0 votes
50 views
in Physical Chemistry by (230 points)
A chemistry student wants to design an electrochemical cell that produces a voltage of at least 1.5 volts. The available electrodes are copper and aluminum. Using Faraday's law, calculate the mass of copper needed to produce the required voltage if aluminum is used as the other electrode. The specific gravity of copper is 8.96 g/cm³, and the standard reduction potential of copper and aluminum are -0.34 V and -1.66

1 Answer

0 votes
by (470 points)
To calculate the mass of copper needed to produce the required voltage, we first need to determine the cell potential  E_cell  using the standard reduction potentials of copper  E_Cu  and aluminum  E_Al . The cell potential can be calculated using the following equation:E_cell = E_cathode - E_anodeSince we want a positive cell potential, we will use copper as the cathode and aluminum as the anode:E_cell =  -0.34 V  -  -1.66 V  = 1.32 VNow, we need to increase the cell potential to at least 1.5 V. To do this, we can increase the mass of copper, which will increase the concentration of Cu ions in the solution and thus increase the cell potential. We can use the Nernst equation to determine the required concentration of Cu ions:E_cell = E_cell -  RT/nF  * ln Q where R is the gas constant  8.314 J/molK , T is the temperature in Kelvin  assume 298 K for room temperature , n is the number of electrons transferred  2 for both Cu and Al redox reactions , F is Faraday's constant  96485 C/mol , and Q is the reaction quotient.Since we want to increase the cell potential to 1.5 V:1.5 V = 1.32 V -  8.314 J/molK * 298 K  /  2 * 96485 C/mol  * ln Q Solving for Q:ln Q  =  1.5 V - 1.32 V  *  2 * 96485 C/mol  /  8.314 J/molK * 298 K ln Q   0.136Q  1.146For the reaction Cu + 2e  Cu, Q = [Cu]. Therefore, the required concentration of Cu ions is approximately 1.146 M.Now, we can calculate the mass of copper needed to achieve this concentration. Assuming a 1 L  1000 cm  solution:moles of Cu = 1.146 mol/L * 1 L = 1.146 molmass of Cu = moles of Cu * molar mass of Cumass of Cu = 1.146 mol * 63.55 g/mol  72.87 gSo, approximately 72.87 grams of copper is needed to produce the required voltage of 1.5 volts when aluminum is used as the other electrode.

Related questions

Welcome to Sarvan Science Q&A, where you can ask questions and receive answers from other members of the community.
...