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For the reaction, \(2 \mathrm{~A}+\mathrm{B} \rightarrow 3 \mathrm{C}+\mathrm{D}\) Which of the following does not express the reaction rate? a. \(\frac{\mathrm{d}[\mathrm{D}]}{\mathrm{dt}}\) b. \(-\frac{d[A]}{2 \mathrm{dt}}\) c. \(-\frac{\mathrm{d}[\mathrm{C}]}{3 \mathrm{dt}}\) d. \(-\frac{d[B]}{d t}\)

Short Answer

Expert verified
Option c is incorrect because it improperly expresses the rate for \(C\).

Step by step solution

01

Understand the Rate of Reaction

The rate of a chemical reaction is defined based on the change in concentration of reactants or products over time, usually expressed as reactant disappearance or product appearance.
02

Identify Rate Expressions from the Reaction Equation

For the given reaction \(2A + B \rightarrow 3C + D\), the rate can be expressed in terms of each species' concentration change divided by their stoichiometric coefficient. It is shown as:- \(-\frac{1}{2} \frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{1}{3} \frac{d[C]}{dt} = \frac{d[D]}{dt}\).
03

Evaluate Given Options Against Correct Expressions

Match each option against the derived rate expressions:- Option a \(\frac{d[D]}{dt}\) matches the rate expression for \(D\).- Option b \(-\frac{d[A]}{2 dt}\) matches the correctly defined rate for \(A\).- Option c \(-\frac{d[C]}{3 dt}\) is incorrect as it should be \(\frac{1}{3} \frac{d[C]}{dt}\).- Option d \(-\frac{d[B]}{dt}\) correctly matches the rate for \(B\).
04

Identify the Incorrect Rate Expression

Among the given options, option c, \(-\frac{d[C]}{3 dt}\), does not correctly express the reaction rate because the negative sign is improperly used.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stoichiometric Coefficients
When looking at a chemical reaction, the stoichiometric coefficients are the numbers placed in front of the chemical formulas. These coefficients serve as a guide to how much of each substance is involved in the reaction. In the reaction \(2 \mathrm{~A} + \mathrm{B} \rightarrow 3 \mathrm{C} + \mathrm{D}\), the coefficients are 2, 1, 3, and 1 for A, B, C, and D, respectively.

These numbers tell you how many molecules or moles of a substance participate in the reaction. For every 2 moles of A and 1 mole of B, 3 moles of C and 1 mole of D are produced. They are critical for balancing equations, ensuring that the law of conservation of mass is maintained. This means the total mass of reactants equals the total mass of products. When calculating reaction rates, these stoichiometric coefficients are used to set up the correct rate expressions for each reactant and product.
Chemical Reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Understanding the basics of a reaction includes knowing the reactants (the starting chemicals) and the products (the chemicals generated from the reaction).

Reactions can vary greatly in speed; some occur almost instantly, while others may take years to complete. Factors like temperature, pressure, and catalyst presence can significantly affect the speed of a reaction. Knowing how to read a chemical equation is crucial. For example, \(2 \mathrm{~A} + \mathrm{B} \rightarrow 3 \mathrm{C} + \mathrm{D}\) indicates the rearrangement of atoms to form new chemical species.
Concentration Change
Concentration change refers to how the amount of a substance in a given volume changes over time during a chemical reaction. It is one of the key factors in determining the rate of reaction.

For example, the concentration of reactant A, given by \([\mathrm{A}]\), will decrease over time as the reaction progresses. Similarly, the concentration of products, such as \([\mathrm{C}]\) and \([\mathrm{D}]\), will increase as they are produced.
  • Decrease in concentration of a reactant indicates a reaction is consuming it.
  • Increase in concentration of a product shows that the reaction is producing it.
"Rate of reaction" is a term often used to describe how quickly these concentration changes occur.
Reaction Equation
The reaction equation is a symbolic representation of what happens during a chemical reaction. It shows the reactants on the left, the products on the right, and the stoichiometric coefficients in between that balance the equation.
In the given example, \(2 \mathrm{~A} + \mathrm{B} \rightarrow 3 \mathrm{C} + \mathrm{D}\), we can quickly identify how molecules of A and B interact to form C and D.

• Reactants: \(2 \mathrm{~A} + \mathrm{B}\)
• Products: \(3 \mathrm{C} + \mathrm{D}\)

The "arrow" signifies the direction of the reaction. A complete and balanced reaction equation ensures that there are equal numbers of each type of atom on both sides, abiding by the law of conservation of mass. This is essential for predicting product yields and understanding overall chemical changes.

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Most popular questions from this chapter

At \(380^{\circ} \mathrm{C}\), half life period for the first order decomposition of \(\mathrm{H}_{2} \mathrm{O}_{2}\) is \(360 \mathrm{~min}\). The energy of activation of the reaction is \(200 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Calculate the time required for \(75 \%\) decomposition at \(450^{\circ} \mathrm{C}\) if half life for decomposition of \(\mathrm{H}_{2} \mathrm{O}_{2}\) is \(10.17 \mathrm{~min}\) at \(450^{\circ} \mathrm{C}\). a. \(20.4 \mathrm{~min}\) b. \(408 \mathrm{~min}\) c. \(10.2 \mathrm{~min}\) d. none

The first order isomerisation reaction: Cyclopropane \(\rightarrow\) propene, has a rate constant of \(1.10 \times 10^{-4} \mathrm{~s}^{-1}\) at \(470^{\circ} \mathrm{C}\) and an activation energy of \(264 \mathrm{~kJ} / \mathrm{mol}\). What is the temperature of the reaction when the rate constant is equal to \(4.36 \times 10^{-3} \mathrm{~s}^{-1}\) ? a. \(240^{\circ} \mathrm{C}\) b. \(150^{\circ} \mathrm{C}\) c. \(540^{\circ} \mathrm{C}\) d. \(450^{\circ} \mathrm{C}\)

If \(60 \%\) of a first order reaction was completed in 60 minutes, \(50 \%\) of the same reaction would be completed in approximately a. 50 minutes b. 45 minutes c. 60 minutes d. 40 minutes \((\log 4=0.60, \log 5=0.69)\)

The rate constant for the reaction, \(2 \mathrm{~N}_{2} \mathrm{O}_{5} \rightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}\) is \(3.0 \times 10^{-4} \mathrm{~s}^{-1}\). If start made with \(1.0 \mathrm{~mol} \mathrm{~L}^{-1}\) of \(\mathrm{N}_{2} \mathrm{O}_{5}\), calculate the rate of formation of \(\mathrm{NO}_{2}\) at the moment of the reaction when concentration of \(\mathrm{O}_{2}\) is \(0.1 \mathrm{~mol} \mathrm{~L}^{-1}\). a. \(1.2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\) b. \(3.6 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\) c. \(9.6 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\) d. \(4.8 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\)

When the reactants are \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) at one mole per litre each the rate equation is, rate \(=\mathrm{k}[\mathrm{A}]^{\mathrm{x}}[\mathrm{B}]^{1 / \mathrm{Y}}\) \([\mathrm{C}]^{\mathrm{X} / \mathrm{Y}}\). The order of the reaction is a. \(X+\frac{(1+X)}{Y}\) b. \(\mathrm{X}-\mathrm{Y}+\frac{\mathrm{X}}{\mathrm{Y}}\) c. \(\mathrm{X}+\mathrm{Y}+\frac{\mathrm{X}}{\mathrm{Y}}\) d. \(2(X+Y)\)

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