Ch.4 - Reactions in Aqueous Solution

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.4 - Reactions in Aqueous Solution

Problem 111

Chapter 4, Problem 111

Ritalin is the trade name of a drug, methylphenidate, used to treat attention-deficit/hyperactivity disorder in young adults. The chemical structure of methylphenidate is (c) Ritalin has a half-life of 3 hours in the blood, which means that after 3 hours the concentration in the blood has decreased by half of its initial value. For the man in part (b), what is the concentration of Ritalin in his blood after 6 hours?

Verified step by step guidance

Identify that the problem involves the concept of half-life, which is the time required for a quantity to reduce to half its initial value.

Recognize that the half-life of Ritalin is given as 3 hours, meaning every 3 hours, the concentration of Ritalin in the blood is halved.

Determine that after 6 hours, which is two half-lives (since 6 hours / 3 hours per half-life = 2), the concentration will be halved twice.

Calculate the concentration after the first half-life (3 hours) by dividing the initial concentration by 2.

Calculate the concentration after the second half-life (6 hours) by dividing the concentration after the first half-life by 2 again.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Half-life

Half-life is the time required for the concentration of a substance in the body to reduce to half its initial value. In pharmacology, understanding half-life is crucial for determining dosing schedules and predicting how long a drug will remain effective in the bloodstream. For Ritalin, with a half-life of 3 hours, the concentration decreases significantly over time, impacting therapeutic effects.

Exponential Decay

Exponential decay describes the process by which a quantity decreases at a rate proportional to its current value. In the context of drug concentration, this means that after each half-life, the remaining amount of the drug is halved. This concept is essential for calculating the concentration of Ritalin in the blood after multiple half-lives, as it follows a predictable pattern.

Concentration Calculation

Concentration calculation involves determining the amount of a substance in a given volume of solution, often expressed in units like mg/L or μg/mL. For Ritalin, knowing the initial concentration and applying the half-life allows for the calculation of remaining concentration after a specified time, which is vital for assessing drug levels in patients and ensuring effective treatment.

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Textbook Question

The arsenic in a 1.22-g sample of a pesticide was converted to AsO₄^3- by suitable chemical treatment. It was then titrated using Ag⁺ to form Ag₃AsO₄ as a precipitate. (b) Name Ag₃AsO₄ by analogy to the corresponding compound containing phosphorus in place of arsenic.

In 2014, a major chemical leak at a facility in West Virginia released 28,390 L of MCHM (4-methylcyclohexylmethanol, C8H16O) into the Elk River. The density of MCHM is 0.9074 g/mL. (a) Calculate the initial molarity of MCHM in the river, assuming that the first part of the river is 2.00 m deep, 90.0 m wide, and 90.0 m long.

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Textbook Question

A sample of 8.69 g of Zn(OH)₂ is added to 155.0 mL of 0.750 M H₂SO₄. (c) How many moles of Zn(OH)₂, H₂SO₄, ZnSO₄ are present after the reaction is complete?

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Textbook Question

The arsenic in a 1.22-g sample of a pesticide was converted to AsO₄^3- by suitable chemical treatment. It was then titrated using Ag⁺ to form Ag₃AsO₄ as a precipitate. (a) What is the oxidation state of As in AsO₄^3-?