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. (a) Predict what kind of reaction dopamine is most likely to undergo in water: redox, acid-base, precipitation, or metathesis? Explain your reasoning. (b) Patients with Parkinson's disease suffer from a shortage of dopamine and may need to take it to reduce symptoms. An IV (intravenous fluid) bag is filled with a solution that contains 400.0 mg dopamine per 250.0 mL. of solution. What is the concentration of dopamine in the IV bag in units of molarity? (c) Experiments with rats show that if rats are dosed with 3.0 \(\mathrm{mg} / \mathrm{kg}\) of cocaine (that is, 3.0 mg cocaine per kg of animal mass), the concentration of dopamine in their brains increases by 0.75\(\mu M\) after 60 seconds. Calculate how many molecules of dopamine would be produced in a rat (average brain volume 5.00 \(\mathrm{mm}^{3} )\) after 60 seconds of a 3.0 \(\mathrm{mg} / \mathrm{kg}\) dose of cocaine.

Step by step solution

01

(a) Analyzing Dopamine's Reactions

Dopamine has the molecular formula C8H11NO2. It contains hydroxyl (-OH) and amine (-NH2) functional groups. The presence of these functional groups suggests that dopamine can act as either a weak acid, donating its OH- group, or as a weak base, accepting an H+ ion for its NH2 group. Further, the structure of dopamine does not suggest any redox, precipitation, or metathesis reactions. Thus, the most likely reaction dopamine will undergo in water is an acid-base reaction.

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(b) Calculating Dopamine Concentration

To find the concentration of dopamine in moles per liter (M), we start by dividing the mass of dopamine by its molar mass to find the moles of dopamine. The molar mass of dopamine is 153.18 g/mol (C8H11NO2). Moles of dopamine = \( \frac{400.0 \, \text{mg}}{153.18 \, \text{g/mol}} \cdot \frac{1 \, \text{g}}{1000 \, \text{mg}} \) Next, we convert the volume of the solution from mL to L: Volume in liters = \( 250.0 \, \text{mL} \cdot \frac{1 \, \text{L}}{1000 \, \text{mL}} \) Now we can find the concentration (in M) by dividing the moles of dopamine by the volume of the solution in liters: Concentration = \(\frac{\text{moles of dopamine}}{\text{volume in liters}}\)

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(c) Calculating Dopamine Molecules Produced

The increase in dopamine concentration is given as 0.75μM. To find the number of dopamine molecules produced, we need to use the increased concentration, rat's brain volume, and Avogadro's number. First, convert the volume of the rat's brain from mm³ to L: Volume in liters = \( 5.00 \, \text{mm}^3 \cdot \frac{1 \, \text{L}}{1000\, \text{mL}} \cdot \frac{1000 \, \text{cm}^3}{1\, \text{L}} \cdot \frac{1\, \text{mL}}{1\, \text{cm}^3} \cdot \frac{1\, \text{cm}^3}{1000\, \text{mm}^3} \) Next, we calculate the moles of dopamine produced by multiplying the increased concentration and the brain volume in liters: Moles of dopamine = increase in concentration × brain volume in liters Finally, we calculate the number of dopamine molecules produced by multiplying the moles of dopamine and Avogadro's number: Number of dopamine molecules = moles of dopamine × Avogadro's number (6.022 × 10²³ molecules/mol)

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