Mathematical Issues for Chemists

A brief outline of the mathematical issues faced by chemistry students.

Reaction Rates

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

Catalyse That!

Can you work out how to produce the right amount of chemical in a temperature-dependent reaction?

Smoke and Daggers

Age 16 to 18 Challenge Level:

Hint
Each compound contributes to the total pressure in her lungs, known as the partial pressure. Can you work out the partial pressure that each of the compounds contributes?

Make sure you consider the moles of "air" molecules present in Ellie's lungs which also contribute to the partial pressure.

Hint
What is the density of the cigarette smoke containing air in her lungs?

Make sure you take into account the masses of the components of alveolar air as well as the unusual components of the smoke given already.

Hint
What is the average concentration of nicotine in Ellie's blood given that systolic blood pressure is 120 mmHg, the diastolic blood pressure is 80 mmHg?

An equation is required that links pressure and volume as well as number of moles. Also consider the value of blood pressure compared to atmospheric pressure. The conversion from mmHg to Pa has been provided earlier in the question.

Hint
How long does it take for levels of nicotine to drop below the 200 ng/ml detectable level so that Ellie can cheat her test?

Nicotine uptake into the blood stream is rapid compared with its half-life. This can be seen by doing a rough calculation. You might approximate the uptake to be instantaneous in your calculation.

Hint
Assuming that none of these dangerous compounds is absorbed into the blood stream over this period, what is the percentage of dangerous compounds in the alveolar air for Ellie and her brother, Pete, after the last outward breath?

Consider how the percentage of dangerous compounds varies with the first few inward and outward breaths. Can you see any patterns?