Ritalin is the trade name of a drug, methylphenidate, used to treat attention- deficit/hyperactivity disorder in young adults. The chemical structure of methylphenidate is (a) Is Ritalin an acid or a base? An electrolyte or a nonelectrolyte? (b) A tablet contains a 10.0 -mg dose of Ritalin. Assuming all the drug ends up in the bloodstream and the average man has a total blood volume of 5.0 \(\mathrm{L}\) , calculate the initial molarity of Ritalin in a man's bloodstream. (c) Ritalin has a half-life of 3 hours in the blood, which means that after 3 hours the concentration in the blood has decreased by half of its initial value. For the man in part (b), what is the concentration of Ritalin in his blood after 6 hours?

Step by step solution

01

Determining the type of compound Ritalin is

Ritalin is the trade name for the compound methylphenidate. The chemical structure of Ritalin is not provided in the exercise, so we cannot determine whether it is an acid or a base and its property as an electrolyte or nonelectrolyte. Therefore, we will move on to the other parts (b) and (c) of the exercise.

02

Converting mass to moles

To find the molarity of Ritalin in a man's bloodstream, we first need to convert the mass of the drug in the tablet to moles. The molecular weight of Ritalin is about 233 g/mol. Given that a tablet contains a 10.0 mg dose of Ritalin, we can use the molecular weight to convert this mass to moles: \(moles\,of\,Ritalin = \dfrac{10.0\,mg}{233\,g/mol} \) Note that we have to convert the mass from mg to g: \(moles\,of\,Ritalin = \dfrac{10.0\,mg \cdot (1\,g / 1000\,mg)}{233\,g/mol} = \dfrac{0.010\,g}{233\,g/mol} = 4.29 \times 10^{-5} \,mol\)

03

Calculating initial molarity

Now that we know the number of moles of Ritalin, we can calculate the initial molarity in the man's bloodstream. To do this, we need to know the total blood volume, which is given as 5.0 L: \(initial\,molarity\,of\,Ritalin\,(M_i) = \dfrac{moles\,of\,Ritalin}{blood\,volume} = \dfrac{4.29 \times 10^{-5}\,mol}{5.0\,L} = 8.58 \times 10^{-6}\,M\) The initial molarity of Ritalin in the man's bloodstream is \(8.58 \times 10^{-6}\,M\).

04

Calculating the concentration after 6 hours

To determine the concentration of Ritalin in the man's blood after 6 hours, we need to take into account the half-life of Ritalin, which is 3 hours. With a half-life of 3 hours, the concentration of Ritalin decreases by half for each 3-hour period. After 3 hours: concentration = initial concentration / 2 After 6 hours: concentration = (initial concentration / 2) / 2 = initial concentration / 4 So after 6 hours, the concentration of Ritalin in the man's blood is: \(Concentration\,after\,6\,hours = \dfrac{8.58 \times 10^{-6}\,M}{4} = 2.15 \times 10^{-6}\,M\) The concentration of Ritalin in the man's blood after 6 hours is approximately \(2.15\times 10^{-6}\,M\).

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