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Chapter 14: Problem 11

Consider the zero-order reaction \(\mathrm{A} \longrightarrow\) product. (a) Write the rate law for the reaction. (b) What are the units for the rate constant? (c) Plot the rate of the reaction versus [A].

Short Answer

Expert verified
The rate law for this zero-order reaction is: \(rate = k\). The units of the rate constant \(k\) are \(M \cdot s^{-1}\). When plotting the reaction rate versus the concentration of A, it gives a horizontal line representing a constant reaction rate, demonstrating the characteristic feature of the zero-order reaction. This line shows the reaction rate is independent of the concentration of reactant A.

Step by step solution

01

Formulating the Rate Law

The rate law for a zero-order reaction is defined as: \[rate = k[A]^0\] Since it is a zero-order reaction, the exponent is zero. Therefore, the concentration of the reactant A is not affecting the rate of the reaction. As a result, this simplifies to: \[rate = k\] Hence, the rate of the reaction is equal to the rate constant (k).
02

Identifying the Units of the Rate Constant

In order to maintain the necessary equality between both sides of the equation (\(rate = k\)), the unit of the rate constant 'k' is determined by the units of rate. Rate is typically expressed in terms of molar concentration per unit time (\(M \cdot s^{-1}\)). Therefore, for zero-order reaction, the unit for rate constant \(k\) is \(M \cdot s^{-1}\).
03

Plotting the Rate of Reaction Versus [A]

Because this is a zero-order reaction, the rate of the reaction is not influenced by the concentration of the reactant, A. So, even as the concentration of A changes, the reaction rate stays constant at 'k'. The plot of rate versus concentration ([A]) will be a horizontal line, which is parallel to the x-axis. Consequently, the rate of the reaction is independent of the concentration of A.

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Most popular questions from this chapter

Radioactive plutonium- \(239\left(t_{\frac{1}{2}}=2.44 \times 10^{5} \mathrm{yr}\right)\) is used in nuclear reactors and atomic bombs. If there are \(5.0 \times 10^{2} \mathrm{~g}\) of the isotope in a small atomic bomb, how long will it take for the substance to decay to \(1.0 \times 10^{2} \mathrm{~g},\) too small an amount for an effective bomb? (Hint: Radioactive decays follow first-order kinetics.)

Write an equation relating the concentration of a reactant \(\mathrm{A}\) at \(t=0\) to that at \(t=t\) for a first-order reaction. Define all the terms and give their units.

The reaction \(2 \mathrm{~A}+3 \mathrm{~B} \longrightarrow \mathrm{C}\) is first order with respect to \(\mathrm{A}\) and \(\mathrm{B}\). When the initial concentrations are \([\mathrm{A}]=1.6 \times 10^{-2} M\) and \([\mathrm{B}]=2.4 \times 10^{-3} M,\) the rate is \(4.1 \times 10^{-4} M / \mathrm{s} .\) Calculate the rate constant of the reaction.

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The thermal decomposition of phosphine \(\left(\mathrm{PH}_{3}\right)\) into phosphorus and molecular hydrogen is a first-order reaction: $$ 4 \mathrm{PH}_{3}(g) \longrightarrow \mathrm{P}_{4}(g)+6 \mathrm{H}_{2}(g) $$ The half-life of the reaction is 35.0 s at \(680^{\circ} \mathrm{C}\). Calculate (a) the first-order rates constant for the reaction and (b) the time required for 95 percent of the phosphine to decompose.
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