3. An electrochemical reaction occurs between an unknown element and zinc. The half-cell reaction for the zinc is:
Zn(s) → Zn2+(aq) + 2e−
The cell potential for the reaction is Eºcell = 1.83 V.
a. Is the reaction spontaneous or nonspontaneous? Explain. (1 point)
b. What is the half-cell potential of the unknown species? (2 points)
c. What is the identity of the unknown element? (2 points)
a. To determine whether the reaction is spontaneous or nonspontaneous, we can use the concept of cell potential (Eºcell). If Eºcell is positive, the reaction is spontaneous, whereas if Eºcell is negative, the reaction is nonspontaneous.
In this case, Eºcell is given as 1.83 V, which means the reaction is spontaneous because the cell potential is positive.
b. To find the half-cell potential of the unknown species, you can use the Nernst equation, which relates the cell potential to the standard cell potential (Eºcell), the reaction quotient (Q), the Faraday constant (F), the temperature (T), and the number of electrons transferred (n).
The Nernst equation is given as follows:
Ecell = Eºcell - (RT/nF) * ln(Q)
Since the reaction for the unknown species is not provided, we need to construct it based on the given reaction of zinc. In the given reaction, 2 electrons are released. Therefore, the half-cell reaction for the unknown species can be written as follows:
Unknown element(aq) + 2e− → Unknown element(s)
Next, you will need to construct the reaction quotient (Q) for the unknown species. Q is the ratio of the concentrations of the products and reactants at any given moment during the reaction.
Since the unknown species is not mentioned, we assume it exists in the aqueous (aq) form in the electrode and solid (s) form in the half-cell. This means that the concentration of the solid is considered to be constant and it does not affect Q.
Thus, Q for the unknown species can be simplified to:
Q = [Unknown element(aq)]
Since we have only one unknown element, we can represent its concentration as [X], where X is the symbol or name of the unknown element.
Using the Nernst equation and the given Eºcell value (1.83 V), you can substitute the appropriate values and solve for the half-cell potential of the unknown species.
c. To determine the identity of the unknown element, you will need to refer to a table of standard reduction potentials. By comparing the measured electrode potential for the unknown species to the standard reduction potential values, you can identify the unknown element. The element with a half-cell potential closest to the measured value will correspond to the unknown element.