To calculate the corrosion current density, we can use the Tafel equation, which relates the corrosion potential E_corr and the corrosion current density i_corr to the anodic and cathodic Tafel slopes b_a and b_c and the exchange current density i_0 .First, we need to find the corrosion potential E_corr . Since the half-cell potential of the metal M is -0.8V and the standard hydrogen electrode potential is 0V, the corrosion potential is:E_corr = E_M - E_H = -0.8V - 0V = -0.8VNext, we need to find the exchange current density i_0 . This can be determined experimentally or estimated from the literature. For this problem, we will assume an exchange current density of 1 x 10^-6 A/cm.Now, we need to find the anodic and cathodic Tafel slopes b_a and b_c . These values can also be determined experimentally or estimated from the literature. For this problem, we will assume b_a = 120 mV/decade and b_c = -120 mV/decade.With these values, we can use the Tafel equation to find the corrosion current density i_corr :i_corr = i_0 * 10^ E_corr - E_M /b_a + 10^ E_corr - E_H /b_c i_corr = 1 x 10^-6 A/cm * 10^ -0.8V - -0.8V /120 mV/decade + 10^ -0.8V - 0V /-120 mV/decade i_corr = 1 x 10^-6 A/cm * 10^0 + 10^6.67 i_corr = 1 x 10^-6 A/cm * 1 + 4.67 x 10^5 i_corr = 4.67 x 10^-1 A/cmThe corrosion current density of the metal M in the 0.5 M H2SO4 solution is approximately 4.67 x 10^-1 A/cm.