The quantity of silver deposited when one coulomb charge is passed through $\mathrm{AgNO}_3$ solution :

<p>To determine the quantity of silver deposited when one coulomb of charge is passed through $\mathrm{AgNO}_3$ solution, we need to refer to Faraday's laws of electrolysis, especially to the concept of the electrochemical equivalent. The electrochemical equivalent (ECE) of a substance is the amount of the substance that is deposited or dissolved at an electrode during electrolysis by one coulomb of charge.</p> <p>The electrochemical equivalent of a substance can be calculated using the formula:</p> <p>$E = \frac{M}{nF}$</p> <p>where:</p> <ul> <li>$E$ is the electrochemical equivalent of the substance in grams per coulomb ($\mathrm{g/C}$).</li> <li>$M$ is the molar mass of the substance in grams per mole ($\mathrm{g/mol}$).</li> <li>$n$ is the number of electrons involved in the oxidation or reduction reaction (the valency).</li> <li>$F$ is the Faraday constant, approximately $96485 \, \mathrm{C/mol}$, which is the charge of one mole of electrons.</li> </ul> <p>In the case of silver ($\mathrm{Ag}$) being deposited from $ \mathrm{AgNO}_3 $, when silver ion ($\mathrm{Ag}^+$) is reduced to metallic silver ($\mathrm{Ag}$), the reaction involves one electron ($n = 1$). The molar mass of silver (Ag) is approximately $107.868 \, \mathrm{g/mol}$. Using this information:</p> <p>$$E = \frac{107.868 \, \mathrm{g/mol}}{1 \cdot 96485 \, \mathrm{C/mol}} \approx 0.001118 \, \mathrm{g/C}$$</p> <p>This means that for every coulomb of charge passed through the solution, $0.001118 \, \mathrm{g}$ of silver is deposited.</p> <p>Given the options:</p> <ul> <li>Option A: $0.1$ g atom of silver - This is incorrect because the calculation shows a much smaller amount is deposited per coulomb.</li> <li>Option B: 1 chemical equivalent of silver - This does not directly relate to the amount deposited per coulomb.</li> <li>Option C: $1 \mathrm{~g}$ of silver - This is incorrect as it overestimates the amount deposited by a large margin.</li> <li>Option D: 1 electrochemical equivalent of silver - This is correct, as it directly relates to the amount of a substance deposited by one coulomb of charge, based on the formula and calculation shown.</li> </ul> <p>Therefore, the correct answer is <strong>Option D</strong>: 1 electrochemical equivalent of silver.</p>