The rate constant for a first order reaction is $20 \min ^{-1}$ The time required for the initial concentration of the reactant to reduce to its $\frac{1}{32}$ level is ___$\times 10^{-2} \min$ (Nearest integer)
(Given: $\ln 10=2.303$ $\log 2=0.3010$ )
The rate constant for a first order reaction is $20 \min ^{-1}$ The time required for the initial concentration of the reactant to reduce to its $\frac{1}{32}$ level is ___$\times 10^{-2} \min$ (Nearest integer)
(Given: $\ln 10=2.303$ $\log 2=0.3010$ )
Show Hint
Correct Answer: 17
Approach Solution - 1
So, the correct answer is 17.
Approach Solution -2
The integrated rate equation for a first order reaction is:
\[ \ln \left( \frac{C_0}{C} \right) = kt \]
Where \( C_0 \) is the initial concentration, \( C \) is the concentration at time \( t \), \( k \) is the rate constant, and \( t \) is the time.
For the reaction to reduce to \( \frac{1}{32} \) of its original concentration, we have:
\[ \frac{C}{C_0} = \frac{1}{32} \]
Taking the natural logarithm:
\[ \ln \left( \frac{C_0}{C} \right) = \ln 32 = 5 \ln 2 = 5 \times 0.693 = 3.465 \]
Thus, the time \( t \) is:
\[ t = \frac{3.465}{k} = \frac{3.465}{20} = 0.17325 \, \text{min} \]
Therefore, the time required for the concentration to reduce to \( \frac{1}{32} \) is \( 17.325 \times 10^{-2} \) min.
Top JEE Main Chemistry Questions
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- At equilibrium the concentrations of and in a sealed vessel at . What will be for the reaction
- Find out the major products from the following reactions
Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are
- The correct order of atomic radii is:
Top JEE Main Chemical Kinetics Questions
- The rate of a first order reaction is \( 0.04 \, \text{mol} \, \text{L}^{-1} \, \text{s}^{-1} \) at 10 minutes and \( 0.03 \, \text{mol} \, \text{L}^{-1} \, \text{s}^{-1} \) at 20 minutes after initiation. Half-life of the reaction is \( \_\_\_\_ \) minutes. (Given \( \log 2 = 0.3010, \, \log 3 = 0.4771 \))
- $\text{Time required for completion of 99.9\% of a first order reaction is \_\_\_\_\_\_ times of half life } (t_{1/2}) \text{ of the reaction.}$
- $\text{NO}_2 \text{ required for a reaction is produced by decomposition of } \text{N}_2\text{O}_5 \text{ in } \text{CCl}_4 \text{ as by equation}$
\[ 2\text{N}_2\text{O}_{5(g)} \rightarrow 4\text{NO}_{2(g)} + \text{O}_{2(g)} \]
$\text{The initial concentration of } \text{N}_2\text{O}_5 \text{ is } 3 \text{ mol L}^{-1} \text{ and it is } 2.75 \text{ mol L}^{-1} \text{ after 30 minutes.}$
$\text{The rate of formation of } \text{NO}_2 \text{ is } x \times 10^{-3} \text{ mol L}^{-1} \text{ min}^{-1} , \text{ value of } x \text{ is \_\_\_\_\_\_.}$ Consider the following data for the given reaction
\(2\)\(\text{HI}_{(g)}\) \(\rightarrow\) \(\text{H}_2{(g)}\)$ + $\(\text{I}_2{(g)}\)
The order of the reaction is __________.- For a reaction taking place in three steps at the same temperature, the overall rate constant \( K = \frac{K_1 K_2}{K_3} \). If \( E_{a1} \), \( E_{a2} \), and \( E_{a3} \) are 40, 50, and 60 kJ/mol respectively, the overall \( E_a \) is ____ kJ/mol.
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
Concepts Used:
Chemical Kinetics
Chemical kinetics is the description of the rate of a chemical reaction. This is the rate at which the reactants are transformed into products. This may take place by abiotic or by biological systems, such as microbial metabolism.
Rate of a Chemical Reaction:
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time. To be more specific, it can be expressed in terms of: (i) the rate of decrease in the concentration of any one of the reactants, or (ii) the rate of increase in concentration of any one of the products. Consider a hypothetical reaction, assuming that the volume of the system remains constant. R → P
Read More: Chemical Kinetics MCQ
Factors Affecting The Reaction Rate:
- The concentration of Reactants - According to collision theory, which is discussed later, reactant molecules collide with each other to form products.
- Nature of the Reactants - The reaction rate also depends on the types of substances that are reacting.
- Physical State of Reactants - The physical state of a reactant whether it is solid, liquid, or gas can greatly affect the rate of change.
- Surface Area of Reactants - When two or more reactants are in the same phase of fluid, their particles collide more often than when either or both are in the solid phase or when they are in a heterogeneous mixture. In a heterogeneous medium, the collision between the particles occurs at an interface between phases. Compared to the homogeneous case, the number of collisions between reactants per unit time is significantly reduced, and so is the reaction rate.
- Temperature - If the temperature is increased, the number of collisions between reactant molecules per second. Increases, thereby increasing the rate of the reaction.
- Effect Of Solvent - The nature of the solvent also depends on the reaction rate of the solute particles.
- Catalyst - Catalysts alter the rate of the reaction by changing the reaction mechanism.