Given below are two statements:
Statement I: When \(E_a = 12.6\) kcal/mol, the room temperature rate constant is doubled by a 10 °C increase in temperature (298 K to 308 K).
Statement II: For a first order reactions \(A \to B\), [the graph of rate vs [A] is a straight line through origin].
Statement I: When \(E_a = 12.6\) kcal/mol, the room temperature rate constant is doubled by a 10 °C increase in temperature (298 K to 308 K).
Statement II: For a first order reactions \(A \to B\), [the graph of rate vs [A] is a straight line through origin].
- Both Statement I and Statement II are true
- Both Statement I and Statement II are false
- Statement I is true but Statement II is false
- Statement I is false but Statement II is true
The Correct Option is A
Solution and Explanation
Statement I involves the Arrhenius equation relating rate constants at two temperatures. Statement II involves the rate law for first-order kinetics.
Step 2: Detailed Explanation:
Statement I: Using \(\log \frac{k_2}{k_1} = \frac{E_a}{2.303R} \left( \frac{T_2 - T_1}{T_1 T_2} \right)\). Given \(E_a = 12.6 \text{ kcal/mol} = 12600 \text{ cal/mol}\), \(R \approx 2 \text{ cal/mol}\cdot\text{K}\), \(T_1 = 298\), \(T_2 = 308\). \[ \log \frac{k_2}{k_1} = \frac{12600}{2.303 \times 2} \left( \frac{10}{298 \times 308} \right) \approx 0.301 \] Since \(\text{antilog}(0.301) = 2\), the rate constant doubles. (True)
Statement II: For a first-order reaction, Rate \(= k[A]^1\). This is an equation of the form \(y = mx\), which represents a straight line passing through the origin. (True)
Step 3: Final Answer:
Both statements are true.
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 Electrochemical Cells and Gibbs Free Energy Questions
Standard electrode potentials for a few half-cells are mentioned below:
Consider the following cell: $ \text{Pt}(s) \, \text{H}_2 (1 \, \text{atm}) | \text{H}^+ (1 \, \text{M}) | \text{Cr}_2\text{O}_7^{2-}, \, \text{Cr}^{3+} | \text{H}^+ (1 \, \text{M}) | \text{Pt}(s) $
Given: $ E^\circ_{\text{Cr}_2\text{O}_7^{2-}/\text{Cr}^{3+}} = 1.33 \, \text{V}, \quad \left[ \text{Cr}^{3+} \right]^2 / \left[ \text{Cr}_2\text{O}_7^{2-} \right] = 10^{-7} $
At equilibrium: $ \left[ \text{Cr}^{3+} \right]^2 / \left[ \text{Cr}_2\text{O}_7^{2-} \right] = 10^{-7} $
Objective: $ \text{Determine the pH at the cathode where } E_{\text{cell}} = 0. $- An electrochemical cell is constructed using half cells in the direction of spontaneous change} \[ Fe(OH)_2(s) + 2e^- \rightarrow Fe(s) + 2OH^- (aq) \qquad E^\circ = -0.88\,V \] \[ AgBr(s) + e^- \rightarrow Ag(s) + Br^- (aq) \qquad E^\circ = +0.07\,V \] Which of the following option is correct?
- Consider the reaction \( aX \rightarrow bY \), for which the rate constant at 30°C is \( 1 \times 10^{-3} \, \text{mol}^{-1} \, \text{L} \, \text{s}^{-1} \). Which of the following statements are true?}
- (A) When concentration of \( X \) is increased to four times, the rate of reaction becomes 16 times.
- (B) The reaction is a second order reaction.
- (C) The half-life period is independent of the concentration of \( X \).
- (D) Decomposition of \( \text{N}_2\text{O}_5 \) is an example of the above reaction.
- (E)
- One half cell in a voltaic cell is constructed by dipping silver rod in $AgNO_3$ solution of unknown concentration, other half cell is Zn rod dipped in 1 molar solution of $ZnSO_4$.
A voltage of 1.60 V is measured at 298 K for this cell. What is the concentration of $Ag^+$ ions used in terms of $\log x$ ($x = [Ag^+]$)?
$E^\ominus_{Zn^{2+}/Zn} = -0.76 V$, $E^\ominus_{Ag^+/Ag} = +0.80 V$, $\frac{2.303 RT}{F} = 0.059 V$
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 ______.