Chapter 1, Problem 93E

Nanotechnology, the field of building ultra-small structures one atom at a time, has progressed in recent years. One potential application of nanotechnology is the construction of artificial cells. The simplest cells would mimic red blood cells, the body’s oxygen transporters. These nanocontainers, constructed of carbon, could be pumped full of oxygen and injected into a person’s bloodstream it me person needed additional oxygen-due to a heart attack perhaps, or for the purpose of space travel-these containers would slowly release oxygen into the blood, allowing tissues that would otherwise die to remain alive. Suppose that the cell-like nanocontainers are cubic and have an edge length of 25 nanometers.
a. What is the volume of one nanocontainer? (Ignore the thickness of the nanocontainer’s wall.)
b. Suppose that each nanocontainer could contain pure oxygen pressurized to a density of 85 g/L. How many grams of oxygen could be contained by each nanocontainor?
c. Normal air contains about 0.28 g of oxygen per minute. An average human inhales about 0.50 L of air per breath and takes about 20 breaths per minute. How many grams of oxygen does a human inhale per hour? (Assume two significant figures.)
d. What is the minimum number of nanocontainers that a person would need in his or her bloodstream to provide ore hour’s worth of oxygen?
e. What is the minimum volume occupied by the number of nanocontainers calculated in part d? Is such a volume feasible, given that total blood volume in an adult is about 5 liters?