An ion is reduced to the element when it absorbs 6 × 10^20 electrons. The number of equivalents of t — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Relate Moles of Electrons to Chemical Equivalents By definition, one mole of electrons carries a charge of exactly $1\text{ Faraday}$ ($1\text{ F}$): $$\text{Charge of } 1\text{ mole of electrons} = 1\text{ F} \approx 96500\text{ C}$$ According to Faraday's laws of electrolysis, the passage of $1\text{ Faraday}$ of electrical charge corresponds to the chemical reduction or oxidation of exactly $1\text{ equivalent}$ (or gram-equivalent) of any substance at an electrode: $$\text{1 Faraday of charge} \equiv 1\text{ mole of electrons} \equiv 1\text{ equivalent of chemical change}$$ Therefore, the number of equivalents of the ion reduced is directly equal to the number of moles of electrons absorbed: $$\text{Number of equivalents} = \text{Moles of electrons absorbed}$$ Step 2 - Calculate the Moles of Electrons Absorbed The number of moles of electrons ($n_{\ce{e-}}$) is determined by dividing the total number of absorbed electrons ($N$) by Avogadro's number ($N_A \approx 6.022 \times 10^{23}\text{ mol}^{-1}$): $$n_{\ce{e-}} = \frac{N}{N_A}$$ Substituting the given values: $$n_{\ce{e-}} = \frac{6 \times 10^{20}}{6.022 \times 10^{23}\text{ mol}^{-1}}$$ $$n_{\ce{e-}} \approx 0.996 \times 10^{-3}\text{ mol} \approx 10^{-3}\text{ mol} = 0.001\text{ mol}$$ Step 3 - Determine the Number of Equivalents of the Ion Using the relationship established in Step 1, the number of equivalents is equal to the moles of electrons absorbed: $$\text{Number of equivalents} = n_{\ce{e-}} = 0.001\text{ equivalents}$$ Thus, the number of equivalents of the ion reduced is $\boxed{0.001}$. Step 4 - Explanation of Options * **Option (A) is incorrect:** An equivalent value of $0.10$ would require the absorption of $0.10\text{ moles}$ of electrons, which corresponds to $6.022 \times 10^{22}$ electrons. * **Option (B) is incorrect:** An equivalent value of $0.01$ would require the absorption of $0.01\text{ moles}$ of electrons, which corresponds to $6.022 \times 10^{21}$ electrons. * **Option (C) is correct:** Our calculated value of $0.001$ equivalents matches this option perfectly. * **Option (D) is incorrect:** An equivalent value of $0.0001$ would require the absorption of $10^{-4}\text{ moles}$ of electrons, which corresponds to $6.022 \times 10^{19}$ electrons. $$\text{Correct Option: } \boxed{\text{C}}$$