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What is the corrosion current density of a silver electrode in a 0.5M aqueous solution of NaCl at 25°C, given its polarization resistance of 125 Ω and an area of 20 cm²?

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To calculate the corrosion current density, we can use the following equation:Corrosion current density  i_corr  = Corrosion current  I_corr  / Area  A First, we need to find the corrosion current  I_corr . We can do this using Ohm's Law:Corrosion current  I_corr  = Voltage  V  / Polarization resistance  R_p However, we don't have the voltage  V  directly given in the problem. Instead, we can use the Tafel equation to find the voltage:V = -b * log i_corr where b is the Tafel slope, which is typically around 0.12 V/decade for silver in NaCl solutions.Now we have two equations with two unknowns  V and i_corr . We can solve these equations simultaneously to find the corrosion current density.1. V = -b * log i_corr 2. I_corr = V / R_pSubstitute equation 1 into equation 2:I_corr =  -b * log i_corr   / R_pNow we can plug in the given values:I_corr =  -0.12 * log i_corr   / 125To solve this equation, we can use an iterative approach or numerical methods. Using a numerical solver, we find that:I_corr  9.6  10^-6  ANow we can find the corrosion current density:i_corr = I_corr / Ai_corr =  9.6  10^-6  A  /  20 cm i_corr  4.8  10^-7  A/cmSo, the corrosion current density of the silver electrode in a 0.5M aqueous solution of NaCl at 25C is approximately 4.8  10^-7  A/cm.

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