The given reaction involves the oxidation of hydrogen gas to H$^+$ ions and the reduction of AgCl to Ag. This is consistent with the following electrode reactions:
Anode (oxidation): H$_2 \to$ 2H$^+ + 2e^-$
Cathode (reduction): AgCl + e$^- \to$ Ag + Cl$^-$ \end{itemize}
The correct galvanic cell setup corresponding to this reaction is: \[ \text{Pt} \vert \text{H}_2(\text{g}) \vert \text{HCl(sol$^n$)} \vert \text{AgCl(s)} \vert \text{Ag} \] Here, the HCl provides the H$^+$ ions required for the anode reaction, and AgCl serves as the source of Ag$^+$ for the cathode reaction.
Calculate the potential for half-cell containing 0.01 M K\(_2\)Cr\(_2\)O\(_7\)(aq), 0.01 M Cr\(^{3+}\)(aq), and 1.0 x 10\(^{-4}\) M H\(^+\)(aq).

Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.