A forensic chemist is given a white solid that is suspected of being pure
cocaine \(\left(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{NO}_{4}, \text { molar
mass }=303.35 \mathrm{g} / \mathrm{mol}\right)\) She dissolves \(1.22 \pm 0.01
\mathrm{g}\) of the solid in \(15.60 \pm 0.01 \mathrm{g}\) benzene. The freezing
point is lowered by \(1.32 \pm 0.04^{\circ} \mathrm{C}\)
a. What is the molar mass of the substance? Assuming that the percent
uncertainty in the calculated molar mass is the same as the percent
uncertainty in the temperature change, calculate the uncertainty in the molar
mass.
b. Could the chemist unequivocally state that the substance is cocaine? For
example, is the uncertainty small enough to distinguish cocaine from codeine
\(\left(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{3}, \text { molar
}\right.\) mass \(=299.36 \mathrm{g} / \mathrm{mol}\) )?
c. Assuming that the absolute uncertainties in the measurements of temperature
and mass remain unchanged, how could the chemist improve the precision of her
results?