Question 12.2: Finding Reaction Order from a Rate Law The second reaction i......
Finding Reaction Order from a Rate Law
The second reaction in Table 12.2, shown in progress in Figure 12.4, is
\mathrm{HCO}_2 \mathrm{H}(a q)+\mathrm{Br}_2(a q) \longrightarrow 2 \mathrm{H}^{+}(a q)+2 \mathrm{Br}^{-}(a q)+\mathrm{CO}_2(g)Colorless Red Colorless
Colorless Red Colorless What is the order of the reaction with respect to each of the reactants? What is the overall reaction order?
STRATEGY
To find the reaction order with respect to each reactant, look at the exponents in the rate law, not the coefficients in the balanced chemical equation. Then sum the exponents to obtain the overall reaction order.
TABLE 12.2 Balanced Chemical Equations and Experimentally Determined Rate Laws for Some Reactions.
| Reaction* | Rate Law | |||
| \left(\mathrm{CH}_3\right)_3 \mathrm{CBr}(\text { soln })+\mathrm{H}_2 \mathrm{O}(\text { soln }) \longrightarrow\left(\mathrm{CH}_3\right)_3 \mathrm{COH}(\text { soln })+\mathrm{H}^{+}(\text {soln })+\mathrm{Br}^{-}(\text {soln }) | Rate = k[ (CH_3)_3CBr ] | |||
| \mathrm{HCO}_2 \mathrm{H}(a q)+\mathrm{Br}_2(a q) \longrightarrow 2 \mathrm{H}^{+}(a q)+2 \mathrm{Br}^{-}(a q)+\mathrm{CO}_2(g) | Rate = k[ Br_2 ] | |||
| \mathrm{BrO}_3^{-}(a q)+5 \mathrm{Br}^{-}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow 3 \mathrm{Br}_2(a q)+3 \mathrm{H}_2 \mathrm{O}(l) | Rate = k[ BrO_{3}^{-} ][ Br^- ][ H^+ ]^2 | |||
| \mathrm{H}_2(g)+\mathrm{I}_2(g) \longrightarrow 2 \mathrm{HI}(g) | Rate = k[ H_2 ][ I_2 ] | |||
*In the first reaction “(soln)” denotes a nonaqueous solution.
In general, the exponents in the rate law are not the same as the stoichiometric coefficients in the balanced chemical equation.
The rate law for the second reaction in Table 12.2 is
Rate = k[ Br_2 ]
Because HCO_2H (formic acid) does not appear in the rate law, the rate is independent of the HCO2H concentration, and so the reaction is zeroth order in HCO_2H. Because the exponent on [ Br_2 ] is 1 (it is understood to be 1 when no exponent is given), the reaction is first order in Br_2. The reaction is first order overall because the sum of the exponents is 1.