International Chemistry Olympiad · 2022

Problems

Problem 1Gold nanoparticles modified with two kinds of single-stranded nucleic acid fragments a and b aggregate in the presence of the target nucleic acid a'b' from the coronavirus, causing a colour change of the solution from red to blue within minutes. Gold nanoparticles are composed of closely packed gold atoms with the density of solid gold, $\rho = 19.3$ g cm $^{-3}$ . (a) Calculate the number of gold atoms $N$ in a spherical gold nanoparticle of diameter 30.0 nm ( $M(\ce{Au}) = 197.0$ g mol $^{-1}$ , $N_A = 6.022\times 10^{23}$ mol $^{-1}$ ). (b) 5.2 mg of $\ce{HAuCl4*3H2O}$ ( $M = 394$ g mol $^{-1}$ ) was completely converted into uniform spherical gold nanoparticles of diameter 30.0 nm in 100.0 mL of solution; the absorbance of the red solution measured at 530 nm in a 1 cm cuvette was 0.800. Calculate the molar extinction coefficient (per mole of nanoparticles) at 530 nm.Solutions: 1