Problem 100 - Chemistry The Central Science In Si Units

Question

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 \(400.0 \mathrm{mg}\) dopamine per \(250.0 \mathrm{~mL}\) 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, \(3.0 \mathrm{mg}\) cocaine per \(\mathrm{kg}\) 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

Answer

(a) Acid-base reaction. (b) Approximately 0.0104 M. (c) 2.26 x 10^12 molecules.

Step 1: Determine Dopamine's Reaction in Water

Dopamine contains hydroxyl groups, making it likely to interact with water via hydrogen bonding. However, considering typical reactivities without strong oxidizing or reducing agents or metals, dopamine is unlikely to undergo redox or metathesis reactions in water. It's more likely to undergo an acid-base reaction, as functional groups can donate or accept protons (H+ ions) without precipitating a new substance.

Step 2: Understand the Concentration Formula

To determine molarity (M), we use the formula \( M = \frac{moles}{liters} \). We need the number of moles of dopamine and the volume of the solution in liters.

Step 3: Convert Mass of Dopamine to Moles

First, find the molar mass of dopamine, which is approximately \(153.18 \, g/mol\). Convert the \(400.0 \, mg\) to grams (\(0.4000 \, g\)), then use the molar mass to convert grams to moles:\[ \frac{0.4000 \text{ g}}{153.18 \text{ g/mol}} \approx 0.00261 \text{ mol} \]

Step 4: Convert Volume to Liters

The volume of solution is given as \(250.0 \, mL\), which is equivalent to \(0.2500 \, L\).

Step 5: Calculate Molarity

Using the moles of dopamine and the volume in liters, find the molarity:\[ M = \frac{0.00261 \text{ mol}}{0.2500 \text{ L}} = 0.01044 \text{ M} \approx 0.0104 \text{ M} \]

Step 6: Understand Dopamine Increase Due to Cocaine

From the experiment, the dopamine concentration increases by \(0.75 \mu M\) after dosing, which needs to be converted to molarity for calculation of molecules.

Step 7: Calculate Molecules of Dopamine

Calculate the total increase in moles for the rat brain.Convert brain volume to liters: \(5.00 \, mm^3 = 5.00 \times 10^{-6} \, L\).Increase in moles: \(0.75 \mu M = 0.75 \times 10^{-6} \, M\). Therefore:\[ \text{Increase in moles} = (0.75 \times 10^{-6} \, M) \times (5.00 \times 10^{-6} \, L) = 3.75 \times 10^{-12} \, mol \]Use Avogadro's number \(6.022 \times 10^{23}\) to find the number of molecules:\[ (3.75 \times 10^{-12} \, mol) \times (6.022 \times 10^{23} \, molecules/mol) \approx 2.26 \times 10^{12} \text{ molecules} \]

Key Concepts

Neurotransmitters

Neurotransmitters are chemical messengers that play a crucial role in transmitting signals between nerve cells across synapses. These important molecules are involved in a variety of functions such as muscle movement, thinking, feeling, and memory. For instance, dopamine is a neurotransmitter that significantly affects brain processes that control physical movement and emotional responses. When dopamine levels are not balanced, it could lead to conditions like Parkinson’s disease, which is marked by low dopamine levels. Hence, understanding how neurotransmitters like dopamine interact in the brain and body is essential for developing treatments for such conditions.

• Dopamine's role is to bind to specific receptors on target cells, leading to various effects.
• An imbalance in neurotransmitter levels can cause various neurological issues.
• Correcting neurotransmitter levels can involve medications that augment or mimic natural neurotransmitters.

Acid-Base Reactions

In chemistry, an acid-base reaction involves the transfer of protons (H⁺ ions) between reactants. Dopamine, by virtue of its chemical structure, is more likely to engage in acid-base reactions in aqueous solutions because it contains functional groups capable of donating and accepting protons. This interaction is crucial in physiological environments, where pH levels can significantly impact the function and effectiveness of neurotransmitters.

• Amine groups in dopamine can act as bases, accepting protons from their environment.
• Hydroxyl groups can donate protons, potentially influencing dopamine's activity.
• The acid-base behavior of dopamine can affect its solubility and reactivity in the body.

Molarity Calculations

Molarity is a way to express the concentration of a solute in a solution and is calculated using the number of moles of solute divided by the volume of the solution in liters. Calculating the molarity of dopamine in a solution requires you to first convert the mass of dopamine (given in milligrams) to moles using its molar mass. Then, convert the solution's volume from milliliters to liters. This conversion is crucial for accurately determining the concentration.

• First, find the molar mass of the substance to convert mass to moles.
• Convert volume to liters where 1 mL is 0.001 L.
• Molarity gives you how many moles of solute are present per liter of solution.

Avogadro's Number

Avogadro's number, which is approximately \(6.022 \times 10^{23}\), is the number of constituent particles, often atoms or molecules, that are contained in one mole of a given substance. It serves as a critical constant for converting between the number of particles and the amount of substance in moles. For example, if given the change in concentration of a substance, you can calculate how many actual molecules are present by multiplying the moles by Avogadro’s number.

• Use Avogadro’s number to transition from a measure of moles to the number of particles.
• This constant is instrumental in understanding the scale of molecular reactions.
• Great for visualizing how many molecules participate in chemical processes.