To this point in the chapter, we have considered the total current, I. However, as you know from your experience, some electrochemical devices are small like a hearing aid battery. Others are significantly larger, such as the battery used to start your car. You would not expect the total current from these devices to be similar. Because electrochemical reactions take place on surfaces, we frequently normalize the total current by the surface area in order for us to better understand and characterize the system. Current density is defined as the current divided by the area of the electrode and will be used extensively throughout this book. Similarly, the molar rate of reaction is often expressed as a flux, [mol·m⁻²·s⁻¹]. These molar fluxes are used extensively in studying mass transfer. Let’s illustrate these concepts with an example.

ILLUSTRATION 1.6

1. The electrode from Illustration 1.4 has an area of 80 cm², what is the current density?From Faraday’s law we can relate the charge to the amount of chloride ions that are consumed. Similar to current density, we define the flux of Cl⁻ to the electrode surface. Namely,
2. For the lead–acid battery described in Illustration 1.3, convert the molar reaction rates to molar fluxes given that the electrode area is 0.04 m². The previous results are divided by the electrode area.This quantity represents the rate of dissolution of Pb from the negative electrode into the electrolyte.Next, consider the flux of sulfate ion (see Illustration 1.3). Because sulfate is consumed at both electrodes, we must calculate the sulfate flux for each electrode.For the negative electrode,For the positive electrode,Thus, we have 0.0026 mol m⁻² s⁻¹ of sulfate ions moving from the electrolyte toward the negative electrode and an equal flux moving toward the positive electrode.

Strictly speaking, molar flux, and therefore current density, are vector quantities—ones that have both a magnitude and direction. The current density, i, is defined as

(1.14)

where N_i is the molar flux [mol·m⁻²·s⁻¹] and z_i is the electrical charge of species i. This equation indicates that for current to flow, there needs to be a net movement of charged species. We will only occasionally need to treat these quantities as having more than one directional component; therefore, our practice will be to not make any special effort to identify these quantities as vectors unless needed. However, even for one-dimensional current flow, we need to pay attention to the direction, which of course depends on how our coordinate system is defined. Referring back to Illustration 1.4, the flux of chloride ions is from right to left, which is a negative flux (in the negative x direction). The charge of the chloride ion, z_i, is also negative. Therefore, current flow is positive in that example.