How do you write a Mass Balance or Charge Balance for Acid-Base Equilibrium?

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To write a mass balance for acid-base equilibrium, identify all species involved in the reaction and their concentrations. In the case of Zn(OH)2 in a saturated NaOH solution, the mass balance would include the concentrations of Zn(OH)2, OH-, and Zn(OH)4(2-). A charge balance requires ensuring that the total positive and negative charges are equal, which involves accounting for the charges of each species. The provided reaction, Zn(OH)2 + 2OH- -> Zn(OH)4(2-), illustrates the stoichiometry needed for these balances. Understanding these principles is crucial for solving acid-base equilibrium problems effectively.
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Can somebody explain how do you write a Mass Balance or Charge balance for a acid-base equilibrium? Let say, if you are given 0.01M Zn(OH)2 in a saturated NaOH solution and also given that Zn(OH)2 + 2OH- -> Zn(OH)4(2-) how would you solve the mass balance/charge balance? I really have no idea how to do these types of quesitons...Thanks!
 
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TL;DR Summary: cannot find out error in solution proposed. [![question with rate laws][1]][1] Now the rate law for the reaction (i.e reaction rate) can be written as: $$ R= k[N_2O_5] $$ my main question is, WHAT is this reaction equal to? what I mean here is, whether $$k[N_2O_5]= -d[N_2O_5]/dt$$ or is it $$k[N_2O_5]= -1/2 \frac{d}{dt} [N_2O_5] $$ ? The latter seems to be more apt, as the reaction rate must be -1/2 (disappearance rate of N2O5), which adheres to the stoichiometry of the...
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