For the following reactions, predict how the rate of the...

For the following reactions, predict how the rate of the reaction will change as the concentration of the reactants triple. (a) $\mathrm{SO}_{2} \mathrm{Cl}_{2} \longrightarrow \mathrm{SO}_{2}+\mathrm{Cl}_{2} \quad$ rate $=k\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]$ (b) $2 \mathrm{HI} \longrightarrow \mathrm{H}_{2}+\mathrm{I}_{2}$ rate $=k[\mathrm{HI}]^{2}$ (c) $\mathrm{ClOO} \longrightarrow \mathrm{Cl}+\mathrm{O}_{2} \quad$ rate $=k$ (d) $\mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{2}^{-}(a q) \rightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}$ rate $=k\left[\mathrm{NH}_{4}^{+}\right]\left[\mathrm{NO}_{2}^{-}\right]$ (e) $2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$ rate $=k\left[\mathrm{H}_{2}\right][\mathrm{NO}]^{2}$

For the following reactions, predict how the rate of the reaction will change as the concentration of the reactants triple.
(a) $\mathrm{SO}_{2} \mathrm{Cl}_{2} \longrightarrow \mathrm{SO}_{2}+\mathrm{Cl}_{2} \quad$ rate $=k\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]$
(b) $2 \mathrm{HI} \longrightarrow \mathrm{H}_{2}+\mathrm{I}_{2}$ rate $=k[\mathrm{HI}]^{2}$
(c) $\mathrm{ClOO} \longrightarrow \mathrm{Cl}+\mathrm{O}_{2} \quad$ rate $=k$
(d) $\mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{2}^{-}(a q) \rightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}$ rate $=k\left[\mathrm{NH}_{4}^{+}\right]\left[\mathrm{NO}_{2}^{-}\right]$
(e) $2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$
rate $=k\left[\mathrm{H}_{2}\right][\mathrm{NO}]^{2}$

Key Concepts

Rate Law

A rate law is a mathematical expression that shows how the rate of a chemical reaction depends on the concentrations of its reactants. It is written as rate = k [A]^m [B]^n, where k is the rate constant and m and n are the orders with respect to reactants A and B respectively. This allows predictions of how changes in concentrations will alter the reaction rate.

Reaction Order

The reaction order is determined by the sum of the exponents of the concentration terms in the rate law. It indicates the sensitivity of the reaction rate to changes in reactant concentrations. For instance, a first-order reaction will have a rate that changes linearly with concentration, while a second-order reaction will change quadratically.

Effect of Concentration Changes

When the concentration of a reactant is changed, the reaction rate changes according to the power law relationship indicated in the rate law. Tripling the concentration in a first-order reaction leads to a threefold increase in rate, while in a second-order reaction it leads to a ninefold increase. This concept allows prediction of reaction behavior under modified concentration conditions.

Zero Order Kinetics

In zero order reactions, the rate of the reaction is independent of the concentration of the reactants. The rate law is expressed as rate = k, meaning that changes in concentration will not affect the overall reaction rate, a key concept in understanding reaction dynamics.

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