Question

The decomposition of N2O5 can be described by the equation

2n2O5>4NO2+O2

Given these data for the reaction at 45�C in carbon tetrachloride solution, calculate the average rate of reaction for each successive time interval.

t(s)       [N2O5]

0             2.04

135         1.87

536         1.46

795          1.24

Reaction rate from 0-135         ??

Reaction rate from 135-536     ??

Reaction rate from 536-795     ??

Answer 1

General guidance

Concepts and reason

The average rate of a chemical reaction is defined as the change of concentration of a reactant or product species with respect to time. In chemical kinetics, the concentration of reactants decreases (consumes) when concentration of products increases during the progress of the chemical reaction.

Fundamentals

Consider an arbitrary chemical reaction.

The rate law expression for the chemical reaction is given below:

${\\rm{ - }}\\frac{{\\rm{1}}}{{\\rm{a}}}\\frac{{{\\rm{d}}\\left[ {\\rm{A}} \\right]}}{{{\\rm{dt}}}}{\\rm{ = }}\\,{\\rm{ - }}\\,\\,\\frac{{\\rm{1}}}{{\\rm{b}}}\\frac{{{\\rm{d}}\\left[ {\\rm{B}} \\right]}}{{{\\rm{dt}}}}\\,\\,{\\rm{ = }}\\,{\\rm{ + }}\\frac{{\\rm{1}}}{{\\rm{c}}}\\frac{{{\\rm{d}}\\left[ {\\rm{C}} \\right]}}{{{\\rm{dt}}}}\\,\\,{\\rm{ = }}\\,{\\rm{ + }}\\frac{{\\rm{1}}}{{\\rm{d}}}\\frac{{{\\rm{d}}\\left[ {\\rm{D}} \\right]}}{{{\\rm{dt}}}}$

• The negative sign indicates the rate of consumption of reactant species.

• The positive sign indicates the rate of formation of product species.

Step-by-step

Step 1 of 4

Consider the reaction,

The average rate of decomposition is expressed as given below:

\\[{\\rm{r = }}\\user1{ - }\\frac{{\\rm{1}}}{{\\rm{2}}}\\frac{{{\\rm{d}}\\left[ {{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}} \\right]}}{{{\\rm{dt}}}}\\]

Here,

\\[{\\rm{d}}\\left[ {{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}} \\right]\\]is a change in concentration of \\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}.\\]

\\[\\user2{dt}\\]is change in time.

Explanation | Common mistakes | Hint for next step

The reaction equation is given, and the rate of decomposition for \\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]reactant species is also given. During the forward reaction, the concentration of reactant species decreases due to this rate of consumption, which has a negative sign.

Step 2 of 4

Consider the reaction,

Given that,

The average rate of reaction of\\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]from \\[\\user2{0}\\user1{ - }\\user2{135s}\\] is as follows:

\\[\\begin{array}{l}\\\\{\\rm{r = }}\\user1{ - }\\frac{{\\rm{1}}}{{\\rm{2}}}\\frac{{{\\rm{d}}\\left[ {{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}} \\right]}}{{{\\rm{dt}}}}\\\\\\\\{\\rm{r = }}\\user1{ - }\\frac{{\\rm{1}}}{{\\rm{2}}} \\times \\frac{{\\user2{final concentration} - \\user2{initial concentration}}}{{135 - 0}}\\\\\\\\\\user2{r = }\\user1{ - }\\frac{{\\rm{1}}}{{\\rm{2}}} \\times \\frac{{\\user2{1}\\user2{.87} - \\user2{2}\\user2{.04}}}{{135}}\\\\\\\\\\user2{r = }6.3 \\times {10^{ - 4}}\\user2{M/s}\\\\\\end{array}\\]

Therefore, the average rate of reaction of\\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]is\\[6.3 \\times {10^{ - 4}}\\user2{M/s}\\user2{.}\\]

Explanation | Common mistakes | Hint for next step

The reaction equation and the average rate of decomposition of \\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]is calculated by using the above equation. By substituting the values of the initial concentration, final concentration and time in the equation and calculated values of average rate of decomposition of\\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]is\\[6.3 \\times {10^{ - 4}}\\user2{M/s}\\user2{.}\\]

Step 3 of 4

Given that,

The average rate of reaction of\\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]from \\[\\user2{135}\\user1{ - }\\user2{536s}\\] is as follows:

\\[\\begin{array}{l}\\\\{\\rm{r = }}\\user1{ - }\\frac{{\\rm{1}}}{{\\rm{2}}}\\frac{{{\\rm{d}}\\left[ {{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}} \\right]}}{{{\\rm{dt}}}}\\\\\\\\{\\rm{r = }}\\user1{ - }\\frac{{\\rm{1}}}{{\\rm{2}}} \\times \\frac{{\\user2{final concentration} - \\user2{initial concentration}}}{{536 - 135}}\\\\\\\\\\user2{r = }\\user1{ - }\\frac{{\\rm{1}}}{{\\rm{2}}} \\times \\frac{{\\user2{1}\\user2{.46} - 1.\\user2{87}}}{{401}}\\\\\\\\\\user2{r = 5}.11 \\times {10^{ - 4}}\\user2{M/s}\\\\\\end{array}\\]

Therefore, the average rate of reaction of\\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]is\\[5.11 \\times {10^{ - 4}}\\user2{M/s}\\user2{.}\\]

Explanation | Common mistakes | Hint for next step

The average rate of decomposition of \\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]is calculated by using the above equation. By substituting the values of initial concentration, the final concentration and time in the equation and calculated values of the average rate of decomposition of\\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]is\\[5.11 \\times {10^{ - 4}}\\user2{M/s}\\user2{.}\\]

Step 4 of 4

Given that,

The average rate of reaction of\\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]from \\[\\user2{536}\\user1{ - }\\user2{795s}\\] is as follows:

\\[\\begin{array}{l}\\\\{\\rm{r = }}\\user1{ - }\\frac{{\\rm{1}}}{{\\rm{2}}}\\frac{{{\\rm{d}}\\left[ {{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}} \\right]}}{{{\\rm{dt}}}}\\\\\\\\{\\rm{r = }}\\user1{ - }\\frac{{\\rm{1}}}{{\\rm{2}}} \\times \\frac{{\\user2{final concentration} - \\user2{initial concentration}}}{{795 - 536}}\\\\\\\\\\user2{r = }\\user1{ - }\\frac{{\\rm{1}}}{{\\rm{2}}} \\times \\frac{{\\user2{1}\\user2{.24} - 1.\\user2{46}}}{{259}}\\\\\\\\\\user2{r = 4}.25 \\times {10^{ - 4}}\\user2{M/s}\\\\\\end{array}\\]

Therefore, the average rate of reaction of\\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]is\\[4.25 \\times {10^{ - 4}}\\user2{M/s}\\user2{.}\\]

The average rate of reaction for each time interval is

\\[\\begin{array}{l}\\\\\\user2{Reaction rate from}{\\rm{ }}0 - 135 = 6.3 \\times {10^{ - 4}}\\user2{M/s}\\\\\\\\\\user2{Reaction rate from}{\\rm{ }}135 - 536\\; = 5.11 \\times {10^{ - 4}}\\user2{M/s}\\\\\\\\\\user2{Reaction rate from}{\\rm{ }}536 - 795\\; = {\\rm{4}}{\\rm{.25}} \\times {10^{ - 4}}{\\rm{M/s}}\\\\\\end{array}\\]

The average rate of decomposition of \\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]is calculated by using the above equation. By substituting the values of initial concentration, the final concentration and time in the equation and calculated value of average rate of decomposition of\\[{\\user2{N}_\\user2{2}}{\\user2{O}_\\user2{5}}\\]is\\[4.25 \\times {10^{ - 4}}\\user2{M/s}\\user2{.}\\]

Answer

The average rate of reaction for each time interval is

\\[\\begin{array}{l}\\\\\\user2{Reaction rate from}{\\rm{ }}0 - 135 = 6.3 \\times {10^{ - 4}}\\user2{M/s}\\\\\\\\\\user2{Reaction rate from}{\\rm{ }}135 - 536\\; = 5.11 \\times {10^{ - 4}}\\user2{M/s}\\\\\\\\\\user2{Reaction rate from}{\\rm{ }}536 - 795\\; = {\\rm{4}}{\\rm{.25}} \\times {10^{ - 4}}{\\rm{M/s}}\\\\\\end{array}\\]

Answer only

The average rate of reaction for each time interval is

\\[\\begin{array}{l}\\\\\\user2{Reaction rate from}{\\rm{ }}0 - 135 = 6.3 \\times {10^{ - 4}}\\user2{M/s}\\\\\\\\\\user2{Reaction rate from}{\\rm{ }}135 - 536\\; = 5.11 \\times {10^{ - 4}}\\user2{M/s}\\\\\\\\\\user2{Reaction rate from}{\\rm{ }}536 - 795\\; = {\\rm{4}}{\\rm{.25}} \\times {10^{ - 4}}{\\rm{M/s}}\\\\\\end{array}\\]