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Question: In a first order reaction the concentration of reactant decreases from \(800\,mol/d{m^3}\) to \(50\,...

In a first order reaction the concentration of reactant decreases from 800 mol/dm3800\,mol/d{m^3} to 50 mol/dm350\,mol/d{m^3} in 2×104 sec⁡2 \times {10^4}\,\sec . The rate constant of reaction in sec⁡−1{\sec ^{ - 1}} is:
A) 2.000×1042.000 \times {10^4}
B) 3.415×10−53.415 \times {10^{ - 5}}
C) 1.386×10−41.386 \times {10^{ - 4}}
D) 2.000×10−42.000 \times {10^{ - 4}}

Explanation

Solution

In order to answer this question, you must recall the concepts and formulae of Chemical Kinetics. Use the formula for finding the rate constant of the reaction and then put all the correct values with proper units and then make the calculation accurately, and hence you will get the required answer.

Complete answer:
The rate constant is a proportionality factor in the rate law of chemical kinetics that relates the molar concentration of reactants to reaction rate. It is also known as the reaction rate constant or reaction rate coefficient and is indicated in an equation by the letter k.
Step 1: In this step we will enlist the given quantities:
The Given quantities in the question are:
Time, t = t\, = \, 2×104 sec⁡2 \times {10^4}\,\sec
Initial concentration of the reactant, a = 800 mol/dm3a\, = \,800\,mol/d{m^3}
Final concentration of the reactant, a−x = 50 mol/dm3a - x\, = \,50\,mol/d{m^3}
Step 2: In this step we will use the General formula of rate constant and put all the values to find the required value of rate constant:
k =  2.303tlog⁡10aa−xk\, = \,\,\frac{{2.303}}{t}{\log _{10}}\frac{a}{{a - x}}
Put the values from step 1:
k =  2.3032×104log⁡1080050k\, = \,\,\frac{{2.303}}{{2 \times {{10}^4}}}{\log _{10}}\frac{{800}}{{50}}
k =  1.386×10−4 sec⁡k\, = \,\,1.386 \times {10^{ - 4}}\,\sec
Hence, we got the required value of rate constant i.e. k =  1.386×10−4 sec⁡k\, = \,\,1.386 \times {10^{ - 4}}\,\sec

Hence the correct answer is option C.

Note: The rate constant is defined as the proportionality constant which explains the relationship between the molar concentration of the reactants and the rate of a chemical reaction. The rate constant is denoted by k and is also known as reaction rate constant or reaction rate coefficient. It is dependent on the temperature. There are two possible ways to calculate rate constant and they are Using the Arrhenius equation and Using the molar concentrations of the reactants and the order of the reaction.