Question

Two thirds of the atoms in a molecule of water \(\left(\mathrm{H}_{2} \mathrm{O}\right)\) are hydrogen. What percentage of the weight of a water molecule is the weight of the two hydrogen atoms? The atomic weight of hydrogen is \(1.008 \mathrm{~g} /\) mole and of oxygen is \(16.00 \mathrm{~g} / \mathrm{mole} .\)

Short answer

The weight of the two hydrogen atoms in a water molecule is approximately \(11.19 \%\) of the total weight of the water molecule.

Step-by-step solution

Understanding the water molecule composition

A water molecule has two Hydrogen (H) atoms and one Oxygen (O) atom. The formula for a water molecule is given as H2O.

Calculate the total weight of a water molecule

To find the total weight of a water molecule, we add the atomic weights of two Hydrogen atoms and one Oxygen atom. The atomic weight of hydrogen is \(1.008 \mathrm{~g} / \mathrm{mole}\) and of oxygen is \(16.00 \mathrm{~g} / \mathrm{mole}\). Total weight of a water molecule = \(2 × 1.008 \mathrm{~g} / \mathrm{mole} + 16.00 \mathrm{~g} / \mathrm{mole}\) Total weight of a water molecule = \(2.016 \mathrm{~g} / \mathrm{mole} + 16.00 \mathrm{~g} / \mathrm{mole}\) Total weight of a water molecule = \(18.016 \mathrm{~g} / \mathrm{mole}\)

Calculate the weight of two Hydrogen atoms

To find the weight of two Hydrogen atoms, we multiply their atomic weight with the number of atoms. Weight of two Hydrogen atoms = \(2 × 1.008 \mathrm{~g} / \mathrm{mole}\) Weight of two Hydrogen atoms = \(2.016 \mathrm{~g} / \mathrm{mole}\)

Compute the percentage of the weight of two Hydrogen atoms

To find the percentage of the weight of two Hydrogen atoms, we divide the weight of two Hydrogen atoms by the total weight of a water molecule and multiply it by 100. Percentage of the weight of two Hydrogen atoms = \(\frac{2.016 \mathrm{~g} / \mathrm{mole}}{18.016 \mathrm{~g} / \mathrm{mole}} × 100\) Percentage of the weight of two Hydrogen atoms = \(\frac{2.016}{18.016} × 100\) Percentage of the weight of two Hydrogen atoms ≈ \(11.19 \% \) The weight of the two hydrogen atoms in a water molecule is approximately 11.19% of the total weight of the water molecule.

Key concepts

Atomic Weight

Understanding the atomic weight is crucial when diving into chemistry. It is defined as the average mass of atoms of an element, measured in atomic mass units (amu), also known as daltons. It accounts for the fact that an element can have different isotopes—atoms with the same number of protons but different numbers of neutrons. Scientists average the masses of these isotopes, weighted by their natural abundance, to calculate the atomic weight.

For instance, the atomic weight of hydrogen is approximately 1.008 amu. This value represents a weighted average of the hydrogen isotopes, primarily protium (with no neutrons) and deuterium (with one neutron). The small decimal points are important as they reflect the precise calculation of these weights and are essential when it comes to accurately determining the mass of molecules or the yields from chemical reactions.

Percentage Composition

In chemical analysis, the percentage composition of a compound is a breakdown of the relative amounts of each element in that compound. This concept is incredibly useful for chemists to understand the makeup of a molecule and to predict how it might behave in reactions. It’s calculated by dividing the total mass of each element in the compound by the compound’s overall molecular weight and then converting this ratio into a percentage.

For our water example, calculating the percentage composition involves dividing the weight of the hydrogen atoms by the total molecular weight of water. The resulting ratio is multiplied by 100 to yield a percentage. This tells us how much of the compound's total weight is due to hydrogen atoms. It’s a window into the compound's structure that can help predict properties such as reactivity and boiling point.

Chemical Formula

A chemical formula represents the types and numbers of atoms in a molecule. It's not just a string of letters and numbers; it is the essential blueprint of a compound’s structure. For example, the chemical formula for water, H₂O, tells us that each molecule is composed of two hydrogen atoms (H) and one oxygen atom (O).

Understanding how to read a chemical formula is vital for various exercises in chemistry, including the calculation of molecular weight. It informs us what elements and how many of each are present, which is required when you're calculating the weight of the molecule, as well as in elucidating its properties and behaviors in chemical reactions. Without the chemical formula, comprehending the composition and characteristics of a substance would be a much more challenging task.