Question

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 μM 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.

Answer 1

The molecules of dopamine would be produced in a rat after 60 seconds of a 3.0 mg/kg dose of cocaine is
`2.258* 10^(12) molecules`.

Step-by-step explanation:

Concentration of dopamine = 0.75 μM =
`7.5* 10^(-7) M`

1 μM =
`10^(-6) M`

Volume of the brain in which dopamine is produced =
`V=5.00 mm^3`

`1 mm^3=10^(-6) L`

`V = 5.00* 10^(-6) L`

Moles of dopamine = n

`Concentration=(moles)/(Volume)`

`7.5* 10^(-7) M=(n)/(5.00* 10^(-6) L)`

`n=7.5* 10^(-7) M* 5.00* 10^(-6) L=3.75* 10^(-12) mol`

`1 mol = 6.022* 10^(23) molecules`

So, molecules in
`3.75* 10^(-12) mol` of dopamine :

`3.75* 10^(-12)* 6.022* 10^(23)=2.258* 10^(12) molecules`