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

The natural abundances of the two stable isotopes of hydrogen (hydrogen and deuterium) are ${ }_{1}^{1} \mathrm{H}$ : 99.985 percent and ${ }_{1}^{2} \mathrm{H}: 0.015$ percent. 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

Natural Isotopic Abundance

This concept refers to the relative percentages of an element's isotopes as naturally occurring. It is crucial when calculating the likelihood of atoms in a compound being a specific isotope, as it directly influences the probabilities of forming molecules with multiple instances of that isotope.

Density-Volume-Mass Relationship

Density is defined as mass per unit volume and is used to relate a given volume of a substance to its mass. This conversion is essential in determining the amount of a substance in grams based on its volume, especially when the density is known.

Mole Concept and Molar Mass

The mole concept provides a bridge between the atomic scale and macroscopic quantities, allowing chemists to count atoms using mass. Molar mass, the mass of one mole of a substance, is utilized to convert between the mass of a substance and the number of moles, which is key for performing quantitative chemical calculations.

Avogadro's Number

Avogadro's number is the constant that defines the number of constituent particles, such as atoms or molecules, in one mole of a substance. It is fundamental for translating the amount in moles to an actual particle count, which is indispensable in stoichiometry.

Probability in Isotopic Substitution

This concept involves calculating the likelihood that multiple atoms in a molecule are replaced by a less abundant isotope. It treats each substitution event as an independent probability, which, when multiplied together, gives the overall probability of forming a molecule composed entirely of the rare isotope.

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