Atmospheric pressure acid leaching was used to achieve clean and efficient recovery of valuable metals from two materials, with pyrolusite and copper smelting and refining slag (CSRS) separately serving as the oxidant and reductant in the leaching process. The influences of the leaching temperature, liquid–solid ratio, initial concentration of sulfuric acid, and mass ratio of pyrolusite to CSRS \((S_{Mn} /S_{Cu} )\) on the leaching rate of manganese (Mn) were investigated. On this basis, the unreacted shrinking core model for heterogeneous reactions was employed explore the macroscopic leaching kinetics of Mn. The results show that the leaching rates of Mn and Cu are separately 98.23% and 63.98% when the leaching temperature, liquid–solid ratio, initial concentration of sulfuric acid, \((S_{Mn} /S_{Cu} )\) ratio, and time are 95 ℃, 10:1 mL/g, 2.5 mol/L, 0.42:1, and 9 h, respectively. The Mn leaching process is governed by interfacial chemical reactions, in which the apparent activation energy Ea is 43.141 kJ/mol, and the orders of reaction under different initial concentrations of sulfuric acid, liquid–solid ratios, and \((S_{Mn} /S_{Cu} )\) ratios are separately 0.4463, 1.0290, and 1.5069. The macrokinetic equation for the leaching of Mn is:
\(1 - \left( {1 - x} \right)^{\frac{1}{3}} = \frac{152055}{{r_{0} }}\exp \left( { - \frac{5621}{T}} \right)c_{{H_{2} SO_{4} }}^{0.4463} \left( {L/S} \right)^{1.0290} \left( {S_{Mn} /S_{Cu} } \right)^{1.5069}\)
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