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Chapter 12: Problem 30

The rate law for the reaction $$ \begin{array}{c}{\mathrm{Cl}_{2}(g)+\mathrm{CHCl}_{3}(g) \longrightarrow \mathrm{HCl}(g)+\mathrm{CCl}_{4}(g)} \\ {\text { Rate }=k\left[\mathrm{Cl}_{2}\right]^{1 / 2}\left[\mathrm{CHCl}_{3}\right]}\end{array} $$ What are the units for \(k,\) assuming time in seconds and concentration in mol/L?

Short Answer

Expert verified
The units for the rate constant \(k\) in the given rate law are: \(k \ [\text{units}] = \frac{\text{L}^{1/2}}{\text{mol}^{1/2}\cdot\text{s}}\).

Step by step solution

01

The given rate law for the reaction is: $$ \text{Rate} = k[\text{Cl}_2]^{1/2}[\text{CHCl}_3] $$ Here, k is the rate constant, and the concentrations of Cl₂ and CHCl₃ are raised to the power of 1/2 and 1, respectively. #Step 2: Write the units for each term#

We know that the rate has the unit of concentration per unit time, which in this case is mol/L·s. The concentrations in the rate law have the unit of mol/L. Rewrite the rate law with units: $$ \frac{\text{mol}}{\text{L}\cdot \text{s}} = k \left(\frac{\text{mol}}{\text{L}}\right)^{1/2} \left(\frac{\text{mol}}{\text{L}}\right) $$ #Step 3: Solve for the units of k#
02

Now, we will solve for the units of k by isolating k in the equation and cancelling out the units: $$ k = \frac{\frac{\text{mol}}{\text{L}\cdot \text{s}}}{\left(\frac{\text{mol}}{\text{L}}\right)^{1/2}\left(\frac{\text{mol}}{\text{L}}\right)} $$ $$ k = \frac{\frac{1}{\text{s}}}{\left(\frac{\text{mol}}{\text{L}}\right)^{1/2}} $$ $$ k = \frac{\text{L}^{1/2}}{\text{mol}^{1/2}\cdot\text{s}} $$ #Step 4: Present the final units for k#

The units for the rate constant k in the given rate law are: $$ k \ [\text{units}] = \frac{\text{L}^{1/2}}{\text{mol}^{1/2}\cdot\text{s}} $$

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Most popular questions from this chapter

The decomposition of hydrogen iodide on finely divided gold at $150^{\circ} \mathrm{C}\( is zero order with respect to \)\mathrm{HI}$. The rate defined below is constant at $1.20 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}$. $$ \begin{aligned} & 2 \mathrm{HI}(g) \stackrel{\text { ?u }}{\longrightarrow} \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \\ \text { Rate }=-\frac{\Delta[\mathrm{HI}]}{\Delta t} &=k=1.20 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s} \end{aligned} $$ a. If the initial HI concentration was \(0.250 \mathrm{~mol} / \mathrm{L},\) calculate the concentration of HI at 25 minutes after the start of the reaction. b. How long will it take for all of the \(0.250 \mathrm{M}\) HI to decompose?

The decomposition of \(\mathrm{NO}_{2}(g)\) occurs by the following bimolecular elementary reaction: $$ 2 \mathrm{NO}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) $$ The rate constant at 273 \(\mathrm{K}\) is $2.3 \times 10^{-12} \mathrm{L} / \mathrm{mol} \cdot \mathrm{s}\( , and the activation energy is 111 \)\mathrm{kJ} / \mathrm{mol}$ . How long will it take for the concentration of \(\mathrm{NO}_{2}(g)\) to decrease from an initial partial pressure of 2.5 \(\mathrm{atm}\) to 1.5 \(\mathrm{atm}\) at \(500 . \mathrm{K}\) ? Assume ideal gas behavior.

Which of the following statement(s) is(are) true? a. The half-life for a zero-order reaction increases as the reaction proceeds. b. A catalyst does not change the value of \(\Delta \mathrm{E}\) . c. The half-life for a reaction, aA \(\longrightarrow\) products, that is first order in A increases with increasing \([\mathrm{A}]_{0} .\) d. The half-life for a second-order reaction increases as the reaction proceeds.

The reaction $$ \mathrm{A} \longrightarrow \mathrm{B}+\mathrm{C} $$ is known to be zero order in A and to have a rate constant of $5.0 \times 10^{-2} \mathrm{mol} / \mathrm{L} \cdot \mathrm{s}\( at \)25^{\circ} \mathrm{C}$ . An experiment was run at \(25^{\circ} \mathrm{C}\) where $[\mathrm{A}]_{0}=1.0 \times 10^{-3} \mathrm{M} .$ a. Write the integrated rate law for this reaction. b. Calculate the half-life for the reaction. c. Calculate the concentration of \(\mathrm{B}\) after $5.0 \times 10^{-3} \mathrm{s}\( has elapsed assuming \)[\mathrm{B}]_{0}=0$

Consider a reaction of the type aA \(\longrightarrow\) products, in which the rate law is found to be rate \(=k[\mathrm{A}]^{3}\) (termolecular reactions are improbable but possible). If the first half-life of the reaction is found to be \(40 .\) s, what is the time for the second half-life? Hint: Using your calculus knowledge, derive the integrated rate law from the differential rate law for a termolecular reaction: $$ \text {Rate} =\frac{-d[\mathrm{A}]}{d t}=k[\mathrm{A}]^{3} $$
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