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Chapter 12: Q37 E (page 706)

What is the half-life for the first-order decay of phosphorus-32?\(_{{\bf{15}}}^{{\bf{32}}}{\bf{P}} \to _{{\bf{16}}}^{{\bf{32}}}{\bf{S + }}{{\bf{e}}^{\bf{ - }}}\)The rate constant for the decay is\({\bf{4}}{\bf{.85 \times 1}}{{\bf{0}}^{{\bf{ - 2}}}}{\bf{da}}{{\bf{y}}^{{\bf{ - 1}}}}\).

Short Answer

Expert verified

The half-life is 14.3 days.

Step by step solution

01

Definition

The half-life of a sample is the time required for half of the sample to undergo the process.

02

First-order reaction half-life

The rate constant has an inverse relationship with the half-life.

A first-order reaction's half-life is specified as

\({t_{1/2}} = \frac{{0.693}}{k}\)

k is the rate constant of the given reaction, and this is the derived formula of half-life.

03

Calculation of Half-life

Replacing the values,

\(\begin{align}{t_{1/2}} &= \frac{{0.693}}{{4.85 \times {{10}^{ - 2}}}}\\{t_{1/2}} &= 14.3days\end{align}\)

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Most popular questions from this chapter

In terms of collision theory, to which of the following is the rate of a chemical reaction proportional?

(a) the change in free energy per second

(b) the change in temperature per second

(c) the number of collisions per second

(d) the number of product molecules

Define these terms: (a) unimolecular reaction (b) bimolecular reaction (c) elementary reaction (d) overall reaction.

For the reaction\({\bf{A}} \to {\bf{B + C}}\), the following data were obtained at 30 掳C:

  1. What is the order of the reaction with respect to (A), and what is the rate law?
  2. What is the rate constant?

Some bacteria are resistant to the antibiotic penicillin because they produce penicillinase, an enzyme with a molecular weight of \({\bf{3 \times 1}}{{\bf{0}}^{\bf{4}}}\)g/mole that converts penicillin into inactive molecules. Although the kinetics of enzyme-catalysed reactions can be complex, at low concentrations this reaction can be described by a rate equation that is first order in the catalyst (penicillinase) and that also involves the concentration of penicillin. From the following data: 1.0 L of a solution containing 0.15 碌g (\({\bf{0}}{\bf{.15 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\)g) of penicillinase, determine the order of the reaction with respect to penicillin and the value of the rate constant.

(Penicillin) (M)

Rate (mole/L/min)

\({\bf{2}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\) \(\)

\({\bf{1}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\)

\({\bf{3}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\)

\({\bf{1}}{\bf{.5 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\)

\({\bf{4}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\)

\({\bf{2}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\)

Go to the PhET Reactions & Rates interactive. Use the Single Collision tab to represent how the collision between monatomic oxygen (O) and carbon monoxide (CO) results in the breaking of one bond and the formation of another. Pull back on the red plunger to release the atom and observe the results. Then, click on 鈥淩eload Launcher鈥� and change to 鈥淎ngled shot鈥� to see the difference.

  1. What happens when the angle of the collision is changed?
  2. Explain how this is relevant to rate of reaction.
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