Question

A standard galvanic cell is constructed so that the overall

cell reaction is

2Al31(aq) 1 3M(s) 88n 3M21(aq) 1 2Al(s)

where M is an unknown metal. If DG8 5 2411 kJ for

the overall cell reaction, identify the metal used to construct

the standard cell.

Short answer

Magnesium is used to construct the standard cell.

Step-by-step solution

analyzing the given data  

The given equation is

2Al³⁺+ 3M —› 3M²⁺ + 2Al

And$∆\mathrm{G}°=411\mathrm{kJ}$

calculating the theoretical maximum voltage for this cell

E° =$\frac{(∆G°)}{(-nF)}$=$-\frac{411000}{-6\left(96485\right)}=0.710$

E°_CELL= -166 –(x) = 0.710

X = E_CATHODE – E_ANODE

X = -237 V (reduction potential of Mg)

Hence, magnesium is the metal that is used to construct the standard cell.