Question

Nanotechnology, the field of building ultrasmall 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 probably mimic red blood cells, the body's oxygen transporters. Nanocontainers, perhaps constructed of carbon, could be pumped full of oxygen and injected into a person's bloodstream. If the person needed additional oxygen - due to a heart attack or for the purpose of space travel, for example - these containers could slowly release oxygen into the blood, allowing tissues that would otherwise die to remain alive. Suppose that the nanocontainers were cubic and had 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 \(\mathrm{g} / \mathrm{L}\) How many grams of oxygen could be contained by each nanocontainer? c. Air typically contains about 0.28 of oxygen per liter. 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 bloodstream to provide 1 hours 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 \(\mathrm{L} ?\)

Short answer

The volume of one nanocontainer is 15.625 x 10^-21 L, each can contain 1.33 x 10^-18 g oxygen, a human inhales approximately 2.8 g of oxygen per hour, at least 2.11 x 10^15 nanocontainers are needed for 1 hour's oxygen, occupying a minimum volume of approximately 0.033 L, which is feasible for injection into the bloodstream.

Step-by-step solution

Calculating the Volume of One Nanocontainer

Calculate the volume of a cube with the provided edge length of 25 nanometers (nm) using the formula for the volume of a cube, which is Volume = edge length^3. First, convert the edge length from nanometers to liters because the density given is in grams per liter. There are (10^9) nanometers in a meter, and 1 cubic meter is equal to 1000 liters.

Calculating the Oxygen Content in One Nanocontainer

Use the volume calculated in Step 1 and the given oxygen density of 85 grams per liter to compute the mass of oxygen in one nanocontainer. This is done by multiplying the volume of the nanocontainer by the density of oxygen.

Determining the Oxygen Intake per Hour

Calculate the total grams of oxygen inhaled by a human in one hour by using the amount of oxygen per liter of air, the volume of air inhaled per breath, the number of breaths per minute, and the number of minutes in an hour.

Calculating the Minimum Number of Nanocontainers Needed

Determine the number of nanocontainers necessary to provide one hour's worth of oxygen by dividing the total mass of oxygen required (found in Step 3) by the mass of oxygen that one nanocontainer can hold (found in Step 2).

Calculating the Total Volume of the Nanocontainers

Calculate the minimum volume occupied by all the necessary nanocontainers by multiplying the number of nanocontainers (found in Step 4) by the volume of one nanocontainer (found in Step 1).

Assessing the Feasibility of the Nanocontainer Volume

Compare the total volume of nanocontainers needed with the total blood volume of an adult (approximately 5 liters) to determine if injecting this volume of nanocontainers into the bloodstream is feasible.

Key concepts

Artificial Cells

Imagine minute particles, intricately designed, performing the functions of human cells – these are artificial cells, remarkable feats of nanotechnology. They can range from simple structures mimicking oxygen carriers in the blood, such as red blood cells, to complex systems potentially replacing a variety of cellular functions. Artificial cells are designed to interact with biological systems and can be used for a myriad of medical applications.

For instance, in the case of heart attacks or during long-duration space travel where oxygen scarcity poses a threat, these synthetic cells could be lifesavers. They can be engineered to release oxygen gradually, a property that can be fine-tuned depending on the specific medical need. The creation of these cells requires meticulous calculation and understanding of nanoscale properties to ensure they are functional, safe, and effective when introduced into human tissue.

In educational exercises, students may encounter scenarios involving the creation and use of artificial cells, which would involve complex calculations such as volume and density to ascertain the practicality of such innovations in real-world applications.

Oxygen Transport Nanotechnology

The transport and delivery of oxygen within the body are fundamental to sustaining life. Nanotechnology brings a revolutionary approach to this by introducing the potential use of nanocontainers or nanocarriers. These are designed to contain and transport oxygen molecules directly to areas that require them. The concept is similar to that of red blood cells, but on a much smaller, more controllable scale.

Exercises involving oxygen transport nanotechnology often revolve around designing these containers to adequate specifications, ensuring they are small enough to circulate without causing blockages, yet large enough to carry a meaningful payload of oxygen. By encapsulating oxygen within these nanocontainers, there's potential for targeted delivery, which could provide a higher efficiency than our own biological systems in cases of emergency.

Understanding Volume-to-Oxygen Delivery Ratios

Learning about oxygen transport via nanocontainers may include volume-to-oxygen delivery ratios. This encompasses how the geometry of the container affects its capacity and release rate, the latter being critical to maintaining bodily function without overloading the system.

Nanocontainer Volume Calculation

Let's delve into calculating the volume of a nanocontainer. Having knowledge of the volume is vital because it helps determine how much oxygen the container can carry. Typically, a nanocontainer might be designed with a cubic shape for ease of manufacturing and calculation. Using a given edge length, one can calculate the volume of the cube using the equation for volume, which is the cube of the edge length.

The challenge for students is converting units from nanometers to liters, because oxygen density is measured in grams per liter. This conversion requires an understanding of the conversion factors between units of length (nanometers to meters) and volume (cubic meters to liters).

Practical Exercises in Volume Calculation

Textbook exercises often ask students to perform such calculations to provide a practical understanding of how these nanostructures could potentially operate within the bloodstream, and to reinforce the relevance of unit conversions in scientific calculations.

Oxygen Density in Nanocontainers

The concept of oxygen density in nanocontainers is at the heart of understanding their functionality. Oxygen density is the mass of oxygen contained within a unit volume of the container. By knowing the density, we can calculate the exact amount of oxygen in each nanocontainer, which is crucial for determining dosages and the number of containers needed for medical interventions.

When students are presented with exercises involving oxygen density, they're learning to calculate the mass of oxygen based on the container's volume and the known density. This calculation is essential in gauging whether the volume of nanocontainers required for treatment would be viable given the physical constraints of the human body, particularly when compared to the volume of blood within which these containers would circulate.

Real-World Applications in Medicine

Understanding oxygen density in nanocontainers is not just an academic exercise. It directly translates to real-world scenarios such as developing treatments for lung diseases or engineering artificial blood substitutes for transfusions. These calculations are a gateway to greater innovations in medical nanotechnology.