The reaction taking place in a galvanic cell is as given A ( s )+ B ²⁺ ( 1 1 1 0 0 ^ - M M ) B _ ( s ) + A ²⁺(0.1 M ). The emf of the cell is +2.651 ~V . If the standard emf of the cell is +2.71 ~V , what is the value of X ?

Step-by-step solution

The cell reaction is A ( s ) + B ²⁺(10^ -X M ) B ( s ) + A ²⁺(0.1 M ) . The Nernst equation for the cell at 298 K is given by E_ cell = E^ _ cell - 0.0591 n Q , where n is the number of electrons transferred. Here, n = 2 , E_ cell = 2.651 ~V , and E^ _ cell = 2.71 ~V . The reaction quotient Q is [ A ²⁺] [ B ²⁺] = 0.1 10^ -X = 10^ X-1 . Substituting the values into the Nernst equation: 2.651 = 2.71 - 0.0591 2 (10^ X-1 ) 2.651 - 2.71 = -0.02955 (X-1) -0.059 = -0.02955 (X-1) X-1 = 0.059 0.02955 2 X = 2 + 1 = 3 . Answe