El sulfito reduce el ion yodato según la reacción siguiente: IO3 ^-(a c)+3 SO3 ^2-(a c) →I^-(a c

El sulfito reduce el ion yodato según la reacción siguiente:...

El sulfito reduce el ion yodato según la reacción siguiente: $$ \mathrm{IO}_3{ }^{-}(a c)+3 \mathrm{SO}_3{ }^{2-}(a c) \rightarrow \mathrm{I}^{-}(a c)+3 \mathrm{SO}_4{ }^{2-}(a c) $$ La velocidad de esta reacción es de primer orden respecto a $\mathrm{IO}_3^{-}$, de primer orden respecto a $\mathrm{SO}_3{ }^{2-}$ y de primer orden respecto $\mathrm{H}^{+}$. (a) Escriba la ecuación de velocidad de la reacción. (b) ¿Por qué factor cambiará la velocidad de la reacción si se reduce el pH de 5.00 a 3.50? ¿Es más rápida o más lenta la reacción al $\mathrm{pH}$ más bajo? (c) Con base en los conceptos analizados en la sección 14.6, explique cómo es que la reacción depende del $\mathrm{pH}$ pese a que el $\mathrm{H}^{+}$no aparece en la reacción global.

El sulfito reduce el ion yodato según la reacción siguiente:
$$
\mathrm{IO}_3{ }^{-}(a c)+3 \mathrm{SO}_3{ }^{2-}(a c) \rightarrow \mathrm{I}^{-}(a c)+3 \mathrm{SO}_4{ }^{2-}(a c)
$$

La velocidad de esta reacción es de primer orden respecto a $\mathrm{IO}_3^{-}$, de primer orden respecto a $\mathrm{SO}_3{ }^{2-}$ y de primer orden respecto $\mathrm{H}^{+}$. (a) Escriba la ecuación de velocidad de la reacción. (b) ¿Por qué factor cambiará la velocidad de la reacción si se reduce el pH de 5.00 a 3.50? ¿Es más rápida o más lenta la reacción al $\mathrm{pH}$ más bajo? (c) Con base en los conceptos analizados en la sección 14.6, explique cómo es que la reacción depende del $\mathrm{pH}$ pese a que el $\mathrm{H}^{+}$no aparece en la reacción global.

Key Concepts

Rate Law

The rate law is a mathematical expression that relates the rate of a chemical reaction to the concentrations of its reactants (and sometimes catalysts). In kinetic studies, if a reaction is first order with respect to IO3–, first order with respect to SO3^2–, and first order with respect to H+, the rate law is written as Rate = k[IO3–][SO3^2–][H+], where k is the rate constant. This law shows how variations in any of these concentrations directly affect the overall reaction rate.

Reaction Order

The reaction order indicates the power to which the concentration of each reactant is raised in the rate law and reflects the sensitivity of the reaction rate to its concentration. In this case, the reaction is first order in each of three reactants, meaning the overall reaction is third order. This designation helps in understanding the kinetic complexity and the number of species involved in the rate-determining steps of the mechanism.

pH and Hydrogen Ion Concentration

pH is a measure of the hydrogen ion concentration in a solution, defined by the equation pH = -log[H+]. Since the rate law includes [H+], any change in the pH results in a change in the hydrogen ion concentration. A lower pH corresponds to a higher [H+], which, according to the rate law, would increase the reaction rate. Thus, a decrease in pH (more acidic conditions) speeds up the reaction.

Acid Catalysis and Reaction Mechanism

Even when H+ does not appear in the overall balanced chemical equation, its presence in the rate law suggests that it plays an important role—often as a catalyst or as part of a pre-equilibrium step—in the reaction mechanism. Acid catalysis can facilitate the formation or stabilization of reaction intermediates, thereby altering the kinetic pathway and accelerating the overall reaction. This illustrates how reaction mechanisms can be influenced by species that are not explicitly shown in the overall stoichiometry.

Transcript

00:01 In this problem, we are asked to, oops, i've got to get back to my problem here, answer a couple questions about the reaction i've written right here.

00:13 The rate of this reaction is found to be first order in the iodate, first order in sulfate, and first order for h plus.

00:49 A asks us to write the rate law, which is easy since they gave us everything.

01:00 So the rate law is this, for this, since it's first order, is the rate is equal to our constant times each concentration that we were just listed, not raised to, or just, i guess, raised to the first power.

01:26 Super simple for that one.

01:27 Next one isn't quite as simple, but that's okay.

01:32 B.

01:40 By what factor will the rate of the reaction change? if the ph is lowered from 5 .00 to 3 .50, does the rate? reaction proceed faster or slower i guess i should have written or slower at the lower ph and that's going to be our b so let's get ready for this one our change in ph will equal ph 2 minus ph 1 .50 now let's take a look at this following working through the equation here almost there okay so this is the equation we're going to use here.

06:02 So, oh, i've got something written there.

06:05 Let's go quickly by that.

06:08 So i get this following.

06:43 So this means that the rate will increase 32 -fold if the ph, let's just, will increase by 32 -fold.

07:13 So this means that the reaction is faster at the lower ph.

07:25 Okay, everything answered is answered for question b or part b.

07:31 Now let's do part c.

07:37 For part c, by using the concepts discussed in section 14 .6, i'm going to write c14 .6...