We have to calculate the number of molecules of dopamine produced in a rat brain when the concentration of dopamine increases by 0.75 M.

We can use the molarity and given volume of rat brain to **calculate the number of moles** of dopamine. Then we can **use the Avogadro’s number to calculate the number of dopamine molecules.**

**The formula for molarity is:**

$\overline{){\mathbf{Molarity}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{moles}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solute}}{\mathbf{liters}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solution}}}$

**The formula for number of molecules is:**

$\overline{){\mathbf{Number}}{\mathbf{}}{\mathbf{of}}{\mathbf{}}{\mathbf{molecules}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{moles}}{\mathbf{\times}}{{\mathbf{N}}}_{{\mathbf{A}}}}$

N_{A} = Avogadro's number = 6.022×10^{23} particles/mol

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.

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 M after 60 seconds. Calculate how many molecules of dopamine would be produced in a rat (average brain volume 5.00 mm^{3}) after 60 seconds of a 3.0 mg/kg dose of cocaine.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Molarity concept. You can view video lessons to learn Molarity. Or if you need more Molarity practice, you can also practice Molarity practice problems.

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Based on our data, we think this problem is relevant for Professor Bartoszek Loza's class at OSU.