An American gallon is 3.78541 liters.
The density of water with a low content of impurities is close to 1*103g/l.
The mass of water in the sample will be 3.78541*2. 65*10-4*1000=1.00313(g).
The Mass of lead at a concentration of 15ppm in the sample will be 1.00313g*15*10-6=1.5047*10-5g. The atomic mass of lead is 207g/mol.
The number of particles in 1mol is expressed by the Avogadro number: Na=6*1023mol-1.
Thus, the amount of lead ions in the sample will be:
nPb=1.5047*10-5g / 207g*mol-1=7.269*10-8mol
The mole fraction of lead is calculated based on the fact that the amount of substance in the sample is close to the amount of water of the corresponding mass, since the content of impurities is very small: n=nH2O=1.00313g / 18g*mol-1=0.0557.
Then the mole fraction of lead:
XPb=nPb/n=7.269*10-8mol/0.0557 mol=1.31*10-6 or 1.31*10-4%.