Question

Calculate the percentage composition by mass for each element in the following: (a) \(\mathrm{NH}_{4} \mathrm{H}_{2} \mathrm{PO}_{4}\) (c) sodium dihydrogen phosphate (b) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}\) (d) calcium sulfate dihydrate

Short answer

To find the percentage composition for each compound, first calculate the molar mass of each, then divide the mass of each element present in one mole of the compound by the compound's molar mass and multiply by 100%.

Step-by-step solution

Finding Molar Mass of (a) \(\mathrm{NH}_{4}\mathrm{H}_{2}\mathrm{PO}_{4}\)

To calculate the percentage composition by mass, first calculate the molar mass of \(\mathrm{NH}_{4}\mathrm{H}_{2}\mathrm{PO}_{4}\) by adding the atomic masses of all the atoms present in the molecule: 1 N (14.01 u), 4 H (4 \(\times\) 1.01 u), 2 additional H (2 \(\times\) 1.01 u), 1 P (30.97 u), and 4 O (4 \(\times\) 16.00 u).

Calculating Percentages for (a)

Calculate the percentage composition of each element by dividing the total mass of each element in one formula unit by the molar mass of \(\mathrm{NH}_{4}\mathrm{H}_{2}\mathrm{PO}_{4}\) and then multiply by 100%. Do this separately for N, H, P, and O.

Finding Molar Mass of (c) Sodium Dihydrogen Phosphate

Calculate the molar mass of sodium dihydrogen phosphate by adding the atomic masses of all atoms present: 1 Na (22.99 u), 1 P (30.97 u), 2 H (2 \(\times\) 1.01 u), and 4 O (4 \(\times\) 16.00 u).

Calculating Percentages for (c)

Calculate the percentage composition of each element by dividing the total mass of each element in one formula unit by the molar mass of sodium dihydrogen phosphate and then multiply by 100%. Do this separately for Na, P, H, and O.

Finding Molar Mass of (b) \(\left(\mathrm{CH}_{3}\right)_{2}\mathrm{CO}\)

Calculate the molar mass of \(\left(\mathrm{CH}_{3}\right)_{2}\mathrm{CO}\) by adding the atomic masses of all atoms present: 3 C (3 \(\times\) 12.01 u), 6 H (6 \(\times\) 1.01 u), and 1 O (16.00 u).

Calculating Percentages for (b)

Calculate the percentage composition of each element by dividing the total mass of each element in one formula unit by the molar mass of \(\left(\mathrm{CH}_{3}\right)_{2}\mathrm{CO}\) and then multiply by 100%. Do this separately for C, H, and O.

Finding Molar Mass of (d) Calcium Sulfate Dihydrate

Calculate the molar mass of calcium sulfate dihydrate by adding the atomic masses of all atoms present: 1 Ca (40.08 u), 1 S (32.07 u), 4 O (4 \(\times\) 16.00 u), and 4 H (4 \(\times\) 1.01 u) from the 2 water (\(\mathrm{H}_{2}\mathrm{O}\)) molecules.

Calculating Percentages for (d)

Calculate the percentage composition of each element by dividing the total mass of each element in one formula unit by the molar mass of calcium sulfate dihydrate and then multiply by 100%. Do this separately for Ca, S, O, and H.

Key concepts

Molar Mass Calculation

Understanding molar mass is fundamental in chemistry, especially when determining the percentage composition of a substance. Simply put, molar mass is the weight of one mole (6.022 \( \times \) 10\(^{23}\) particles) of a substance, usually expressed in grams per mole (g/mol). The molar mass of a compound is calculated by summing the atomic masses of each element within the molecule, which can be found on the periodic table.

For instance, in the exercise above, the molar mass of ammonia phosphate \( \mathrm{NH}_{4}\mathrm{H}_{2}\mathrm{PO}_{4} \) was found by adding the atomic masses of nitrogen, hydrogen, phosphorus, and oxygen accordingly. This step is critical because the molar mass serves as a conversion factor that takes us from the submicroscopic scale of atoms and molecules to the macroscopic scale that we can measure in the lab.

Elemental Composition

Moving on from molar mass, let's focus on elemental composition. This term refers to the proportional weight of each element within a compound. Knowing the elemental composition is essential because it informs us about the relative amount of each element in a given substance. This is particularly useful in chemical analysis and synthesis.

Take the sodium dihydrogen phosphate example. By breaking down the compound into its constituent elements - sodium, phosphorus, hydrogen, and oxygen - and calculating the mass contributed by each, we have a clearer picture of the substance's makeup. The exercise demonstrates how to determine the percentage of each element in the compound, highlighting how even complex molecules can be understood in terms of their simpler components.

Stoichiometry

Lastly, stoichiometry is the aspect of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is grounded in the law of conservation of mass, where the total mass of the reactants equals the total mass of the products. Stoichiometry uses the molar mass concept and elemental composition to compute the amounts of reactants needed or products formed.

In the context of the exercises provided, stoichiometry might come into play when using the calculated percentage compositions to predict how much of each element would be present in a certain amount of the compound, or to figure out how much of the compound is needed to obtain a certain amount of a particular element. It's essential for accurately scaling reactions and for operational tasks such as cost estimation and quality control in chemical manufacturing.