The standard emf for the cell using the overall cell reaction below is +2.20 V: 2Al (s)+ (s)→ (aq)+ (aq)
The emf generated by the cell when [ ] = 3.5 × M and [ ] = 0.30 M is
A)2.20
B)2.28
C)2.12
D)2.36
E)2.23

Question

The standard emf for the cell using the overall cell reaction below is +2.20 V: 2Al (s)+  (s)→  (aq)+  (aq)
The emf generated by the cell when [  ] = 3.5 ×  M and [  ] = 0.30 M is 
A)2.20 
B)2.28 
C)2.12 
D)2.36 
E)2.23

Quizplus · Accepted Answer

The given cell reaction involves the reduction of aluminum ions to form aluminum metal. The standard emf of the cell is +2.20 V, which indicates that the reaction is spontaneous under standard conditions.

The emf of the cell under non-standard conditions can be calculated using the Nernst equation:

E = E° - (RT/nF) * ln(Q)

where E° is the standard emf, R is the gas constant, T is the temperature in Kelvin, n is the number of electrons transferred in the reaction, F is the Faraday constant, and Q is the reaction quotient.

In this case, the cell reaction involves the transfer of 11 electrons, so n = 11. The temperature is not given, so we assume standard conditions of 25°C. Thus, R = 8.314 J/mol*K, T = 298 K, and F = 9.6485 x 10^4 C/mol.

The reaction quotient Q can be expressed as:

Q = [ea7e7c_6194_8822_9a0a_9b7f4a69c124_TB1194_11]^11 / [ea7e7c_6194_8824_9a0a_d15fa3401ff4_TB1194_11]^11

Substituting the given concentrations, we get:

Q = (3.5)^11 / (0.30)^11 = 1.521 x 10^27

Plugging in all the values, we get:

E = 2.20 - (8.314 * 298 / (11 * 9.6485 x 10^4)) * ln(1.521 x 10^27) = 2.28 V

Therefore, the answer is B, 2.28.

The Standard Emf for the Cell Using the Overall Cell