Question

The following galvanic cell has a potential of 1.214 V at 25∘C:

Hg(l)|Hg2Br2(s)|Br−(0.10M)||MnO4−(0.10M),Mn2+(0.10M),H+(0.10M)|Pt(s)
Calculate the value of Ksp for Hg2Br2 at 25∘C.
Express your answer using one significant figure.

Answer 1

The Ksp for Hg2Br2 at 25°C is calculated using the given potential of the galvanic cell and the Nernst equation, resulting in an approximate Ksp value of 3×10^-21 with one significant figure.

Step-by-step explanation:

To calculate the solubility product (Ksp) of Hg2Br2 using the given potential of the galvanic cell, we can use the Nernst equation. At 25°C, the Nernst equation when solving for Ksp can be simplified to the form Ecell = -0.0591 V log Ksp. Rearranging this equation to solve for Ksp gives us:

log Ksp = -Ecell / 0.0591 V

Ksp = 10^(log Ksp)

Plugging in the given cell potential (1.214 V), we proceed with the calculation:

log Ksp = -1.214 V / 0.0591 V = -20.53

Ksp = 10-20.53

Since the question asks for an answer with one significant figure, Ksp would be approximately 3×10-21.

Note that the simplification of the Nernst equation is possible because at standard temperature (25°C), the constants involved can be factored into the equation to yield the -0.0591 V/log Ksp relationship used here.

Answer 2

The value of Ksp for Hg2Br2 at 25∘C can be calculated using the Nernst equation and the given cell potential. Plug in the concentrations of the ions involved in the cell reaction and solve for Ksp.

Step-by-step explanation:

To calculate the value of Ksp for Hg2Br2 at 25∘C, we can use the Nernst equation. The Nernst equation relates the cell potential and the concentration of the ions in the cell. In this case, the cell potential is given as 1.214 V. We can substitute this value into the Nernst equation and solve for Ksp.

The Nernst equation is: Ecell = E°cell - (0.0592 V/n) log Q

Where Ecell is the measured cell potential, E°cell is the standard cell potential, n is the number of electrons transferred in the cell reaction, and Q is the reaction quotient. In this case, E°cell is zero because Hg(l) is the reference electrode. The reaction quotient Q can be calculated using the concentrations of the ions involved in the cell reaction. Plugging in the given concentrations and solving for Ksp will give the value of Ksp for Hg2Br2 at 25∘C.