Question

Consider the kinetic data given in the following table for the reaction \[A + B + C\xrightarrow{{}}{\text{Product}}\] .

Ex. No.	[A]	[B]	[C]	Rate of Reaction
1.	0.2	0.1	0.1	6 x 10-5
2.	0.2	0.2	0.1	6 x 10-5
3.	0.2	0.1	0.2	1.2 x 10-4
4.	0.3	0.1	0.1	9 x 10-3

When \[\left[ A \right] = 0.15\] , \[\left[ B \right] = 0.25\] , \[\left[ C \right] = 0.15\] , Rate of reaction is \[Y \times {10^{ - 5}}\] . Find \[Y\] .

Answer 1

Hint: Here, in this question, there are concentrations of A, B, and C are given. The rate of reaction is also given. The pace at which a chemical reaction takes place, sometimes referred to as the reaction rate or rate of reaction is proportional to the rise in product concentration per unit time and the fall in reactant concentration per unit time. The reaction might move at many different speeds.

Complete Step by Step Solution:
From the rate law, we know that the rate of the reaction is,
\[Rate = k{\left[ A \right]^x}{\left[ B \right]^y}{\left[ C \right]^z}\]
Now, from Ex. No. 1, the rate can be written as follows:
\[6 \times {10^{ - 5}} = k{\left( {0.2} \right)^x}{\left( {0.1} \right)^y}{\left( {0.1} \right)^z}\,\,\,\,\,...(1)\]
From Ex. No. 2, the rate can be written as follows:
\[6 \times {10^{ - 5}} = k{\left( {0.2} \right)^x}{\left( {0.2} \right)^y}{\left( {0.1} \right)^z}\,\,\,\,\,...(2)\]
from Ex. No. 3, the rate can be written as follows:
\[1.2 \times {10^{ - 4}} = k{\left( {0.2} \right)^x}{\left( {0.1} \right)^y}{\left( {0.2} \right)^z}\,\,\,\,\,...(3)\]
From Ex. No. 4, the rate can be written as follows:
\[9 \times {10^{ - 5}} = k{\left( {0.3} \right)^x}{\left( {0.1} \right)^y}{\left( {0.1} \right)^z}\,\,\,\,\,...(4)\]
Now, from equations (1) and (2),
\[ k{\left( {0.2} \right)^x}{\left( {0.1} \right)^y}{\left( {0.1} \right)^z} = k{\left( {0.2} \right)^x}{\left( {0.2} \right)^y}{\left( {0.1} \right)^z} \\
   \Rightarrow {\left( {0.1} \right)^y} = {\left( {0.2} \right)^y} \\
   \Rightarrow y = 0 \\ \]
From equations (2) and (3),
\[ \dfrac{{1.2 \times {{10}^{ - 4}}}}{{6 \times {{10}^{ - 5}}}} = \dfrac{{k{{\left( {0.2} \right)}^x}{{\left( {0.1} \right)}^y}{{\left( {0.2} \right)}^z}}}{{k{{\left( {0.2} \right)}^x}{{\left( {0.2} \right)}^y}{{\left( {0.1} \right)}^z}}} \\
   \Rightarrow 2 = {\left( 2 \right)^z} \\
   \Rightarrow z = 1 \\ \]
From equations (1) and (4),
\[ \dfrac{{9 \times {{10}^{ - 5}}}}{{6 \times {{10}^{ - 5}}}} = \dfrac{{k{{\left( {0.3} \right)}^x}{{\left( {0.1} \right)}^y}{{\left( {0.1} \right)}^z}}}{{k{{\left( {0.2} \right)}^x}{{\left( {0.1} \right)}^y}{{\left( {0.1} \right)}^z}}} \\
   \Rightarrow \dfrac{3}{2} = {\left( {\dfrac{3}{2}} \right)^x} \\
   \Rightarrow x = 1 \\ \]
Thus, the reaction rate is,
\[Rate = k\left[ A \right]\left[ C \right]\]
Let us calculate the value of \[k\] from equation (1) as follows:
\[ 6 \times {10^{ - 5}} = k\left( {0.2} \right)\left( {0.1} \right) \\
   \Rightarrow k = \dfrac{{6 \times {{10}^{ - 5}}}}{{\left( {0.2} \right)\left( {0.1} \right)}} \\
   \Rightarrow k = 3 \times {10^{ - 3}} \\ \]
Let’s calculate the rate of the reaction for the given concentration of A, B, and C as follows:
\[ Rate = k\left[ A \right]\left[ C \right] \\
   \Rightarrow rate = 3 \times {10^{ - 3}} \times 0.15 \times 0.15 \\
   \Rightarrow rate = 6.75 \times {10^{ - 5}} \\ \]
Therefore, the value of \[Y\] is \[6.75\] .

Additional Information:

• • The order of the reaction can be defined as the power dependence of rate on all reactant concentrations. For instance, the concentration of one species in the reaction alone determines the pace of a first-order reaction. The reaction order of a chemical reaction includes the following characteristics.

• Reaction order determines the number of species whose abundance directly influences the rate of reaction.

• It can be obtained by adding all of the exponents of the concentration terms in the rate expression.

• The reaction order is unaffected by the stoichiometric coefficients for any species in the balanced reaction.

• Reactant concentrations rather than product concentrations are frequently used to establish the sequence of chemical reactions. Both an integer and a fraction can be used to describe the order of the reaction. It might also be zero, which is also a possibility.

Note: As pressure rises, the concentration of the gases grows, causing the reaction to happen more quickly. When there are fewer gaseous molecules present, the reaction rate rises, and when there are more gaseous molecules present, it falls.