3. You have a gold nanoparticle dispersion with a molar concentration of 3.14E-8 M and a total volume of 10.0 mL. Assume that all gold nanoparticles are perfectly spherical and exhibit an average core diameter of 32.3 nm.
(i) Calculate the combined surface area from all nanoparticles in your 10.0-mL dispersion.
(ii) You want to use your spherical gold nanoparticles as drug delivery vehicles to deliver the small molecule anti-cancer drug Doxorubicin to cancer cells. Assume that you can load Doxorubicin onto the surface of your gold nanoparticles with a maximum loading density of 4.10 Doxorubicin molecules per nm² of nanoparticle surface area. How many Doxorubicin molecules can you load per nanoparticle?
(iii) For cancer therapy, Doxorubicin is administered in the clinic at 50.0 mg/m² (i.e. 50.0 mg of drug per m² body surface area of the cancer patient). Calculate how much Doxorubicin-loaded gold nanoparticles need to be administered theoretically into a cancer patient with a body surface area of 1.9 m² to reach 50.0 mg/m² in that patient. Provide your results as (a) number of nanoparticles; and (b) amount of nanoparticles in mol.