A student wants to determine the maximum voltage and power output of a primary cell that consists of a zinc electrode in 1M Zn(NO3)2 solution and a silver electrode in 1M AgNO3 solution. The student knows the standard reduction potentials of Zn2+/Zn and Ag+/Ag to be -0.76V and +0.80V, respectively. Assuming the cell operates under standard conditions at 298K, what is the maximum voltage that the cell can generate and the maximum power output it can deliver?

Question

A student wants to determine the maximum voltage and power output of a primary cell that consists of a zinc electrode in 1M Zn(NO3)2 solution and a silver electrode in 1M AgNO3 solution. The student knows the standard reduction potentials of Zn2+/Zn and Ag+/Ag to be -0.76V and +0.80V, respectively. Assuming the cell operates under standard conditions at 298K, what is the maximum voltage that the cell can generate and the maximum power outpu

Answer 1

To determine the maximum voltage that the cell can generate, we need to find the difference in the standard reduction potentials of the two half-cells. The cell potential  E_cell  can be calculated using the Nernst equation:E_cell = E_cathode - E_anodeSince Ag+/Ag has a higher reduction potential, it will act as the cathode, and Zn2+/Zn will act as the anode. So,E_cell =  +0.80V  -  -0.76V  = 0.80V + 0.76V = 1.56VThe maximum voltage that the cell can generate is 1.56V.To find the maximum power output, we need to know the cell's internal resistance. However, this information is not provided in the problem. In general, the maximum power output can be calculated using the formula:P_max =  E_cell^2  /  4 * R where P_max is the maximum power output and R is the internal resistance of the cell. Without the value of R, we cannot determine the maximum power output of the cell.