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

Answer:

6.70 × 10²⁰ molecules of D₂O

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:

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