A molecule undergoes two independent first order reactions whose respective half lives are 12 min and 3 min. If both the reactions are occurring then the time taken for the 50% consumption of the reactant is _____ min. (Nearest integer)
Show Hint
Always combine the reciprocal contributions of individual half-lives to find the effective rate.
Correct Answer: 2
Solution and Explanation
Step 1: Relationship Between Rate Constants and Effective Half-Life
For independent first-order reactions, the effective rate constant (\( k_\text{eff} \)) is given by:
\[ k_\text{eff} = k_1 + k_2 \]
The effective half-life (\( t_\text{eff} \)) is related to the individual half-lives (\( t_1 \) and \( t_2 \)) as:
\[ \frac{1}{t_\text{eff}} = \frac{1}{t_1} + \frac{1}{t_2} \]
Step 2: Substitute the Given Half-Lives
Substitute \( t_1 = 12 \, \text{min} \) and \( t_2 = 3 \, \text{min} \):
\[ \frac{1}{t_\text{eff}} = \frac{1}{12} + \frac{1}{3} \]
Convert to a common denominator:
\[ \frac{1}{t_\text{eff}} = \frac{1}{12} + \frac{4}{12} = \frac{5}{12} \]
Step 3: Calculate \( t_\text{eff} \)
Solve for \( t_\text{eff} \):
\[ t_\text{eff} = \frac{12}{5} = 2.4 \, \text{min} \]
Round to the nearest integer:
\[ t_\text{eff} = 2 \, \text{min} \]
Final Answer:
The time taken for 50% consumption of the reactant is: 2 minutes.
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 Order of Reaction Questions
- Consider the following reaction
\[A + B \rightarrow C\]
The time taken for A to become 1/4th of its initial concentration is twice the time taken to become 1/2 of the same. Also, when the change of concentration of B is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis.
The overall order of the reaction is ____. - Consider the two different first-order reactions given below: \[\text{A + B} \rightarrow \text{C (Reaction 1)} \\\text{P} \rightarrow \text{Q (Reaction 2)}\]The ratio of the half-life of Reaction 1 : Reaction 2 is $5 : 2$. If $t_1$ and $t_2$ represent the time taken to complete $\frac{2}{3}^\text{rd}$ and $\frac{4}{5}^\text{th}$ of Reaction 1 and Reaction 2, respectively, then the value of the ratio $t_1 : t_2$ is ____ $\times 10^{-1}$ (nearest integer).[Given: $\log_{10}(3) = 0.477$ and $\log_{10}(5) = 0.699$]
- For a first-order reaction, the ratio of time required is $ \frac{t_1}{t_2} $, if $ t_1 $ is the time consumed when reactant reaches $ \frac{1}{4} $ of initial concentration and $ t_2 $ is the time when it reaches $ \frac{1}{8} $ of initial concentration.
The cycloalkene (X) on bromination consumes one mole of bromine per mole of (X) and gives the product (Y) in which C : Br ratio is \(3:1\). The percentage of bromine in the product (Y) is _________ % (Nearest integer).
Given:
\[ \text{H} = 1,\quad \text{C} = 12,\quad \text{O} = 16,\quad \text{Br} = 80 \]- The reaction between X and Y is first order with respect to X and zero order with respect to Y.
Examine the data of table and calculate ratio of numerical values of M and L. (Nearest integer)
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 ______.