Question

Consider samples of phosphine $\left({\mathrm{PH}}_3\right),$ water $\left({\mathrm{H}}_2\mathrm{O}\right),$ hydrogen sulfide $\left({\mathrm{H}}_2\mathrm{S}\right),$ and hydrogen fluoride (HF), each with a mass of 119 $\mathrm{g}.$ Rank the compounds from the least to the greatest number of hydrogen atoms contained in the samples.

Short answer

The samples rank from the least to the greatest number of hydrogen atoms as follows: Hydrogen fluoride (HF) with 5.95 moles of H, hydrogen sulfide (H2S) with 6.98 moles of H, phosphine (PH3) with 10.5 moles of H, and water (H2O) with 13.22 moles of H: HF < H2S < PH3 < H2O.

Step-by-step solution

Calculate the molar mass of each compound

First, we need to find the molar mass of the compounds given: For phosphine (PH3): Molar mass = (1 x P) + (3 x H) = $1\times 30.97+3\times 1.01=34\mathrm{g}/\mathrm{mol}$ For water (H2O): Molar mass = (2 x H) + (1 x O) = $2\times 1.01+1\times 16.00=18\mathrm{g}/\mathrm{mol}$ For hydrogen sulfide (H2S): Molar mass = (2 x H) + (1 x S) = $2\times 1.01+1\times 32.07=34.09\mathrm{g}/\mathrm{mol}$ For hydrogen fluoride (HF): Molar mass = (1 x H) + (1 x F) = $1\times 1.01+1\times 19.00=20.01\mathrm{g}/\mathrm{mol}$

Determine the number of moles of each compound in the samples

Now we need to find the number of moles of each compound in the 119 gram samples. For phosphine (PH3): Moles = $\frac{Mass}{Molarmass}=\frac{119}{34}=3.5\mathrm{moles}$ For water (H2O): Moles = $\frac{119}{18}=6.61\mathrm{moles}$ For hydrogen sulfide (H2S): Moles = $\frac{119}{34.09}=3.49\mathrm{moles}$ For hydrogen fluoride (HF): Moles = $\frac{119}{20.01}=5.95\mathrm{moles}$

Calculate the number of moles of hydrogen atoms for each compound

Now, we need to find the number of moles of hydrogen atoms in each compound. For phosphine (PH3): Moles of hydrogen = $3.5\mathrm{moles}(\mathrm{PH}3)\times 3\mathrm{H}\mathrm{atoms}=10.5\mathrm{moles}\mathrm{of}\mathrm{H}$ For water (H2O): Moles of hydrogen = $6.61\mathrm{moles}(\mathrm{H}2\mathrm{O})\times 2\mathrm{H}\mathrm{atoms}=13.22\mathrm{moles}\mathrm{of}\mathrm{H}$ For hydrogen sulfide (H2S): Moles of hydrogen = $3.49\mathrm{moles}(\mathrm{H}2\mathrm{S})\times 2\mathrm{H}\mathrm{atoms}=6.98\mathrm{moles}\mathrm{of}\mathrm{H}$ For hydrogen fluoride (HF): Moles of hydrogen = $5.95\mathrm{moles}(\mathrm{HF})\times 1\mathrm{H}\mathrm{atom}=5.95\mathrm{moles}\mathrm{of}\mathrm{H}$

Compare and rank the compounds based on the number of moles of hydrogen atoms

Now that we have the number of moles of hydrogen atoms for each compound, we can compare and rank them. From least to greatest number of moles of hydrogen atoms in the samples: 1. Hydrogen fluoride (HF): 5.95 moles of H 2. Hydrogen sulfide (H2S): 6.98 moles of H 3. Phosphine (PH3): 10.5 moles of H 4. Water (H2O): 13.22 moles of H Thus, the samples rank from the least to the greatest number of hydrogen atoms as follows: HF < H2S < PH3 < H2O.

Key concepts

Chemical Compounds

Chemical compounds are formed when two or more elements combine through chemical bonds. These bonds can be covalent, ionic, or metallic. Understanding the composition of chemical compounds is crucial in chemistry as it helps in predicting reactions and understanding material properties.
In the exercise provided, we have four different chemical compounds: phosphine (PH₃), water (H₂O), hydrogen sulfide (H₂S), and hydrogen fluoride (HF). Each of these compounds is made up of hydrogen atoms bonded with other elements: phosphorous in phosphine, oxygen in water, sulfur in hydrogen sulfide, and fluorine in hydrogen fluoride.
Each compound has its specific molecular formula which indicates the number and type of atoms present. For instance, the molecular formula for water, H₂O, tells us that each molecule consists of two hydrogen atoms and one oxygen atom. Similarly, PH₃ consists of one phosphorus atom and three hydrogen atoms. Understanding these formulas is the first step in calculating properties like molar mass, which is necessary for many stoichiometric calculations.

Stoichiometry

Stoichiometry is the area of chemistry that pertains to quantifying the relationships between reactants and products in chemical reactions. In this context, stoichiometry helps in determining how much of each substance is needed or produced.
For the compounds described in the exercise, stoichiometry is applied to find their molar masses—a crucial step to determining the number of moles from a given mass of each compound. Molar mass is essentially the weight of one mole of a chemical compound and can be determined by summing up the atomic masses of its constituent elements, as seen in the step-by-step solution.

• PH₃ has a molar mass of 34 g/mol.
• H₂O has a molar mass of 18 g/mol.
• H₂S has a molar mass of 34.09 g/mol.
• HF has a molar mass of 20.01 g/mol.

After finding the molar mass, stoichiometry is used to compute the number of moles in a 119 g sample of each compound. This involves dividing the mass of the sample by the compound's molar mass. The stepwise breakdown in the original solution illustrates how stoichiometry is indispensable in calculating the quantities involved in chemical reactions.

Mole Concept

The mole concept is a fundamental aspect of stoichiometry and chemistry as a whole. A mole is a unit that measures the quantity of a substance, much like a dozen measures a quantity of twelve items. One mole of any substance contains Avogadro's number of entities, which is approximately 6.022 x 10²³.
In the exercise, the mole concept is used to equate the mass of the compounds to the number of moles. This is done by using the formula: $$\text{Number of moles}=\frac{\text{mass (in g)}}{\text{molar mass (in g/mol)}}$$By applying this formula, the number of moles of each compound in the 119 g samples was determined. Further, understanding the number of moles gives insight into the number of hydrogen atoms present. For example, PH₃, with 3.5 moles, contains 10.5 moles of hydrogen atoms because there are three hydrogen atoms per phosphine molecule.
The mole concept not only aids in determining the amount of a compound but also plays a vital role in comparing different quantities, which is essential for ranking them as required in this problem. Mastery of the mole concept allows chemists to make accurate predictions about the outcomes of reactions.