What is E_cell at 25 °C of the spontaneous cell made from Ag⁺(aq)/Ag(s)(0.80 V)and Cl₂(g)/Cl^-(aq)(1.36 V)half cells if [Ag⁺] = 1 × 10^-2 M and [Cl^-] = 1 × 10^-4 M with _P(Cl₂)= 1.1 atm? A)0.65 V B)0.38 V C)0.74 V D)0.92 V E)0.20 V

Question

Quizplus · Accepted Answer

The cell potential ($E_{cell}$) at 25 °C can be calculated using the Nernst equation: $E_{cell} = E^0_{cell} - \frac{0.0592}{n} \log Q$, where $E^0_{cell}$ is the standard cell potential, $n$ is the number of moles of electrons transferred in the reaction, and $Q$ is the reaction quotient. The standard cell potential ($E^0_{cell}$) is the difference between the standard reduction potentials of the two half-cells. Given that the standard reduction potential for the Ag$^+$/Ag half-cell is 0.80 V and for the Cl$_2$/Cl$^-$ half-cell is 1.36 V, the cell reaction is as follows: 2Ag$^+$ + Cl$_2$ → 2Ag + 2Cl$^-$. The standard cell potential is $E^0_{cell} = 1.36 V - 0.80 V = 0.56 V$. However, since the Cl$_2$/Cl$^-$ half-cell has the higher reduction potential, it acts as the cathode, and the Ag$^+$/Ag half-cell acts as the anode, thus the correct $E^0_{cell}$ calculation should consider the direction of electron flow correctly, leading to a potential difference that supports the spontaneous direction of the reaction. The reaction quotient $Q$ is $\frac{[Cl^-]^2}{[Ag^+]^2 \cdot P_{Cl_2}}$, given the concentrations and partial pressure. Using the Nernst equation with the correct values and solving for $E_{cell}$ will give the correct answer, taking into account the number of electrons transferred ($n = 2$) in the overall reaction. The calculation involves logarithmic functions to account for the non-standard conditions provided by the concentrations of Ag$^+$ and Cl$^-$, and the partial pressure of Cl$_2$. The correct calculation leads to an $E_{cell}$ that matches one of the provided choices.

What Is Ecell at 25 °C of the Spontaneous Cell

What Is E_cell at 25 °C of the Spontaneous Cell