14) Which of the following statement(s) IV are correct for the reaction below. Pt,H_(2)(580torr)vert HCl(0.0016M)Vert Pd^wedge 200M(s) (E^circ Pa^ast /Pd=0.987V)(760torr:1atm) The reaction type is spontaneous II. Ecell=0.809V III- Keq=2.19times 10^33 A) Only I B) I and II C I and III D) II and III

To determine which statements are correct for the given reaction, we need to analyze each statement individually.<br /><br />Statement I: The reaction type is spontaneous.<br />To determine if the reaction is spontaneous, we need to calculate the cell potential (E_cell) and compare it to the standard cell potential (E^°_cell). If E_cell is positive, the reaction is spontaneous.<br /><br />Statement II: E_cell = 0.809 V.<br />To calculate E_cell, we can use the Nernst equation:<br /><br />E_cell = E^°_cell - (0.0592/n) * log(Q)<br /><br />where n is the number of moles of electrons transferred in the reaction, and Q is the reaction quotient.<br /><br />Statement III: Keq = 2.19 x 10^33.<br />To calculate the equilibrium constant (K_eq), we can use the relationship between E_cell and K_eq:<br /><br />E^°_cell = (0.0592/n) * log(K_eq)<br /><br />Now let's analyze each statement:<br /><br />Statement I: To determine if the reaction is spontaneous, we need to calculate E_cell. We can use the given values to calculate E_cell:<br /><br />E^°_cell = 0.987 V<br />n = 2 (since 2 moles of electrons are transferred in the reaction)<br />P_H2 = 580 torr = 580/760 atm = 0.7639 atm<br />P_HCl = 0.0016 M * 0.987 V = 0.0015768 atm<br /><br />Using the Nernst equation:<br /><br />E_cell = 0.987 - (0.0592/2) * log((0.7639/760) * (0.0015768/0.0016))<br />E_cell = 0.987 - 0.0296 * log(0.00100658)<br />E_cell = 0.987 - 0.0296 * (-3.007)<br />E_cell = 0.987 + 0.0894<br />E_cell = 1.0764 V<br /><br />Since E_cell is positive, the reaction is spontaneous. Therefore, statement I is correct.<br /><br />Statement II: E_cell = 0.809 V.<br />From our calculation above, we found that E_cell = 1.0764 V, which is not equal to 0.809 V. Therefore, statement II is incorrect.<br /><br />Statement III: Keq = 2.19 x 10^33.<br />To calculate K_eq, we can use the relationship between E^°_cell and K_eq:<br /><br />E^°_cell = (0.0592/n) * log(K_eq)<br />0.987 = (0.0592/2) * log(K_eq)<br />0.987 = 0.0296 * log(K_eq)<br />log(K_eq) = 33.38<br />K_eq = 10^33.38 = 2.19 x 10^33<br /><br />Therefore, statement III is correct.<br /><br />Based on our analysis, the correct answer is C) I and III.