert conductor
   C. It supplies electrons as a reactant
   D. It increases the temperature
   Answer: B. Pt black adsorbs hydrogen gas and conducts electrons without taking part in the reaction. (Key point: Role of platinum black)

2. What is the cell reaction for Mg | Mg2+ || Ag+ | Ag?
   A. Mg2+ + 2Ag -> Mg + 2Ag+
   B. Mg + 2Ag+ -> Mg2+ + 2Ag
   C. Mg + Ag+ -> Mg2+ + Ag
   D. 2Mg + Ag+ -> Mg2+ + Ag
   Answer: B. Mg is oxidised (loses 2e-) and two Ag+ are reduced, n = 2. (Key point: Cell reaction)

3. E°(Mg2+/Mg) = -2.37 V, E°(Ag+/Ag) = +0.80 V. E°cell is:
   A. 1.57 V
   B. 3.17 V
   C. -3.17 V
   D. 2.37 V
   Answer: B. E°cell = E°cathode - E°anode = 0.80 - (-2.37) = 3.17 V. (Key point: Standard cell emf)

4. Q = 0.1/1^2 = 0.1 so log Q = -1. What is E?
   A. 3.14 V
   B. 3.20 V
   C. 3.17 V
   D. 3.23 V
   Answer: B. E = 3.17 - (0.0591/2)(-1) = 3.17 + 0.0296 = 3.20 V. (Key point: Nernst correction)

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