Calculate the potential of a copper electrode immersed in (a) 0.0380 M Cu(NO_(3))_(2) (b) 0.0650 M in NaCl and saturated with CuCl

To calculate the potential of a copper electrode immersed in a solution, we can use the Nernst equation. The Nernst equation relates the cell potential to the concentration of the ions in the solution.<br /><br />The Nernst equation is given by:<br /><br />\[ E = E^0 - \frac{0.0592}{n} \log Q \]<br /><br />where:<br />- \( E \) is the cell potential,<br />- \( E^0 \) is the standard cell potential,<br />- \( n \) is the number of moles of electrons transferred in the redox reaction,<br />- \( Q \) is the reaction quotient.<br /><br />For a copper electrode, the standard cell potential (\( E^0 \)) is +0.34 V, and the number of moles of electrons transferred (\( n \)) is 2.<br /><br />(a) For a 0.0380 M $Cu(NO_{3})_{2}$ solution, the reaction quotient (\( Q \)) is equal to the concentration of the copper ions (\( Cu^{2+} \)):<br /><br />\[ Q = [Cu^{2+}] = 0.0380 \, M \]<br /><br />Substituting these values into the Nernst equation:<br /><br />\[ E = 0.34 - \frac{0.0592}{2} \log(0.0380) \]<br /><br />\[ E = 0.34 - 0.0296 \log(0.0380) \]<br /><br />\[ E = 0.34 - 0.0296(-1.42) \]<br /><br />\[ E = 0.34 + 0.0421 \]<br /><br />\[ E = 0.3821 \, V \]<br /><br />Therefore, the potential of the copper electrode immersed in a 0.0380 M $Cu(NO_{3})_{2}$ solution is approximately 0.3821 V.<br /><br />(b) For a 0.0650 M NaCl solution saturated with $CuCl_{2}$, we need to consider the solubility of $CuCl_{2}$ in water. The solubility of $CuCl_{2}$ is approximately 0.0025 M.<br /><br />The reaction quotient (\( Q \)) is given by:<br /><br />\[ Q = \frac{[Cu^{2+}][Cl^-]^2}{[CuCl_{2}]} \]<br /><br />Since the solution is saturated with $CuCl_{2}$, we can assume that the concentration of $CuCl_{2}$ is equal to its solubility (0.0025 M).<br /><br />Substituting these values into the Nernst equation:<br /><br />\[ E = 0.34 - \frac{0.0592}{2} \log \left( \frac{(0.0650)(0.0650)^2}{0.0025} \right) \]<br /><br />\[ E = 0.34 - 0.0296 \log \left( \frac{0.0650^3}{0.0025} \right) \]<br /><br />\[ E = 0.34 - 0.0296 \log \left( \frac{0.000274625}{0.0025} \right) \]<br /><br />\[ E = 0.34 - 0.0296 \log (0.1095) \]<br /><br />\[ E = 0.34 - 0.0296(-0.96) \]<br /><br />\[ E = 0.34 + 0.0284 \]<br /><br />\[ E = 0.3684 \, V \]<br /><br />Therefore, the potential of the copper electrode immersed in a 0.0650 M NaCl solution saturated with $CuCl_{2}$ is approximately 0.3684