(Solution) - Suppose mA g of species A molecular weight MA heat capacity -(2025 Original AI-Free Solution)

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Suppose mA (g) of species A {molecular weight MA, heat capacity CpA [J/ (g?°C)]} at temperature TA0 (°C) and mB (g) of species B (MB, CpB) at temperature TB0 are mixed adiabatically. The heat of mixing of A and B at 25°C is ?Hm (r) (J/mol A in solution), where r = (mB/MB)/ (mA/MA). The heat capacity of the product solution is Cps [J/ (g?°C)]. All heat capacities may be considered independent of temperature.
(a) Derive an expression for Tmax, the highest temperature attainable by the product solution, in terms of the other quantities defined. State the conditions that would have Co be met for this temperature to be approached.
(b) Use your expression to estimate Tmax for a process in which 100.0 g of sodium hydroxide at 25°C and 225.0 g of water at 40°C are combined to form a product solution with a heat capacity of 3.35 J/(g?°C).