Question

What is the calculated value of the cell potential at 298K for an electrochemical cell with the following reaction?

What is the calculated value of the cell potential at 298K for an electrochemical cell with the following reaction, when the Cl2 pressure is 1.14 atm, the Cl- concentration is 2.62×10-3M, and the Sn2+ concentration is 7.76×10-4M ?

Cl2(g) + Sn(s)=2Cl-(aq) + Sn2+(aq)

Answer 1

`E_text(cell) = "-1.25 V"`

Explanation:

The standard reduction potentials for each half-reaction are:

`ulbb("Standard Reduction Potentials"color(white)(ml)E^@//"V"`
`"Cl"_2"(g)" + "2e"^"-" ⇌ "2Cl"^"-""(aq)" color(white)(mmmmmmm)"+1.358"`
`"Sn"^"2+""(aq)" + "2e"^"-" ⇌ "Sn(s)"color(white)(mmmmmmmll)"-0.14"`

Calculate the standard cell potential

`bb(color(white)(mmmmmmmmmmmmmmmmmll)ul(E^@//"V")`
`"2Cl"^"-""(aq)" ⇌ "Cl"_2"(g)" + "2e"^"-"color(white)(mmmmmmml)"+1.358"`
`ul("Sn"^"2+""(aq)" + "2e"^"-" ⇌ "Sn(s)"color(white)(mmmmmmm))color(white)(l)ul("+0.14"color(white)(m))`
`"2Cl"^"-""(aq)" + "Sn"^"2+""(aq)" ⇌ "Cl"_2"(g)" + "Sn(s)"color(white)(m)1.498`

You want `E_text(cell)^@` for the reverse process, so the equation for your reaction is

`"Cl"_2"(g)" + "Sn(s)" ⇌ "2Cl"^"-""(aq)" + "Sn"^"2+""(aq)"; E_text(cell)^@ = "-1.498 V"`

Your standard cell is not spontaneous as written.

Calculate the cell potential

`"Cl"_2"(1.14 atm)" + "Sn(s)"`
`⇌ "2Cl"^"-"(2.62 × 10^"-3"color(white)(l) "mol/L") + "Sn"^"2+"(7.76 × 10^"-4"color(white)(l) "mol/L");`

You have non-standard pressure and concentrations, so you must use the Nernst equation:

`color(blue)(bar(ul(|color(white)(a/a)E_text(cell) = E_text(cell)^° - (RT)/(nF)lnQcolor(white)(a/a)|)))" "`

`Q = (["Cl"^"-"]^2["Sn"^"2+"])/p_text(Cl₂) = ((2.62 × 10^"-3")^2 × 7.76 × 10^"-4")/1.14 = 4.67 × 10^"-9"`

`lnQ = ln(4.05 ×10^"-9") = "-19.2"`

`E_text(cell) = "-1.498 V" +(8.314 color(red)(cancel(color(black)("J·K"^"-1""mol"^"-1"))) × 298 color(red)(cancel(color(black)("K"))))/(2 × "96 485" color(red)(cancel(color(black)("J·V"^"-1"))))× 19.2 = 0.180 color(red)(cancel(color(black)("V"))) = "-1.498 V + 0.246 V = -1.25 V"`

Your cell is not spontaneous as written.