In the body, caffeine, $\mathrm{C}_8 \mathrm{H}_{10} \mathrm{~N}_4 \mathrm{O}_2$, acts as a stimulant and diuretic. How many moles of nitrogen are in $2.50 \mathrm{~g}$ of caffeine?

The rate at which drugs are eliminated from the body is called the clearance rate. The clearance rate depends on the individual person as well as the amount of drugs present. Suppose that in a healthy adult the clearance rate r(t) of 110 mg of caffeine (about one cup of coffee) is given by $r(t)=25 e^{-0.22 t} \mathrm{mg} \mathrm{h}^{-1},$ where t is the number of hours after which the caffeine is taken. a. Sketch the graph of r(t) for $0 \leqslant t \leqslant 4.$ b. Show that 4 hours after the intake of 110 mg of caffeine, the amount of caffeine left in the body is between 10 and 70 mg. c. By considering the maximum and minimum clearance for each hour, estimate the amount of caffeine left in the body 4 hours after an intake of 110 mg. d. Suggest a way of improving the accuracy of your estimate in c.

The equilibrium constant $K_{\mathrm{n}}$ for the neutralization of boric acid $\left(\mathrm{H}_3 \mathrm{BO}_3\right)$ and caffeine $\left(\mathrm{C}_8 \mathrm{H}_{10} \mathrm{~N}_4 \mathrm{O}_2\right)$ is 24 . What is $K_{\mathrm{b}}$ for caffeine?

Identify the heterocyclic amine1s2 in each of the following: a. caffeine

The molar mass of caffeine is $194.19 \mathrm{~g}$. Is the molecular formula of caffeine $\mathrm{C}_4 \mathrm{H}_5 \mathrm{~N}_2 \mathrm{O}$ or $\mathrm{C}_8 \mathrm{H}_{10} \mathrm{~N}_4 \mathrm{O}_2$ ?

An adult consumes an espresso containing 75 mg of caffeine. If the caffeine has a half-life of 5.5 hours, when will the amount of cafferne in her bloodstream equal 30 mg?

Why can't water be used to dissolve the caffeine found in coffee and tea?

There is $1.00 \times 10^{2}$ mg of caffeine in a shot of espresso. The chemical formula of caffeine is $\mathrm{C}_{\mathrm{8}} \mathrm{H}_{\mathrm{1} 0} \mathrm{N}_{\mathrm{4}} \mathrm{O}_{\mathrm{2}}$. Determine the moles of each element present in the caffeine in one shot of espresso.

A $1.0$ ounce piece of chocolate contains $15 \mathrm{mg}$ of caffeine, and a $6.0$ ounce cup of regular coffee contains $105 \mathrm{mg}$ of caffeine. How much chocolate would you have to consume to get as much caffeine as you would from $2.0$ cups of coffee?

Although other solvents are available, dichloromethane $\left(\mathrm{CH}_2 \mathrm{Cl}_2\right)$ is still often used to "decaffeinate" foods because the solubility of caffeine in $\mathrm{CH}_2 \mathrm{Cl}_2$ is $8.35$ times that in water.
(a) A 100.0-mL sample of cola containing $10.0 \mathrm{mg}$ of caffeine is extracted with $60.0 \mathrm{~mL}$ of $\mathrm{CH}_2 \mathrm{Cl}_2$. What mass of caffeine remains in the aqueous phase?

A cup of coffee contains about 100 mg of caffeine. Caffeine is metabolized and leaves the body at a continuous rate of about 17% every hour. Write a differential equation for the amount, A, of caffeine in the body as a function of the number of hours, t, since the coffee was consumed.

The caffeine content of a cup of home-brewed coffee is a normally distributed random variable with a mean of 115 mg with a standard deviation of 20 mg. (a) What is the probability that a randomly chosen cup of home-brewed coffee will have more than 130 mg of caffeine? (b) Less than 100 mg? (c) A very strong cup of tea has a caffeine content of 91 mg. What is the probability that a cup of coffee will have less caffeine than a very strong cup of tea?

One $8\text{-oz}$ serving each of brewed coffee, Red Bull energy drink, and Mountain Dew soda contains a total of $197 \text{mg}$ of caffeine. One serving of brewed coffee has $6 \text{mg}$ more caffeine than two servings of Mountain Dew. One serving of Red Bull contains $37 \text{mg}$ less caffeine than one serving each of brewed coffee and Mountain Dew. Find the amount of caffeine in one serving of each beverage.

A cup of coffee contains $100 \mathrm{mg}$ of caffeine, which leaves the body at a continuous rate of $17 \%$ per hour.

Write a formula for the amount, $A\ \mathrm{mg}$, of caffeine in the body $t$ hours after drinking a cup of coffee.