How Do You Model the Changing Concentration of Nitric Acid in a Tank?

[Tapias5000]

Summary:: A nitric acid solution enters at a constant rate of 6 liters / minute into a large tank that originally contained 200 liters of a 0.5% nitric acid solution. The solution inside the tank is kept well stirred and leaves the tank at a rate of 8 liters / minute. If the solution entering the tank has 20% nitric acid, determine the volume of nitric acid in the tank after t minutes. When will the percentage of nitric acid in the tank reach 10%?

A nitric acid solution enters at a constant rate of 6 liters / minute into a large tank that originally contained 200 liters of a 0.5% nitric acid solution. The solution inside the tank is kept well stirred and leaves the tank at a rate of 8 liters / minute. If the solution entering the tank has 20% nitric acid, determine the volume of nitric acid in the tank after t minutes. When will the percentage of nitric acid in the tank reach 10%?

How do I solve the 10% question I got this far.

[Moderator's note: moved from a technical forum.]

 

[berkeman]

What's "edo"?

Acronym	Definition
EDO	Extended Data Out (RAM)
EDO	Eating Disorder
EDO	Extended Data Output
EDO	Engineering Distributed Object
EDO	Event Delivery Object
EDO	Executive District Officer (Pakistan)
EDO	Economic Development Officer
EDO	Extended Duration Orbiter
EDO	Extra Day(s) Off
EDO	Engineering Duty Officer
EDO	Eastern District Office (various organizations)
EDO	Electronic Door Opener (various companies)
EDO	Electronic Distribution Only (US Marine Corps)
EDO	Education Development Officer (job title)
EDO	Earned Day Off (Canadian federal government)
EDO	Enlisted Dining Out (US Air Force)
EDO	Écurie de Dressage Orbecoise (French equestrian association)
EDO	Ethadione (medication)
EDO	Education Development Organization
EDO	Estate Duty Office (United Kingdom)
EDO	Emergency Detention Order (court order for mental health evaluation)
EDO	Engineering Duty Only (US Navy)
EDO	Engineering Data Center
EDO	Employer Deduction Order
EDO	Earl Dodge Osborne (EDO Corporation)
EDO	Electric Drive Option
EDO	Environmental Development Office
EDO	Expeditionary Decisive Operations
EDO	Exploratory Development Objective
EDO	Engineering Design Outsourcing

https://acronyms.thefreedictionary.com/EDO

 

[jedishrfu]

I think it’s related to Electron Deficit Olefin Ligands

https://pubmed.ncbi.nlm.nih.gov/32348673/

Placing a collect call to @Borek

 

[Chestermiller]

I'd like to see your derivation of the equations. Here is my derivation: I think you are supposed to assume the percentage nitric acid is the volume percentage and that the solution overall density doesn't change. So, based on this, the volume of fluid in the tank is V = 200-2t, the amount of nitric acid in the tank at any time is FV, the rate of nitric acid entering is (6)(0.2), and the rate of nitric acid leaving at any time is 8F, where F is the fraction nitric acid in the tank at any time. So my nitric acid balance o the tank is $$\frac{d(VF)}{dt}=(6)(0.2)-8F$$ The initial condition is F = 0.005