Concentration of reactants is one of the factors that can affect the reaction rate. Collision theory can be used to show that the higher the concentration of reactants the more collisions they undergo. Consequently, the number of inelastic collisions between these particles increases, and results in a higher reaction rate.
The relationship between the concentration of reactants and the reaction rate is not always directly proportional: for example, doubling the concentration does not necessarily double the reaction rate. It depends on the type of reaction and the nature of the reactants.
This relationship can be expressed mathematically using the rate law.
Rate law is a mathematical relationship between the concentration of reactants in a chemical reaction and its rate. It can be used to calculate the reaction rate at a given temperature.
For a hypothetical chemical reaction |a\ \text{A} + b\ \text{B} \rightarrow c\ \text{C} + d\ \text{D},| the rate law is:
||v = k[\text{A}]^m[\text{B}]^n||
where
|r\!:| reaction rate in |\text{mol/L}{\cdot\text{s}}|
|k\!:| rate constant in varying units
|[\text{A},] [\text{B}]\!:| concentration of reactants in |\text{mol/L}|
|m, n\!:| reaction order with respect to the corresponding reactant
Only concentrations of reactants in solution (e.g. in the gaseous state or in the aqueous state) are included in the rate law. Reactants in the liquid state or solid state are not included in the equation as they are not in solution.
For example, in the reaction |{\text{H}_{2\color{#3A9A38}{\text{(g)}}} + \text{I}_{2\color{#3A9A38}{\text{(g)}}} → 2\ \text{HI}_{\text{(g)}},}| both reactants are gases, so the rate law is: ||r = k[\text{H}_2]^m[\text{I}_2]^n||
However, in the reaction |\text{MgCO}_{3\color{#EC0000}{\text{(s)}}} + 2\ \text{HCl}_\color{#3A9A38}{\text{(aq)}} \rightarrow \text{MgCl}_{2\text{(aq)}} + \text{CO}_{2\text{(g)}} + \text{H}_2\text{O}_{\text{(g)}},| only one of the reactants is in aqueous state, so the rate law is: ||r = k[\text{HCl}]^m||
Before applying the rate law, the reaction order and the rate constant must be determined experimentally.
The reaction order is an experimentally determined value that indicates how the reaction rate changes when the concentration of a given reactant increases or decreases.
The higher the reaction order, the more significant the effect of concentration variation on the reaction rate.
Since the rate of a reaction varies as it progresses, it is often the initial rates that are measured experimentally in order to determine the order of the reaction.
To determine the reaction order with respect to a given reactant, the same chemical reaction is run with two different initial concentrations of the reactant of interest, while all other parameters are kept constant. The reaction rates at each initial concentration are measured and recorded. Then, the ratio of concentrations is compared to the ratio of reaction rates.
In the following equation, the exponent |m| corresponds to the reaction order with respect to Reactant A:
||\left(\dfrac{[\text{A}]_2}{[\text{A}]_1}\right)^m=\dfrac{r_2}{r_1}||
Consider a chemical reaction where the concentration of an aqueous or gaseous Reactant A is doubled: the concentration ratio is |\dfrac{2}{1}| or simply |2.| In response to this change, the reaction rate can remain constant, double, quadruple or octuple, as shown in the following table. The exponent on the base |2| corresponds to the reaction order with respect to Reactant A |(m).|
|
Initial concentration ratio |\left(\dfrac{[\text{A}]_2}{[\text{A}]_1}\right)| |
Initial rate ratio |\left(\dfrac{r_2}{r_1}\right)| |
Comparison between the concentration and rate ratio |\left(\dfrac{[\text{A}]_2}{[\text{A}]_1}\right)^m = \dfrac{r_2}{r_1}| |
Reaction order with respect to Reactant A |(m)| |
|---|---|---|---|
| |\dfrac{2}{1} = 2| |
The rate remains constant: |\dfrac{1}{1} = 1| |
|2^m = 1| |
|\begin{align} 2^m &= 1\\ |
|
The rate doubles: |\dfrac{2}{1} = 2| |
|2^m = 2| |
|\begin{align} 2^m &= 2\\ |
|
|
The rate quadruples: |\dfrac{4}{1} = 4| |
|2^m = 4| |
|\begin{align} 2^m &= 4\\ |
|
|
The rate octuples: |\dfrac{8}{1} = 8| |
|2^m = 8| |
|\begin{align} 2^m &= 8\\ |
The reaction order is usually a positive integer, although reactions with negative or fractional orders exist as well.
Once the reaction order with respect to each reactant is known, we can calculate the impact of a variation in reactant concentration on the initial reaction rate. To do this, we compare the ratio of the rates |(\dfrac{r_2}{r_1})| of the two reactions to the ratio of the expression of their rate law |(\dfrac{[\text{A}]_2^m\times[\text{B}]_2^n}{[\text{A}]_1^m\times[\text{B}]_1^n}).|
||\text{A}_{(aq)}+\text{B}_{(aq)}\rightarrow\text{C}_{(aq)}+\text{D}_{(aq)}||
||r_1 = k[\text{A}]_1^m[\text{B}]_1^n\ \text{and}\ r_2 = k[\text{A}]_2^m[\text{B}]_2^n\\
\dfrac{r_2}{r_1}=\dfrac{\cancel{k}[\text{A}]_2^m\times[\text{B}]_2^n}{\cancel{k}[\text{A}]_1^m\times[\text{B}]_1^n}\\ \dfrac{r_2}{r_1}=\left(\dfrac{[\text{A}]_2}{[\text{A}]_1}\right)^m \times \left(\dfrac{[\text{B}]_2}{[\text{B}]_1}\right)^n||
The reaction order with respect to a given reactant is not necessarily equal to the stoichiometric coefficient found in front of that reactant in the chemical equation. The reaction order has to be determined experimentally.
Only in elementary reactions, can it be assumed that the reaction order is equal to the stoichiometric coefficient.
The synthesis reaction between nitrogen dioxide gas |(\text{NO}_2)| and carbon monoxide gas |(\text{CO})| is conducted in a lab several times:
||\text{NO}_{2\text{(g)}} + \text{CO}_{\text{(g)}} → \text{NO}_{\text{(g)}} + \text{CO}_{2\text{(g)}}||
The initial concentrations of the reactants are recorded along with the initial reaction rates:
|
Experiment |
Initial |[\text{NO}_2], (\text{mol/L})| |
Initial |[\text{CO}], (\text{mol/L})| |
Initial |r, (\text{mol/L}{\cdot\text{s}})| |
|---|---|---|---|
|
Average values from Experiment 1 |
|1.00| |
|2.00| |
|0.0002| |
|
Average values from Experiment 2 |
|2.00| |
|2.00| |
|0.0008| |
|
Average values from Experiment 3 |
|2.00| |
|1.00| |
|0.0004| |
What is the reaction order with respect to each reactant?
Lors d’un laboratoire, on réalise trois expériences au cours desquelles se déroule une réaction de synthèse entre le dioxyde d’azote |(\text{NO}_2)| et le monoxyde de carbone |(\text{CO})|.
Voici l’équation chimique de la réaction.
||\text{NO}_{2\text{(g)}} + \text{CO}_{\text{(g)}} → \text{NO}_{\text{(g)}} + \text{CO}_{2\text{(g)}}||
Le tableau suivant présente, pour chaque expérience, les concentrations initiales de chacun des réactifs ainsi que la vitesse initiale de réaction.
|
Valeur approximative pour chaque expérience |
Concentration initiale de dioxyde d’azote |([\text{NO}_2]), (\text{mol/L})| |
Concentration initiale de monoxyde de carbone |([\text{CO}]), (\text{mol/L})| |
Vitesse initiale de réaction |v, (\text{mol/L}{\cdot\text{s}})| |
|---|---|---|---|
|
Expérience 1 |
|1{,}00| |
|2{,}00| |
|0{,}0002| |
|
Expérience 2 |
|2{,}00| |
|2{,}00| |
|0{,}0008| |
|
Expérience 3 |
|2{,}00| |
|1{,}00| |
|0{,}0004| |
Quel est l’ordre de réaction par rapport à chacun des réactifs de la réaction chimique?
Reaction order with respect to |\text{NO}_2\!:|
-
Determine the |\text{NO}_2| concentration ratio between experiments 2 and 1, while the concentration of |\text{CO}| remains constant:
|\dfrac{[\text{NO}_2]_2}{[\text{NO}_2]_1} = \dfrac{2.00\ \cancel{\text{mol/L}}}{1.00\ \cancel{\text{mol/L}}} = \dfrac{2}{1} = 2| -
Determine the |r| ratio between experiments 2 and 1:
|\dfrac{r_2}{r_1} = \dfrac{0.0008\ \cancel{\text{mol/L}{\cdot\text{s}}}}{0.0002\ \cancel{\text{mol/L}{\cdot\text{s}}}} = \dfrac{4}{1} = 4| -
Compare the ratio of rates to the ratio of concentrations to determine the order.
|\dfrac{r_2}{r_1} = \left(\dfrac{[\text{NO}_2]_2}{[\text{NO}_2]_1}\right)^m|
|4=2^m=4 \Rightarrow m = 2|
When the concentration of |\text{NO}_2| doubles, the |r| quadruples. The order of this reaction with respect to |\text{NO}_2| is |\bf 2.|
Reaction order with respect to |\text{CO}\!:|
-
Determine the |\text{CO}| concentration ratio between experiments 2 and 3, while the concentration of |\text{NO}_2| remains constant:
|\dfrac{[\text{CO}]_2}{[\text{CO}]_3} = \dfrac{2.00\ \cancel{\text{mol/L}}}{1.00\ \cancel{\text{mol/L}}} = \dfrac{2}{1} = 2| -
Determine the |r| ratio between experiments 2 and 3:
|\dfrac{r_2}{r_3} = \dfrac{0.0008\ \cancel{\text{mol/L}{\cdot\text{s}}}}{0.0004\ \cancel{\text{mol/L}{\cdot\text{s}}}} = \dfrac{2}{1} = 2| -
Compare the ratio of rates to the ratio of concentrations to determine the order.
|\dfrac{r_2}{r_3} = \left(\dfrac{[\text{CO}]_2}{[\text{CO}]_3}\right)^m|
|2=2^m \Rightarrow m = 1|
When the concentration of |\text{CO}| doubles, the |r| doubles. The order of this reaction with respect to |\text{CO}| is |\bf 1.|
The overall reaction order is the sum of individual orders determined relative to each aqueous or gaseous reactant.
In the previous example, it was determined that the order of the following reaction is |2| with respect to |\text{NO}_2| and |1| with respect to |\text{CO}.|
|\text{NO}_{2\text{(g)}} + \text{CO}_{\text{(g)}} → \text{NO}_{\text{(g)}} + \text{CO}_{2\text{(g)}}|
What is the overall reaction order?
To determine the overall reaction order, add individual reaction orders: |2 + 1 = 3.|
The overall reaction order is |\bf 3.|
The overall reaction order can be used to predict the effect of varying the concentrations of all reactants on the reaction rate. In the previous example, the overall reaction order is |3.| This means that when the concentration of all reactants doubles, the reaction rate increases by a factor of 8, as shown in the following procedure:
-
In the following formula, the ratio of initial concentration of reactants and the ratio of initial reaction rates are compared using the exponent |x,| which corresponds to the overall reaction order.
|\dfrac{r_2}{r_1}=\left(\dfrac{[Reactants]_2}{[Reactants]_1}\right)^x|
-
In this example, the known values are:
|\begin{align}\dfrac{[Reactants]_2}{[Reactants]_1} &= \dfrac{2}{1}=2\\x &= 3\end{align}|
-
Plug in the values and determine the ratio of reaction rates:
|\begin{align}\dfrac{r_2}{r_1}&=2^3\\\\\dfrac{r_2}{r_1} &= \dfrac{8}{1} = 8\end{align}|
The overall reaction order can be used to determine the units of the rate constant |(k),| as shown in this table.
The rate constant |(k)| is a proportionality constant between the reaction rate and the concentration of reactants for a given chemical reaction at a given temperature.
The rate constant is calculated based on the experimentally obtained values.
The rate constant is calculated by isolating it from the rate law.
|k = \dfrac{r}{[\text{A}]^m[\text{B}]^n}|
where
|k\!:| rate constant in varying units
|r\!:| reaction rate in |\text{mol/L}{\cdot\text{s}}|
|[\text{A},] [\text{B}]\!:| concentration of reactants in |\text{mol/L}|
|m, n\!:| reaction order with respect to the corresponding reactant
Rate Constant Units
There are two ways to determine the units of the rate constant:
-
By isolating |k| from the rate law and simplifying the units.
-
By determining the overall reaction order and finding the corresponding units in the following table.
|
Overall reaction order |
Rate constant |(k)| units |
|---|---|
|
|0| |
|\text{mol/L}{\cdot\text{s}}| |
|
|1| |
|\text{s}^{-1}| |
|
|2| |
|\text{L/mol}{\cdot\text{s}}| |
|
|3| |
|\text{L}^2\text{/mol}^2{\cdot\text{s}}| |
The following table shows that the rate constant units are derived from the rate law formula, which varies depending on the order of the reaction. As a result, the rate constant units are different for each overall reaction order.
|
Overall reaction order |
Rate law |
Rate constant isolated from the rate law, |(k)| |
Rate law units |
|---|---|---|---|
|
|0| |
|v = k| |
|k = r| |
|\text{mol/L}{\cdot\text{s}}| |
|
|1| |
|r = k[\text{A}]| |
|k = \dfrac{r}{[\text{A}]}| |
|\dfrac{\cancel{\text{mol/L}}{\cdot\text{s}}}{\cancel{\text{mol/L}}} = \dfrac{1}{\text{s}} = \text{s}^{-1}| |
|
|2| |
|r = k[\text{A}]^2| |
|k = \dfrac{r}{[\text{A}]^2}| |
|\dfrac{\cancel{\text{mol/L}}{\cdot\text{s}}}{\cancel{\text{mol/L}}\ \times \text{mol/L}} = \dfrac{1/\text{s}}{\text{mol/L}} = \text{L/mol}{\cdot\text{s}}| |
|
|3| |
|r = k[\text{A}]^3| |
|k = \dfrac{r}{[\text{A}]^3}| |
|\dfrac{\cancel{\text{mol/L}}{\cdot\text{s}}}{\cancel{\text{mol/L}}\ \times \text{mol/L}\ \times \text{mol/L}}= \dfrac{\text{1/s}}{\text{mol/L}\ \times \text{mol/L}} = \text{L}^2\text{/mol}^2{\cdot\text{s}}| |
The synthesis reaction between nitrogen dioxide gas |(\text{NO}_2)| and carbon monoxide gas |(\text{CO})| is conducted in a lab several times at a specific temperature:
||\text{NO}_{2\text{(g)}} + \text{CO}_{\text{(g)}} → \text{NO}_{\text{(g)}} + \text{CO}_{2\text{(g)}}.||
The initial concentrations of the reactants are recorded along with the initial reaction rates:
|
Experiment |
Initial |[\text{NO}_2], (\text{mol/L})| |
Initial |[\text{CO}], (\text{mol/L})| |
Initial |r, (\text{mol/L}{\cdot\text{s}})| |
|---|---|---|---|
|
Average values from Experiment 1 |
|1.00| |
|2.00| |
|0.0002| |
|
Average values from Experiment 2 |
|2.00| |
|2.00| |
|0.0008| |
|
Average values from Experiment 3 |
|2.00| |
|1.00| |
|0.0004| |
In previous examples, it was determined that the order of the following reaction is |2| with respect to |\text{NO}_2| and |1| with respect to |\text{CO}.| The overall reaction order is 3.
Determine the value of the rate constant |(k)| at this temperature.
La réaction de synthèse entre le dioxyde d’azote gazeux |(\text{NO}_2)| et le monoxyde de carbone gazeux |(\text{CO})| est réalisée à plusieurs reprises dans un laboratoire à une température spécifique. Elle se déroule selon l’équation suivante.
||\text{NO}_{2\text{(g)}} + \text{CO}_{\text{(g)}} → \text{NO}_{\text{(g)}} + \text{CO}_{2\text{(g)}}.||
Le tableau suivant présente la concentration initiale de chaque réactif et la vitesse initiale de réaction pour chaque expérience.
|
Expérience |
Concentration initiale de |\text{NO}_2 (\text{mol/L})| |
Concentration initiale de |\text{CO} (\text{mol/L})| |
Vitesse initiale de la réaction |v, (\text{mol/L}{\cdot\text{s}})| |
|---|---|---|---|
|
Valeurs moyennes de l’expérience 1 |
|1{,}00| |
|2{,}00| |
|0{,}0002| |
|
Valeurs moyennes de l’expérience 2 |
|2{,}00| |
|2{,}00| |
|0{,}0008| |
|
Valeurs moyennes de l’expérience 3 |
|2{,}00| |
|1{,}00| |
|0{,}0004| |
L’ordre de réaction est de |2| par rapport à |\text{NO}_2| et de |1| par rapport à |\text{CO},| alors l’ordre global de la réaction est |3.|
Détermine la valeur de la constante de vitesse de la réaction |(k)|.
In the following procedure, we use the data from Experiment 1.
-
Identify the given values.
||\begin{align}r &= 0.0002\ \text{mol/L}{\cdot\text{s}}\\ [\text{NO}_2] &= 1.00\ \text{mol/L}\\ [\text{CO}] &= 2.00\ \text{mol/L}\\ m &= 2\\ n &= 1\\ k &=\ ?\ \text{L}^2\text{/mol}^2{\cdot\text{s}}\end{align}|| -
Write down the rate constant formula:
|k = \dfrac{r}{[\text{NO}_2]^2[\text{CO}]}| -
Plug in the values and calculate the final answer:
|\begin{align}k &= \dfrac{0.0002\ \cancel{\text{mol/L}}{\cdot\text{s}}}{(1.00\ \text{mol/L})^2 \times 2.00\ \cancel{\text{mol/L}}}\\\\
k &= 0.0001\ \text{L}^2\text{/mol}^2{\cdot\text{s}} = 1\ \times 10^{-4}\ \text{/mol}^2{\cdot\text{s}} \end{align}|
At this temperature, |k = 0.0001\ \text{L}^2\text{/mol}^2{\cdot\text{s}}.| Note that these units can be obtained by simplifying the units during the calculations or simply determined based on the overall reaction order.
The decomposition of |\text{N}_2\text{O}_5| is a first-order reaction:
||2\ \text{N}_2\text{O}_{5\text{(g)}}\rightarrow 4\ \text{N}\text{O}_{2\text{(g)}} + \text{O}_{2\text{(g)}}||
At a given temperature, the concentration of |\text{N}_2\text{O}_5| is measured at |0.020\ \text{mol/L}| and the reaction rate is |1.4 \times 10^{-4}\ \text{mol/L}{\cdot\text{s}}.| Determine the rate constant for this reaction at the given temperature.
Since there is only one reactant, this is a first-order reaction with respect to |\text{N}_2\text{O}_5| and overall.
-
First, identify the given values:
|\begin{align}r &= 1.4 \times 10^{-4}\ \text{mol/L}{\cdot\text{s}}\\
[\text{N}_2\text{O}_5] &= 0.020\ \text{mol/L}\\
m &= 1\\
k &=\ ?\ \text{s}^{-1}\end{align}|
-
Write down the rate constant formula:
|k = \dfrac{r}{[\text{N}_2\text{O}_5]}|
-
Plug in the values and calculate the final answer:
|\begin{align}k &= \dfrac{1.4 \times 10^{-4}\ \cancel{\text{mol/L}}{\cdot\text{s}}}{0.020\ \cancel{\text{mol/L}}}\\\\
k &= 0.0070\ \text{s}^{-1} = 7.0\ \times 10^{-3}\ \text{s}^{-1}\end{align}|
At this temperature, |k = 0.0070\ \text{s}^{-1}.| Note that these units can be obtained by simplifying the units during the calculations or simply determined based on the overall reaction order.
The synthesis reaction between fluorine gas |(\text{F}_2)| and chlorine dioxide gas |(\text{ClO}_2)| is conducted in a lab several times at the same temperature:
||\text{F}_{2\text{(g)}} + \text{ClO}_{2\text{(g)}} → 2\ \text{FClO}_{2\text{(g)}}||
The initial concentrations of the reactants are recorded along with the initial reaction rates:
|
Experiment |
|[\text{F}_2], (\text{mol/L})| |
|[\text{ClO}_2], (\text{mol/L})| |
|r, (\text{mol/L}{\cdot\text{s}})| |
|---|---|---|---|
|
Average values from Experiment 1 |
|0.070| |
|0.080| |
|6.72\times 10^{-3}| |
|
Average values from Experiment 2 |
|0.070| |
|0.160| |
|13.44\times 10^{-3}| |
|
Average values from Experiment 3 |
|0.140| |
|0.080| |
|13.44\times 10^{-3}| |
Determine the value of the rate constant for this reaction.
In order to determine the value of the rate constant, the rate law must be expressed first.
Determine the reaction order with respect to |\text{F}_2\!:|
The values measured in Experiments 1 and 3 are used, since only the concentration of |\text{F}_2\!| varies.
-
Determine the |\text{F}_2| concentration ratio between experiments 3 and 1, while the concentration of |\text{ClO}_2| remains constant:
|\dfrac{[\text{F}_2]_3}{[\text{F}_2]_1} = \dfrac{0.140\ \text{mol/L}}{0.070\ \text{mol/L}} = \dfrac{2}{1} = 2| -
Determine the |r| ratio between experiments 3 and 1:
|\dfrac{r_3}{r_1} = \dfrac{13.44\times 10^{-3}\ \text{mol/L}{\cdot\text{s}}}{6.72\times 10^{-3}\ \text{mol/L}{\cdot\text{s}}} = \dfrac{2}{1} = 2| -
Compare the ratio of rates to the ratio of concentrations to determine the order.
|2^m=2 \Rightarrow m = 1|When the concentration of |\text{F}_2| doubles, the |r| doubles. The order of this reaction with respect to |\text{F}_2| is |\bf 1.|
Determine the reaction order with respect to |\text{ClO}_2\!:|
The values measured in Experiments 2 and 1 are used, since only the concentration of |\text{F}_2\!| varies.
-
Determine the |\text{ClO}_2| concentration ratio between experiments 2 and 1, while the concentration of |\text{F}_2| remains constant:
|\dfrac{[\text{ClO}_2]_2}{[\text{ClO}_2]_1} = \dfrac{0.140\ \text{mol/L}}{0.070\ \text{mol/L}} = \dfrac{2}{1} = 2|
-
Determine the |r| ratio between experiments 2 and 1:
|\dfrac{r_2}{r_1} = \dfrac{13.44\times 10^{-3}\ \text{mol/L}{\cdot\text{s}}}{6.72\times 10^{-3}\ \text{mol/L}{\cdot\text{s}}} = \dfrac{2}{1} = 2| -
Compare the ratio of rates to the ratio of concentrations to determine the order.
|\dfrac{r_2}{r_1} =\left(\dfrac{[\text{ClO}_2]_2}{[\text{ClO}_2]_1}\right)^n\\ 2^n=2 \Rightarrow n = 1|
When the concentration of |\text{ClO}_2| doubles, the |r| doubles. The order of this reaction with respect to |\text{ClO}_2| is |\bf 1.|
Once the reaction order with respect to each of the reactants in solution has been determined, we need to express the rate law for the reaction and isolate the rate constant |(k).|
Express the rate law for this reaction:
|r = k[\text{F}_2][\text{ClO}_2]|
We isolate the rate constant from the law of reaction rates.
The units can be simplified during the calculation or determined based on the overall reaction order which is |1 + 1 = 2.|
|\begin{align}k &= \dfrac{r}{[\text{F}_2][\text{ClO}_2]}\\\\
k &= \dfrac{6.72\times10^{-3}\ \cancel{\text{mol/L}}{\cdot\text{s}}}{0.070\ \cancel{\text{mol/L}}\times 0.080\ \text{mol/L}}\\\\
k &= 1.2\ \text{L/mol}{\cdot\text{s}}\\\\
\end{align}|
The rate constant for this reaction at the given temperature is |\bf 1.2\ \text{L/mol}{\cdot\text{s}}.|
The reaction from the previous example is conducted again at the same temperature. The concentration of |\text{F}_2| is |0.900\ \text{mol/L}| and the concentration of |\text{ClO}_2| is |1.20\ \text{mol/L}.| Determine the rate of the reaction.
The rate law and the rate constant |(k)| for this reaction were already determined in the previous example.
-
Identify the given values:
|\begin{align}r &=\ ?\ \text{mol/L}{\cdot\text{s}}\\
[\text{F}_2] &= 0.900\ \text{mol/L}\\
[\text{ClO}_2] &= 1.20\ \text{mol/L}\\
k &= 1.2\ \text{L/mol}{\cdot\text{s}}\end{align}|
-
Replace the variables in the rate law determined in the previous example and calculate the final answer:
|\begin{align}r &= k[\text{F}_2][\text{ClO}_2]\\
r &= 1.2\ \text{L/mol}{\cdot\text{s}}\times0.900\ \text{mol/L}\times 1.20\ \text{mol/L}\\
r &\approx 1.3\ \text{mol/L}{\cdot\text{s}}
\end{align}|
The reaction rate at the given temperature is approximately |\bf 1.3\ \text{mol/L}{\cdot\text{s}}.|
A second-order chemical reaction with a single aqueous reactant occurs at a rate of |6.76\times10^{-4}\ \text{mol/L}{\cdot\text{s}}| when the rate constant is |0.040\ \text{L/mol}{\cdot\text{s}}.|
||\text{A}_{(aq)}+\text{B}_{(s)}\rightarrow\text{C}_{(aq)}+\text{D}_{(aq)}||
Determine the concentration of Reactant A.
-
Identify the given values.
|\begin{align}r &=6{,}76\times10^{-4}\ \text{mol/L}{\cdot\text{s}}\\ [\text{A}] &=\ ?\ \text{mol/L}\\ m &= 2\\k & = 0.040\ \text{L/mol}{\cdot\text{s}}\end{align}| -
Express the reaction rate and isolate the unknown variable |[\text{A}]\!:| |\begin{align}r &= k[\text{A}]^2 \Rightarrow [\text{A}]= \sqrt{\dfrac{r}{k}}\end{align}|
-
Replace the variables with the known values and calculate the final answer:
|\begin{align} [\text{A}]&= \sqrt{\dfrac{r}{k}}\\\\ [\text{A}]&= \sqrt{\dfrac{6.76\times10^{-4}\ \text{mol/L}{\cdot\text{s}}}{0.040\ \text{L/mol}{\cdot\text{s}}}}\\\\ [\text{A}]&=0.13\ \text{mol/L}\end{align}|
The concentration of Reactant A is |\bf 0.13\ \text{mol/L}.|
Consider a chemical reaction with the following rate law: |r = k[\text{A}]^2[\text{B}]^2|
If the concentration of Reactant A is doubled and the concentration of Reactant B is tripled, how will the reaction rate change? Assume the temperature remains constant.
-
Identify the given values.
||\begin{align}\dfrac{[\text{A}]_2}{[\text{A}]_1} &= \dfrac{2}{1}\\\\m &= 2\\\\\dfrac{[\text{B}]_2}{[\text{B}]_1} &= \dfrac{3}{1}\\\\n & = 2\\\\\dfrac{v_2}{v_1} &=\ ?\end{align}|| -
Compare the ratio of reactant concentrations to the ratio of rates. Keep in mind, that since two different concentration ratios are involved, they must be multiplied to determine the effect on the rates:
||\dfrac{\cancel{k}[\text{A}]_2^m\times[\text{B}]_2^n}{\cancel{k}[\text{A}]_1^m\times[\text{B}]_1^n}= \dfrac{v_2}{v_1}\\\left(\dfrac{[\text{A}]_2}{[\text{A}]_1}\right)^m \times \left(\dfrac{[\text{B}]_2}{[\text{B}]_1}\right)^n= \dfrac{r_2}{r_1}|| - Plug in the known values and determine the ratio of reaction rates:
||\begin{align}\left(\dfrac{2}{1}\right)^2 \times \left(\dfrac{3}{1}\right)^2&= \dfrac{r_2}{r_1}\\\\\dfrac{4}{1} \times\dfrac{9}{1}&= \dfrac{r_2}{r_1}\\\\36 &= \dfrac{r_2}{r_1}\end{align}||
The ratio of 36 indicates that the new reaction rate |(r_2)| is |\bf 36| times faster.