To calculate the exchange current density at the cathode of a lithium-ion battery, we can use the Tafel equation: = b * log i / i0 where: = overpotential 0.1 V b = Tafel slope 120 mV/decade = 0.120 V/decade i = current density unknown i0 = exchange current density unknown First, we need to rearrange the equation to solve for i0:i0 = i / 10^ / b Since we don't have the value of i current density , we can't directly calculate i0. However, we can express the relationship between i and i0 using the given overpotential and Tafel slope:0.1 V = 0.120 V/decade * log i / i0 Now, we can solve for the ratio i / i0:log i / i0 = 0.1 V / 0.120 V/decadelog i / i0 = 0.8333Taking the antilog inverse log of both sides:i / i0 = 10^0.8333i / i0 6.79This means that the current density i is approximately 6.79 times the exchange current density i0 . Unfortunately, without the value of i, we cannot directly calculate the exchange current density. However, this relationship can be used to determine i0 once the current density is known.