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.

Short answer

Dopamine is likely to undergo an acid-base reaction in water due to its molecular structure. The concentration of dopamine in the IV bag is 0.0104 M. After 60 seconds of a 3.0 mg/kg dose of cocaine, 2.26 x 10^15 molecules of dopamine would be produced in a rat's brain.

Step-by-step solution

(a) Prediction of Dopamine Reaction in Water

To determine the type of reaction dopamine will most likely undergo in water, we need to examine its molecular structure. Dopamine consists of an amine group (-NH2) and a hydroxyl group (-OH), which makes it an amino alcohol. It is most likely to undergo an acid-base reaction in water, as the amine group can act as a weak base, while the hydroxyl group can act as a weak acid. Redox reactions are unlikely since there is no apparent electron transfer, and precipitation/metathesis reactions are unlikely due to the presence of polar, charged groups.

(b) Concentration of Dopamine in the IV Bag

To find the concentration of dopamine in the IV bag, we first need to convert the mass of dopamine to moles and then divide this value by the volume of the solution. The molecular weight of dopamine (C8H11NO2) is approximately 153.18 g/mol. Therefore, the concentration can be found by the following steps: 1. Convert the mass of dopamine in the IV bag to moles: \(400.0 \: \mathrm{mg} \times \frac{1 \: \mathrm{g}}{1000 \: \mathrm{mg}} \times \frac{1 \: \mathrm{mol}}{153.18 \: \mathrm{g}} = 0.00261 \: \mathrm{mol}\) 2. Convert the volume of the solution to liters: \(250.0 \: \mathrm{mL} \times \frac{1 \: \mathrm{L}}{1000 \: \mathrm{mL}} = 0.250 \: \mathrm{L}\) 3. Calculate the concentration of dopamine: \(\frac{0.00261 \: \mathrm{mol}}{0.250 \: \mathrm{L}} = 0.0104 \: \mathrm{M} \) The concentration of dopamine in the IV bag is 0.0104 M.

(c) Number of Dopamine Molecules Produced in a Rat's Brain

To find the number of dopamine molecules produced in a rat's brain, we will first convert the concentration increase into moles and then multiply by Avogadro's number (6.022 x 10^23 molecules/mol). 1. Convert the volume of a rat's brain to liters: \(5.00 \: \mathrm{mm}^3 \times \frac{1 \: \mathrm{cm}^3}{1000 \: \mathrm{mm}^3} \times \frac{1 \: \mathrm{L}}{1000 \: \mathrm{cm}^3} = 0.000005 \: \mathrm{L}\) 2. Calculate the moles of dopamine produced: \((0.75 \mu \mathrm{M}) \times (0.000005 \: \mathrm{L}) = 3.75 \times 10^{-9} \mathrm{mol}\) 3. Calculate the number of dopamine molecules produced: \((3.75 \times 10^{-9} \mathrm{mol}) \times (6.022 \times 10^{23} \: \mathrm{molecules/mol}) = 2.26 \times 10^{15} \: \mathrm{molecules}\) In a rat's brain, after 60 seconds of a 3.0 mg/kg dose of cocaine, 2.26 x 10^15 molecules of dopamine would be produced.

Key concepts

Neurotransmitter Reactions

Imagine how our brains communicate. They use chemicals called neurotransmitters like dopamine. When dopamine enters water, we can expect an acid-base reaction. This is because dopamine has both amine and hydroxyl groups. The amine group can accept a proton, making it a weak base. The hydroxyl group can donate a proton, functioning as a weak acid. This interaction leads to an acid-base reaction. Acid-base reactions are among the easiest for molecules like dopamine to undergo because they involve protons which are smaller and quicker to transfer compared to electrons in redox reactions.

Molarity Calculations

Calculating molarity means determining the concentration of a solution. Imagine dissolving your favorite drink powder into a glass of water, the concentration would vary based on how much powder you add. In our case, figuring out dopamine's molarity in an IV bag involves a few steps:

• First, **convert mass to moles**. Since dopamine weighs 153.18 grams per mole, we calculate the amount of moles in 400 mg of dopamine.
• Second, **convert solution volume** to liters from milliliters.
• Finally, use the formula: \(\frac{\text{moles of dopamine}}{\text{liters of solution}}\) to find molarity.

This gives us dopamine's molarity in the IV bag, ensuring correct dosage for patients.

Acid-Base Reactions

Acid-base reactions are a specific type of chemical reaction involving proton transfer. In dopamine's case, we see this with its functional groups.
Dopamine's amino group can accept protons, behaving as a base, while its hydroxyl structure can donate protons, acting as an acid. When these groups interact with water, they can form weak acid-base reactions. This behavior is common with many biological molecules, allowing them to participate in diverse chemical processes inside the body. Understanding this helps us predict how neurotransmitters like dopamine will behave in different environments.

Molecular Calculations

Molecular calculations help us predict the number of molecules in a given environment. In experiments with rats, knowing how increased dopamine levels occur is vital. We start by converting the brain volume into liters. Then, knowing the micromolar increase, we estimate the moles of dopamine added. Finally, by using Avogadro's number, which is 6.022 x 10^23 molecules per mole, the total number of dopamine molecules can be found. This step helps in understanding the scale of molecular changes in the brain after specific drug doses, critical when studying drug effects.

Dopamine Structure

To understand dopamine's reactions, we must look at its structure. Dopamine has a carbon skeleton with an added amine group and two hydroxyl groups.
The amine group features a nitrogen atom known for forming readily accessible bonds in biological reactions. The hydroxyl groups on dopamine also contribute to its reactivity, particularly with water and within the body. They create polar sites because these groups can engage in hydrogen bonding. Consequently, dopamine's structure dictates its solubility and reactivity, making it versatile in various chemical and biological processes. Recognizing these features helps predict its behavior in human physiology.