Question

If a Neanderthal excreted 500mL of urine into the ocean 50,000 years ago,how many molecules in 500mL of water you drink today are from that urine,and assume complete mixing of the waters of Earth over 50,000 years.

Answer 1

Volume of ocean = 3.5*10^8 mi^3 approx

change to mL (factor is 4.171428*10^15)

V = 1.46*10^24 mL are present

then

conver cooncentrations

500 mL urine / ( 1.46*10^24 mL ocean) --> 3.42*10^-22 mL per 1 mL of ocean (simply inver ratios)

since we have 500 mL

then

(3.42*10^-22 mL) per mL of water * 500 mL of water

3.42*10^-22)(500) =1.71 *10^-19 mL

the density of water (assume)

D = 1 g/mL

so

1.71*10^-19 g of water

change to mol so

mol = mass/MW

MW of water = 18 g/mol

1.71*10^-19 g ---> 1.71*10^-19)/(18) = 9.5*10^-21 mol

so

1 mol = 6.022*10^23 molecules

molecules in sample = (6.022*10^23) * (9.5*10^-21) = 5720.9 molecules will be found