Problem 152 - Chemistry An Atoms First Approach

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.

Step-by-Step Solution

Answer

The moles of each compound are as follows: \(1.18 \, \text{moles of PH}_3\), \(6.61 \, \text{moles of H}_2\text{O}\), \(2.96 \, \text{moles of H}_2\text{S}\), and \(13.23 \, \text{moles of HF}\). Multiplying the moles by the number of hydrogen atoms in each compound, we find that there are \(3.54 \times 10^{24}\) hydrogen atoms in PH3, \(7.95 \times 10^{24}\) in H2O, \(5.93 \times 10^{24}\) in H2S, and \(7.97 \times 10^{24}\) in HF. Thus, the ranking from least to greatest number of hydrogen atoms is: PH3, H2S, H2O, and HF.

Step 1: Compute the moles of each compound

For each compound, calculate the number of moles using the formula: moles = mass / molar mass For each compound: - compute the molar mass (mass of one mole). - calculate the number of moles.

Step 2: Determine the number of hydrogen atoms in each compound

For each compound, determine the number of hydrogen atoms it contains based on its chemical formula.

Step 3: Calculate the total number of hydrogen atoms in the samples of each compound

Multiply the number of moles of each compound by the number of hydrogen atoms it contains.

Step 4: Rank the compounds based on the total number of hydrogen atoms

Now that we have the total number of hydrogen atoms in the samples of each compound, rank them from the least to the greatest number of hydrogen atoms.

Key Concepts

Counting Hydrogen Atoms in Compounds

When trying to figure out how many hydrogen atoms are in a sample, we need to look closely at the chemical formula of each compound.
This formula tells us how many of each type of atom are present in a single molecule of the compound.
For example, let's take water \( \ ext{H}_2\text{O} \).
The subscript \( 2 \) next to hydrogen indicates that each water molecule contains two hydrogen atoms.
Hydrogen sulfide \( \ ext{H}_2\text{S} \) and phosphine \( \ ext{PH}_3 \) also have subscripts indicating the number of hydrogen atoms per molecule.
Meanwhile, hydrogen fluoride (HF) has no subscript for hydrogen, meaning there is only one hydrogen atom in each molecule.
By counting these hydrogen atoms, we can determine the starting point for our calculations.
However, to find out the total hydrogen atoms in a particular mass of a compound, we need to consider not only how many hydrogen atoms are in one molecule but also how many molecules are in the sample.

Understanding Chemical Formula Analysis

A chemical formula is like a simple map that shows which atoms are in a compound and how many of each kind there are.
This is crucial for understanding how to calculate various properties such as molar mass or the number of moles.
In the chemical formula \( \text{PH}_3 \), each molecule contains one phosphorus atom and three hydrogen atoms.
For water \( \text{H}_2\text{O} \), each molecule has two hydrogen atoms and one oxygen atom.
In hydrogen sulfide \( \text{H}_2\text{S} \), you have two hydrogen atoms and one sulfur atom per molecule.
Lastly, hydrogen fluoride (HF) has one hydrogen atom and one fluorine atom per molecule.
By breaking down these formulas, we can better understand the composition of each compound.
This allows us to accurately calculate the molar mass, which is the mass of one mole of a substance.

The Mole Concept in Chemistry

The mole is a basic unit in chemistry that tells us how many molecules or atoms are present in a sample.
It is a huge number, specifically Avogadro's number, which is about 6.022 \( \times 10^{23} \).
Using the mole concept, we can turn the mass of a sample into a count of molecules, giving us a better understanding of the scale we are dealing with.For any given compound, the number of moles is calculated as the mass of the sample divided by the molar mass.
The molar mass, in turn, is computed from the sum of the atomic masses of all the atoms in the compound's formula.
Once we know the number of moles, we use it to find the exact number of molecules and in this situation, the total number of hydrogen atoms.
This is done by multiplying the number of moles by Avogadro's number and then by the number of hydrogen atoms in one molecule of the compound.
By using the mole concept, we can tackle complex calculations with just simple multiplication and division.