The natural abundances of the two stable isotopes of...

The natural abundances of the two stable isotopes of hydrogen (hydrogen and deuterium) are 99.99 percent $_{1}^{1} \mathrm{H}$ and 0.01 percent i. $\mathrm{H}$. Assume that water exists as either $\mathrm{H}_{2} \mathrm{O}$ or $\mathrm{D}_{2} \mathrm{O}$. Calculate the number of $\mathrm{D}_{2} \mathrm{O}$ molecules in exactly $400 \mathrm{mL}$ of water (density $1.00 \mathrm{g} / \mathrm{mL})$.

The natural abundances of the two stable isotopes of hydrogen (hydrogen and deuterium) are 99.99 percent $_{1}^{1} \mathrm{H}$ and 0.01 percent
i. $\mathrm{H}$. Assume that water exists as either $\mathrm{H}_{2} \mathrm{O}$ or $\mathrm{D}_{2} \mathrm{O}$. Calculate the number of $\mathrm{D}_{2} \mathrm{O}$ molecules in exactly $400 \mathrm{mL}$ of water (density $1.00 \mathrm{g} / \mathrm{mL})$.

Key Concepts

Probability in Independent Events

In the context of isotopic composition, the formation of a molecule containing two specific isotopic atoms is an independent event for each atom. The overall probability of forming such a molecule is the product of the individual probabilities for each atom being a specific isotope, allowing us to determine the fraction of a compound with a particular isotopic configuration.

Avogadro's Number

Avogadro's number is the constant that defines the number of particles (atoms, molecules, etc.) in one mole of a substance. It serves as the bridge between the macroscopic scale (grams and moles) and microscopic scale (individual molecules), which is critical when calculating the count of molecules in a given sample.

Isotopic Abundance

Isotopic abundance refers to the relative percentages of different isotopes of an element found naturally. In problems like this, it is essential to understand how the naturally occurring proportions of isotopes (such as hydrogen and deuterium) affect the composition of compounds, leading to variations in the type of molecules (for instance, H2O versus D2O).

Molar Mass and Density

This concept involves converting a given volume of a substance (using its density) into mass and then into moles using the substance’s molar mass. It is a fundamental stoichiometric process used to relate physical amounts of material to the number of particles involved in a reaction or mixture.

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