Question

The quantity of $\text{Ca}$ that can be produced from molten $\text{CaCl}_2$, with the same quantity of electricity (in coulombs) required to produce $8\text{ g}$ of $\text{Mg}$ from molten $\text{MgCl}_2$ is: [Atomic mass of $\text{Mg} = 24\text{ u}$; Atomic mass of $\text{Ca} = 40\text{ u}$]}

• A. $5.2\text{ g}$
• B. $4.8\text{ g}$
• C. $6.0\text{ g}$
• D. $8.0\text{ g}$

Hint:

Since both $\text{Ca}^{2+}$ and $\text{Mg}^{2+}$ share the exact same charge valency ($z=2$), the number of moles of each metal produced by a given quantity of electricity will be identical. $4.8\text{ g}$ of $\text{Mg}$ corresponds to $\frac{4.8}{24} = 0.2\text{ moles}$. Therefore, you will get exactly $0.2\text{ moles}$ of calcium: $0.2 \times 40 = 8.0\text{ g}$ immediately!

Answer 1

The Correct Option is D

Concept: According to Faraday's Second Law of Electrolysis, when the same quantity of electricity is passed through different electrolytic solutions connected in series, the masses of the substances liberated ($m$) are directly proportional to their chemical equivalent weights ($E_{\text{eq}}$): \[ \frac{m_1}{m_2} = \frac{E_1}{E_2} \] The equivalent weight of an ion is calculated by dividing its atomic mass by its valence charge factor ($z$).

Step 1: Calculate the equivalent weights of both metals.
Both calcium and magnesium are alkaline earth metals that form divalent cations in molten salts:
• $\text{Mg}^{2+} + 2e^- \rightarrow \text{Mg}(s) \implies z = 2 \implies E_{\text{Mg}} = \frac{\text{Atomic Mass}}{2} = \frac{24}{2} = 12\text{ g eq}^{-1}$
• $\text{Ca}^{2+} + 2e^- \rightarrow \text{Ca}(s) \implies z = 2 \implies E_{\text{Ca}} = \frac{\text{Atomic Mass}}{2} = \frac{40}{2} = 20\text{ g eq}^{-1}$

Step 2: Set up the ratio to solve for the mass of calcium ($m_{\text{Ca}}$).
Given mass of magnesium liberated $m_{\text{Mg}} = 4.8\text{ g}$: \[ \frac{m_{\text{Ca}}}{m_{\text{Mg}}} = \frac{E_{\text{Ca}}}{E_{\text{Mg}}} \implies \frac{m_{\text{Ca}}}{4.8} = \frac{20}{12} \] Isolating $m_{\text{Ca}}$: \[ m_{\text{Ca}} = 4.8 \times \frac{20}{12} = 0.4 \times 20 = 8.0\text{ g} \]