Question

The rate of a gaseous reaction is given by \( r = k[A]^x[B]^y \). If the volume of the reaction vessel is suddenly reduced to \( \frac{1}{4} \)th of its initial value, the reaction rate relating to the initial rate will become

• A. 2 times
• B. \( \frac{1}{4} \) times
• C. 16 times
• D. \( \frac{1}{16} \) times
• A. second order
• B. half order
• C. first order
• D. zero order
• A. bar\(^2\) min\(^{-1}\)
• B. bar\(^3\) min\(^{-1}\)
• C. bar\(^1\) min\(^{-1}\)
• D. bar\(^3/2\) min\(^{-1}\)
• A. 0
• B. 1
• C. 3
• D. 2
• A. Gibbs energy of the reaction.
• B. Enthalpy of a reaction.
• C. Activation energy of a reaction.
• D. Equilibrium constant.

Answer 1

The Correct Option is C

Step 1: Understanding the relationship.
The reaction rate is contingent on reactant concentrations. The rate law is expressed as \( r = k[A]^x[B]^y \). A reduction in volume escalates reactant concentrations, as concentration \( [A] \) and \( [B] \) are inversely proportional to the vessel's volume.
Step 2: How volume change affects concentration.
Given that concentration is \( \frac{n}{V} \), decreasing the volume to \( \frac{1}{4} \) its original size quadruples the concentration.
Step 3: Applying this to the rate equation.
For \( r = k[A]^x[B]^y \), a fourfold increase in \( [A] \) and \( [B] \) results in a rate increase of \( 4^2 = 16 \) times, assuming the reaction order with respect to both reactants is one, leading to a total order of two.
Step 4: Conclusion.
The reaction rate will increase by a factor of 16.
Final Answer: \[\boxed{\text{The correct answer is (3) 16 times.}}\]

Answer 2

Step 1: Understanding the rate equation.
The rate law for the reaction is defined as: \[\text{Rate} = k[A]^{1/2}[B]^{3/2}\]The overall order of the reaction is determined by summing the exponents of the concentration terms. Step 2: Calculating the order.
The order of the reaction with respect to reactant \( A \) is \( \frac{1}{2} \), and the order with respect to reactant \( B \) is \( \frac{3}{2} \).\[\text{Total order} = \frac{1}{2} + \frac{3}{2} = 2\]Step 3: Conclusion.
The reaction is of the second order.
Final Answer: \[\boxed{\text{The correct answer is (1) second order.}}\]

Answer 3

Step 1: Rate Law Identification.
The rate law is expressed as \( r = k[\text{CH}_3\text{OCH}_3]^{3/2} \), indicating the reactant's concentration is raised to the power of \( \frac{3}{2} \).
Step 2: Unit Analysis.
Given that the reaction rate \( r \) has units of concentration/time (bar/min) and the concentration is in bar, the units of the rate constant \( k \) can be determined by balancing the units in the rate equation.
The rate equation is: \[[\text{rate}] = k[\text{concentration}]^{3/2}\]Substituting the units: \[\text{bar/min} = k (\text{bar})^{3/2}\]To balance the exponents, the unit of \( k \) must be \( \text{bar}^{-1/2} \text{min}^{-1} \).
Step 3: Conclusion.
The unit of the rate constant \( k \) is bar\(^{-1/2}\) min\(^{-1}\).
Final Answer: \[\boxed{\text{The correct answer is (2) bar}^{-1/2} \text{min}^{-1}.}\]

Answer 4

Step 1: Analyzing the rate law's dependence on concentration.
The rate law is expressed as: \[r = k[A]^n\]Here, \( [A] \) represents the reactant concentration, and \( n \) is the reaction order. When the concentration increases by a factor of 3, the rate increases by a factor of 27. This relationship is described by:\[\frac{\text{new rate}}{\text{old rate}} = \left( \frac{\text{new concentration}}{\text{old concentration}} \right)^n\]Substituting the given factors:\[27 = 3^n\]Step 2: Determining the reaction order \( n \).
Applying logarithms to both sides of the equation:\[\log(27) = n \log(3)\]Solving for \( n \):\[n = \frac{\log(27)}{\log(3)} = 3\]Step 3: Final determination of reaction order.
The reaction order is determined to be (3).
Final Answer: \[\boxed{\text{The reaction order is 3.}}\]

Answer 5

Step 1: Understanding the role of a catalyst.
A catalyst facilitates a reaction by offering a reaction pathway with reduced activation energy. It does not influence the Gibbs energy or the equilibrium constant of the reaction.
Step 2: Conclusion.
A catalyst's function is to decrease the activation energy, thereby simplifying the conversion of reactants into products.
Final Answer: \[\boxed{\text{The correct answer is (3) Activation energy of a reaction.}}\]