Question

A student is attempting to reverse the tarnishing (silver sulfide, Ag2S(s), formation) on her silver necklace using a method she found online. She lined a bowl with aluminum foil, added some baking soda, a sprinkling of table salt, and finally boiling water. She then placed the tarnished silver object into the water, making sure there was contact between it and the aluminium foil. Amazingly, the silver sulphide tarnish began to disappear, being replaced by discoloration of the Al foil. The overall reaction is: Identifying which solid is serving as the anode and which as the cathode in this a. reaction. b. Based on the description provided in the question above, what must be true about the cell potential (Ecel) under these conditions? Briefly explain your answer. c. In the crystalline solid, Al2Sse adopts a rectangular unit cell with dimensions of 7.03 A x 7.03 A x 29.82 A with 32 () Al atoms inside the unit cell. Use this information to calculate the density of aluminum sulfide. 23(s)

Answer 1

a. In Ag₂S , Ag remains in +1 oxidation state but upon reaction it becomes elementary Ag, having oxidation state 0 (zero). So, upon reaction Ag⁺ gets reduced to Ag. Again on the other hand, Al before reaction was in elementary state, having oxidation state 0, but after reaction it goes to +3 in Al₂S₃. So, Al gets oxidized to Al³⁺ due to reaction. We, know, the reduction occurs in cathode and oxidation occurs in anode, so here Ag₂S is acting as cathode and Al is acting as anode.

Tips for oxidation state calculation:

i. Overall molecule has oxidation state zero

ii. Consider sulpher having oxidation state -2 per atom

So, for Ag₂S, if oxidation state per Ag atom is x, then,

SO. T

Similarly for Al₂S₃, $x\times 2 + (-2)\times 3 = 0, So, x = 3$

b. From the reaction given above and the observations, it is clear that, the reaction is highly spontaneous. The reaction  started just after adding the neckless into the bowl. So, from the knowledge of therrmodynamics we can say $\bigtriangleup G$ for the reaction is highly negative. Now, from the knowledge of electrochemistry we know, $\bigtriangleup G = -nFE_{cell}$ . n stands for no of electron transferred in the process, F is Faraday constant and they both are positive. The term left is the E_Cell , i.e, the cell potential for the electrochemical cell formed in the reaction medium. In order to make $\bigtriangleup G$ negative, E_cell must be positive. So, under the reaction condition, E_cell is highly positive.

c. If 32 Al atoms reside there, then the number of Al₂S₃ molecule there is 16. Molar mass of Al₂S₃ is

(27 x 2 +32 x 3) q.mol-- 150q.mol
. In 1 mole of molecule there are Avogadro number of molecules, i.e,
023 × 102
molecules.

So,6.023 x 102*molecules have total mass 150q

then 16 molecules have total mass150 (6.023 x 1023)] x 16g

21 3.985 × 10-g

Al so, the unit cell has volume (7.03 x 7.03 x 29.82)A3 1473.4

Now, 1 angstrom = 10^-8 cm, so actual volume is

21 24 1473 × 10- cm3-1.473 × 10-cm2 ง

Now, density = (mass) / (volume), thus,

") = 2.70 q.crn- 73 × 10- cm (1.4 density = (3.985 × 10-219)