Question

Rank samples \(A-D\) from least number of atoms to greatest number of atoms. A: 1.0 \(\mathrm{mol}\) of \(\mathrm{H}_{2} ; \mathrm{B} : 0.75 \mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O} ; \mathrm{C} : 1.5 \mathrm{mol}\) of \(\mathrm{NaCl} ; \mathrm{D} : 0.50 \mathrm{mol}\) of \(\mathrm{Ag}_{2} \mathrm{S}\)

Short answer

The ranked order of samples from least number of atoms to greatest number of atoms is D (1.5 \(\times 10^{23}\) atoms), A (2.0 \(\times 10^{23}\) atoms), B (2.25 \(\times 10^{23}\) atoms), and C (3.0 \(\times 10^{23}\) atoms).

Step-by-step solution

Find the number of atoms in 1 mole of each substance

Recall that 1 mole of any substance contains Avogadro's number of particles (atoms, molecules, etc.), which is approximately \(6.022 \times 10^{23}\) particles. For the given substances, 1 mole of each substance contains the following number of atoms: - \(\text{H}_2\): 2 atoms of hydrogen (H) - \(\text{H}_2 \text{O}\): 2 atoms of hydrogen (H) + 1 atom of oxygen (O) = 3 atoms in total - \(\text{NaCl}\): 1 atom of sodium (Na) + 1 atom of chlorine (Cl) = 2 atoms in total - \(\text{Ag}_2 \text{S}\): 2 atoms of silver (Ag) + 1 atom of sulfur (S) = 3 atoms in total

Calculate the total number of atoms for each sample

Now we'll multiply the number of atoms in 1 mole by the number of moles given for each sample: - A: \(1.0 \, \text{mol} \, \text{H}_{2}\) \(\times\) 2 atoms = 2.0 \(\times 10^{23}\) atoms - B: \(0.75 \, \text{mol} \, \text{H}_{2} \text{O}\) \(\times\) 3 atoms = 2.25 \(\times 10^{23}\) atoms - C: \(1.5 \, \text{mol} \, \text{NaCl}\) \(\times\) 2 atoms = 3.0 \(\times 10^{23}\) atoms - D: \(0.50 \, \text{mol} \, \text{Ag}_{2} \text{S}\) \(\times\) 3 atoms = 1.5 \(\times 10^{23}\) atoms

Rank the samples from least to greatest number of atoms

Now that we have the total number of atoms for each sample, we can rank them as follows: 1. Sample D with 1.5 \(\times 10^{23}\) atoms 2. Sample A with 2.0 \(\times 10^{23}\) atoms 3. Sample B with 2.25 \(\times 10^{23}\) atoms 4. Sample C with 3.0 \(\times 10^{23}\) atoms So, the ranked order of samples is D, A, B, and C from the least number of atoms to the greatest number of atoms.

Key concepts

Avogadro's Number

Avogadro's number is one of the cornerstones of chemistry. It provides the bridge between the microscopic world of atoms and molecules and the macroscopic world we experience every day. Scientifically, Avogadro's number is defined as the number of carbon-12 atoms in exactly 12 grams of carbon-12 isotope, and it is approximately \( 6.022 \times 10^{23} \). This number is crucial because it allows chemists to count particles by weighing them. When dealing with chemical reactions and compounds, substances are measured in moles, akin to how we count eggs by the dozen.
Understanding Avogadro's number is essential for determining how many atoms are in a given sample if you know the number of moles. For instance, if you have 1 mole of a substance, you have \( 6.022 \times 10^{23} \) molecules or atoms of it. This counting method is incredibly useful in complex chemical reactions where precise amounts of elements are crucial.
When applied in a practical example, such as ranking how many atoms are in different substances, Avogadro's number allows us to make these calculations straightforwardly, multiplying the number of moles of the substance by the number of atoms in one molecule of that substance.

Stoichiometry

Stoichiometry is like the recipe book of chemistry. It helps us manage the proportions of reactants and products in chemical reactions, ensuring that the equations are balanced based on the conservation of mass. Stoichiometry uses the concept of the mole to quantify the amounts of each substance involved in a reaction.
To apply stoichiometry, one must use the balanced chemical equation to find the relationship between the amounts of reactants and products. For example, in the exercise provided, stoichiometry allows us to determine the total number of atoms in a sample by using the number of moles given in the query.
The process involves several steps:

• Firstly, you determine the amount of reactants, measured in moles.
• Secondly, you use stoichiometry to calculate how many entities (like atoms) these moles represent using Avogadro's number.
• Finally, these quantities help to deduce relationships and transformations during chemical reactions or when comparing sample amounts as shown in the ranking task.

Stoichiometry is invaluable for chemists to ensure reactions proceed correctly and predictably, making it a central concept in both theoretical and practical chemistry.

Atomic Structure

Understanding atomic structure is fundamental to comprehending how substances interact in chemical processes. Atoms consist of three basic components: protons, neutrons, and electrons. The way these particles arrange themselves determines the identity and properties of each element.

Basic Components of Atoms

- **Protons**: Positively charged particles found in the nucleus.- **Neutrons**: Neutral particles that also reside in the nucleus.- **Electrons**: Negatively charged particles that orbit the nucleus in electron clouds.
The number of protons in an element's nucleus defines the atomic number and thus, the identity of the element (for example, carbon always has 6 protons). Electrons play a crucial role in chemical bonding and reactions, enabling the formation of molecules like \( H_2 \) and \( H_2O \).
When examining molecules or compounds, considering their atomic structure is essential for understanding how many atoms are involved. As seen in the problem, knowing the structure of a molecule (like \( NaCl \) containing one sodium and one chlorine atom) allows us to calculate the total number of atoms from a given amount of the substance.