Question

The natural abundances of the two stable isotopes of hydrogen (hydrogen and deuterium) are 99.99 percent and 0.01 percent. Assume that water exists as either _1^1 H_2O or _1^2 D_2O. Calculate the number of D_2O molecules in 200.0 mL of water (density = 1.00 g/mL). Enter your answer in scientific notation.

Answer 1

6.70 × 10²⁰ molecules of D₂O

Step-by-step explanation:

The number of D₂O molecules is related to the abundance of deuterium. If the word "Hydrogen" refers to both isotopes, while H and D refer to each one.

We will use these relations:

The molar mass of water is 18.0g/mol

The molar mass of Hydrogen is 1.00 g/mol

Avogadro's number is 6.02 × 10²³

Every 100 atoms of Hydrogen, there are 0.01 atoms of D.

We can pose the following proportions:

`200.0mL(water).(1.00g(water))/(1mL(water)) .(2.00g(Hydrogen))/(18.0g(water)) .(1mol(atomsof Hydrogen))/(1g(Hydrogen)) .(6.02 * 10^(23)(atomsofHydrogen)  )/(1mol(atomsof Hydrogen)) =1.34 * 10^(25)(atomsofHydrogen)\\1.34 * 10^(25)(atomsofHydrogen).(0.01atoms(D))/(100(atomsofHydrogen)) .(1molecule(D_(2)O))/(2atoms(D)) =6.70 * 10^(20) molecules(D_(2)O)`