If standard reduction potential ( E ^ ) of ( Mg _ ( aq ) ⁺² Mg _ ( s ) ) , ( Ag ⁺ _ ( aq ) Ag _ ( s ) ), ( Zn ⁺² _ ( aq ) Zn _ ( s ) ) and ( Cu ⁺² _ ( aq ) Cu _ ( s ) ) are -2.37 V , +0.79 ~V ,-0.76 ~V and +0.34 V respectively. Which of the following reaction is spontaneous?

Step-by-step solution

A reaction is spontaneous if its standard cell potential E^ _ cell > 0 , where E^ _ cell = E^ _ reduction ( cathode ) - E^ _ reduction ( anode ) . Using the standard reduction potentials: E^ ( Mg ⁺² Mg ) = -2.37 V , E^ ( Ag ⁺ Ag ) = +0.79 V , E^ ( Zn ⁺² Zn ) = -0.76 V , and E^ ( Cu ⁺² Cu ) = +0.34 V : For reaction A : Zn _ ( s ) + Mg _ ( aq ) ⁺² Zn _ ( aq ) ⁺²+ Mg _ ( s ) E^ _ cell = E^ ( Mg ⁺²) - E^ ( Zn ⁺²) = -2.37 - (-0.76) = -1.61 V Spontaneous? No For reaction B : 2 Ag _ ( s ) + Zn _ ( aq ) ⁺² 2 Ag _ ( aq ) ⁺+