A 90-wt-% aqueous H₂SO₄ solution at 25°C is added over a period of 6 hours to a tank containing 4000 kg of pure water also at 25°C. The final concentration of acid in the tank is 50-wt-%. The contents of the tank are cooled continuously to maintain a constant temperature of 25°C. Because the cooling system is designed for a constant rate of heat transfer, this requires the addition of acid at a variable rate. Determine the instantaneous 90-%-acid rate as a function of time, and plot this rate (kg·s⁻¹) vs. time. The data of the preceding problem may be fit to a cubic equation expressing H^E/(x₁x₂) as a function of x₁, and the equations of the preceding problem then provide expressions for H̅^E₁ and H̅^E₂.