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A student is designing an electrochemical cell using zinc and copper electrodes. The student wants to know the current density (in A/cm²) when the cell operates at a voltage of 1.5 V and a temperature of 25°C. The area of the zinc electrode is 10 cm², and the area of the copper electrode is 5 cm². Assuming a 2:1 ratio for the transfer of electrons between the two electrodes, calculate the current densi

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To calculate the current density, we first need to find the current flowing through the cell. We can use Ohm's law to find the current, which states:I = V/Rwhere I is the current, V is the voltage, and R is the resistance.However, we don't have the resistance  R  in the problem. Instead, we are given the ratio of electron transfer between the two electrodes  2:1 . This means that for every 2 electrons transferred from the zinc electrode, 1 electron is transferred to the copper electrode. Since the current is directly proportional to the number of electrons transferred, we can use this ratio to find the equivalent resistance of the cell.Let's assume that the resistance of the zinc electrode is Rz and the resistance of the copper electrode is Rc. The equivalent resistance of the cell can be found using the formula:1/Req = 1/Rz + 1/RcSince the ratio of electron transfer is 2:1, we can assume that the resistance of the zinc electrode is twice that of the copper electrode:Rz = 2 * RcNow we can substitute this into the equivalent resistance formula:1/Req = 1/ 2 * Rc  + 1/Rc1/Req =  1 + 2  /  2 * Rc 1/Req = 3 /  2 * Rc Now we can use Ohm's law to find the current:I = V/ReqI = 1.5 V /  3 /  2 * Rc  To find the current density, we need to divide the current by the area of the electrode. Since the current flows through both electrodes, we can use the smaller area  copper electrode  to find the current density:Current density = I / Area of copper electrodeCurrent density =  1.5 V /  3 /  2 * Rc    / 5 cmUnfortunately, we cannot find an exact value for the current density without knowing the resistance of the copper electrode  Rc . However, the formula above can be used to calculate the current density once the resistance values are known.

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