Problem 29 - Chemistry Matter and Change

Question

Calculate the mass percent of hydrogen in water and the mass percent of oxygen in water.

Step-by-Step Solution

Answer

The mass percent of hydrogen in water is approximately \(11.19 %\) and the mass percent of oxygen in water is approximately \(88.81 %\).

Step 1: Determine the Atomic Mass of Hydrogen and Oxygen

Refer to the periodic table and find the atomic masses of hydrogen and oxygen: Hydrogen: \(1.01 \, u\) Oxygen: \(16.00 \, u\)

Step 2: Calculate the Molecular Mass of Water

To calculate the molecular mass of water (H₂O), add the atomic masses of the elements in the molecule. Molecular Mass of Water (H₂O) = 2 * atomic mass of hydrogen + atomic mass of oxygen Molecular Mass of Water (H₂O) = 2 * \(1.01 \, u\) + \(16.00 \, u\) Molecular Mass of Water (H₂O) = \(2.02 \, u\) + \(16.00 \, u\) Molecular Mass of Water (H₂O) = \(18.02 \, u\)

Step 3: Calculate the Mass Percent of Hydrogen in Water

To calculate the mass percent of hydrogen in water, divide the total mass of hydrogen in water by the molecular mass of water and multiply by 100. Mass Percent of Hydrogen = (Total mass of hydrogen in water / Molecular mass of water) * 100 Mass Percent of Hydrogen = (\(2.02 \, u\) / \(18.02 \, u\)) * 100 Mass Percent of Hydrogen ≈ \(11.19 %\)

Step 4: Calculate the Mass Percent of Oxygen in Water

To calculate the mass percent of oxygen in water, divide the mass of oxygen in water by the molecular mass of water and multiply by 100. Mass Percent of Oxygen = (Mass of oxygen in water / Molecular mass of water) * 100 Mass Percent of Oxygen = (\(16.00 \, u\) / \(18.02 \, u\)) * 100 Mass Percent of Oxygen ≈ \(88.81 %\) The mass percent of hydrogen in water is approximately \(11.19 %\) and the mass percent of oxygen in water is approximately \(88.81 %\).

Key Concepts

Molecular Mass of Water

Understanding the molecular mass of water is critical in chemistry, particularly when computing the mass percent composition of compounds. The molecular mass is the sum of the atomic masses of all the atoms in a molecule. For water (H₂O), the calculation involves adding twice the atomic mass of hydrogen to the atomic mass of oxygen.

Each hydrogen atom has an approximate atomic mass of 1.01 atomic mass units (u), and oxygen's atomic mass is about 16.00 u. Doing the math, the molecular mass of water is given by:
$$\text{Molecular Mass of H}_2\text{O} = 2 \times 1.01 \, u + 16.00 \, u = 18.02 \, u.$$
Grasping this concept is key to solving a range of problems in chemistry, from reaction yields to concentration calculations.

Atomic Mass

Atomic mass is a fundamental concept in chemistry that represents the mass of a single atom, usually expressed in atomic mass units (u). It is essentially the weight of an atom on a scale where the mass of a carbon-12 atom is exactly 12 u. Hydrogen, being the lightest element, has an atomic mass of about 1.01 u, and oxygen, a more massive atom, has an atomic mass of approximately 16.00 u.

Understanding atomic mass is crucial because it allows us to calculate the amounts of substances needed or produced in a chemical reaction (stoichiometry) and to determine the percent composition of compounds. Remember, these masses can be found on the periodic table and are critical for the calculations that follow.

Stoichiometry

Stoichiometry is at the heart of chemical equations and reactions. It is a branch of chemistry that deals with the quantitative relationships between the substances as they participate in chemical reactions. The principle of stoichiometry dictates that the amounts of reactants and products in a chemical reaction are proportionate to their respective molar ratios as represented in the balanced equation.

For instance, in the formation of water, stoichiometry helps us understand that two hydrogen atoms will react with one oxygen atom to produce one molecule of water. This ratio must be maintained to respect the law of conservation of mass. If the ratio is altered, the water will not form properly. Stoichiometry is also used to determine the amount of reactants needed to produce a desired quantity of product.

Percent Composition

Percent composition is a measure of the relative amount of each element within a compound. It is expressed as a percentage of the total mass of the compound that each constituent element contributes. For the exercise in calculating the mass percent of hydrogen and oxygen in water, you divide the total mass of an element in one mole of the compound by the molar mass of the compound and then multiply the result by 100.

You can think of it like a recipe that states what fraction of the total mass each ingredient contributes. In water's case, the hydrogen atoms contribute approximately 11.19%, while the oxygen atom contributes approximately 88.81%. This composition helps chemists understand the makeup of substances and is crucial for tasks like creating mixtures or analyzing samples.