For the reaction: Ba(OH)2 (s) + 2 NH4Cl (s) → BaCl2 (s) + 2 H2O (l) + NH3 (g)

If ammonia gas (NH3) is produced at the rate of 0.72 mol/s, what is the corresponding rate of
consumption of ammonium chloride?
ANS: NH4Cl is consumed at a rate of 1.4 mol/s, twice as quickly as NH3 is produced

im confused how they came to this solution. is it by rate=k(A)^a(B)^b ??

No, not that. The ammonia is coming from the ammonium chloride alone. The rate of one has to equal the negative rate of the other. However, there is an error in your balanced equation, here it is corrected, and it might reveal a secret to you.

Ba(OH)2 (s) + 2 NH4Cl (s) → BaCl2 (s) + 2 H2O (l) + 2NH3 (g)

So in fact, your balanced equation was wrong, as was the answer provided.

So considering stoichiometry does that mean that ammonium chloride is being produced at a equal (0.72 mol/s) rate as it is being consumed

No, the rate equation is not used to solve this problem. The given reaction equation tells us the stoichiometry of the reaction, which allows us to determine the relationship between the rates of reactant consumption and product formation.

From the balanced equation: Ba(OH)2 (s) + 2 NH4Cl (s) → BaCl2 (s) + 2 H2O (l) + NH3 (g)

We can see that 2 moles of NH4Cl are consumed for every 2 moles of NH3 produced. Therefore, the rate of consumption of NH4Cl will be equal to the rate of production of NH3, but with opposite signs.

Given that NH3 is produced at a rate of 0.72 mol/s, the corresponding rate of NH4Cl consumption will be -0.72 mol/s. The negative sign indicates consumption rather than production.

However, the answer provided, "NH4Cl is consumed at a rate of 1.4 mol/s," seems to be incorrect. Based on the given reaction and the information provided, the correct rate of NH4Cl consumption should be -0.72 mol/s, as explained above.

Yes, you are referring to the rate law equation, which is used to express the relationship between the rate of a chemical reaction and the concentrations of the reactants.

In this case, the given reaction is: Ba(OH)2 (s) + 2 NH4Cl (s) → BaCl2 (s) + 2 H2O (l) + NH3 (g)

To determine the rate of consumption of ammonium chloride (NH4Cl), we need to consider the coefficients of the balanced equation. According to the balanced equation, 2 moles of NH4Cl are consumed for every 1 mole of NH3 produced.

Given that the rate of NH3 production is 0.72 mol/s, we can infer that the rate of NH4Cl consumption is twice that, or 2 * 0.72 = 1.44 mol/s.

Hence, the corresponding rate of consumption of ammonium chloride is 1.44 mol/s.

The equation you mentioned, rate=k(A)^a(B)^b, is the generic form of the rate law equation, where A and B represent the reactants, and a and b are the respective reaction orders with respect to A and B. In this case, since the concentration of NH4Cl is not given and there is no information about the reaction order, we cannot use the rate law equation to solve this specific problem.

Instead, we rely on the stoichiometry of the balanced equation to determine the ratio between the rate of NH3 production and the rate of NH4Cl consumption.