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Ch.4 - Reactions in Aqueous Solution
Chapter 4, Problem 100c

Neurotransmitters are molecules that are released by nerve cells to other cells in our bodies, and are needed for muscle motion, thinking, feeling, and memory. Dopamine is a common neurotransmitter in the human brain. (c) Experiments with rats show that if rats are dosed with 3.0 mg/kg of cocaine (that is, 3.0 mg cocaine per kg of animal mass), the concentration of dopamine in their brains increases by 0.75 mM after 60 seconds. Calculate how many molecules of dopamine would be produced in a rat (average brain volume 5.00 mm3) after 60 seconds of a 3.0 mg/kg dose of cocaine.

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Key Concepts

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

Molarity and Concentration

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. In this context, the concentration of dopamine is given in millimoles per liter (mM), which indicates how much dopamine is present in a specific volume of the rat's brain. Understanding how to convert between concentration and the number of molecules is essential for solving the problem.
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Volume and Density Relationships

The volume of the rat's brain is provided in cubic millimeters (mm³), which must be converted to liters for consistency with molarity calculations. Knowing that 1 mm³ equals 1 x 10^-6 liters allows for the correct conversion of brain volume, enabling the calculation of the total amount of dopamine present in the brain after cocaine administration.
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Relationship of Volume and Moles Example

Avogadro's Number

Avogadro's number (approximately 6.022 x 10²³) is the number of molecules in one mole of a substance. This concept is crucial for converting moles of dopamine, derived from the concentration and volume calculations, into the actual number of molecules. By applying Avogadro's number, one can determine how many dopamine molecules are produced in the rat's brain after the cocaine dose.
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Related Practice
Textbook Question

Consider the following reagents: zinc, copper, mercury (density 13.6 g/mL), silver nitrate solution, nitric acid solution. (a) Given a 500-mL Erlenmeyer flask and a balloon, can you combine two or more of the foregoing reagents to initiate a chemical reaction that will inflate the balloon? Write a balanced chemical equation to represent this process. What is the identity of the substance that inflates the balloon?

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Textbook Question

Bronze is a solid solution of Cu(s) and Sn(s); solutions of metals like this that are solids are called alloys. There is a range of compositions over which the solution is considered a bronze. Bronzes are stronger and harder than either copper or tin alone. (b) Based on part (a), calculate the concentration of the solute metal in the alloy in units of molarity, assuming a density of 7.9 g/cm3.

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Textbook Question

Bronze is a solid solution of Cu(s) and Sn(s); solutions of metals like this that are solids are called alloys. There is a range of compositions over which the solution is considered a bronze. Bronzes are stronger and harder than either copper or tin alone. (c) Suggest a reaction that you could do to remove all the tin from this bronze to leave a pure copper sample. Justify your reasoning.

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Textbook Question

Hard water contains Ca2+, Mg2+, and Fe2+, which interfere with the action of soap and leave an insoluble coating on the insides of containers and pipes when heated. Water softeners replace these ions with Na+. Keep in mind that charge balance must be maintained. (a) If 1500 L of hard water contains 0.020 M Ca2+ and 0.0040 M Mg2+, how many moles of Na+ are needed to replace these ions?

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Textbook Question

Hard water contains Ca2+, Mg2+, and Fe2+, which interfere with the action of soap and leave an insoluble coating on the insides of containers and pipes when heated. Water softeners replace these ions with Na+. Keep in mind that charge balance must be maintained. (b) If the sodium is added to the water softener in the form of NaCl, how many grams of sodium chloride are needed?

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Textbook Question

Citric acid, C6H8O7, is a triprotic acid. It occurs naturally in citrus fruits like lemons and has applications in food flavouring and preservatives. A solution containing an unknown concentration of the acid is titrated with KOH. It requires 23.20 mL of 0.500 M KOH solution to titrate all three acidic protons in 100.00 mL of the citric acid solution. Write a balanced net ionic equation for the neutralization reaction.

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