Instructions: Show all your work, include correct units, and express your final answers to the correct number of significant figures. Assume all gases are at STP (22.4 L/mol).

Mass to Molecules: Calculate the number of molecules present in a 14.5 g sample of carbon dioxide $\left(CO_2\right)$.

Volume to Atoms: How many individual atoms of oxygen are contained in a 5.60 L sample of oxygen gas $\left(O_2\right)$ at STP?

Molecules to Mass: Find the mass, in grams, of $3.01 \times 10^{24}$ formula units of sodium chloride (NaCl).

Question

01-11-2026
Chemistry

Answered

Instructions: Show all your work, include correct units, and express your final answers to the correct number of significant figures. Assume all gases are at STP (22.4 L/mol).

Mass to Molecules: Calculate the number of molecules present in a 14.5 g sample of carbon dioxide $\left(CO_2\right)$.

Volume to Atoms: How many individual atoms of oxygen are contained in a 5.60 L sample of oxygen gas $\left(O_2\right)$ at STP?

Molecules to Mass: Find the mass, in grams, of $3.01 \times 10^{24}$ formula units of sodium chloride (NaCl).

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-01T20:36:50-05:00

For the mass of $\text{CO}_2$, we calculate the molar mass, convert mass to moles, then moles to molecules: $1.98 \times 10^{23} \text{ molecules}$.
For the volume of $\text{O}_2$, we convert volume to moles, moles to molecules, then molecules to individual atoms: $3.01 \times 10^{23} \text{ atoms O}$.
For formula units of $\text{NaCl}$, we convert units to moles, then moles to mass: $\boxed{292 \text{ g}}$.

Explanation

Analysis of Mole Conversion Principles

To solve these multi-step mole conversions, we utilize the relationship between mass, moles, particles, and volume. The primary conversion factors are:

Molar mass ($g/mol$), calculated from atomic masses.
Avogadro's number ($6.022 \times 10^{23} \text{ particles/mol}$).
Molar volume of a gas at STP ($22.4 \text{ L/mol}$).

We must identify the starting unit and the desired unit, then convert via the mole as an intermediate bridge. Significant figures are determined by the starting data provided.

Solving Mass to Molecules: CO2

Starting with $14.5 \text{ g}$ of $\text{CO}_2$, we first find the molar mass:
$\text{C} = 12.011 \text{ g/mol}$, $\text{O} = 15.999 \text{ g/mol}$.
$\text{Molar mass of CO}_2 = 12.011 + 2(15.999) = 44.009 \text{ g/mol}$.
Next, convert mass to moles:
$\text{Moles} = \frac{14.5 \text{ g}}{44.009 \text{ g/mol}} \approx 0.329478 \text{ mol}$.
Finally, convert moles to molecules using Avogadro's number:
$\text{Molecules} = 0.329478 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.9841 \times 10^{23} \text{ molecules}$.
Reporting to 3 significant figures, we get $1.98 \times 10^{23} \text{ molecules}$.

Solving Volume to Atoms: O2

For a $5.60 \text{ L}$ sample of $\text{O}_2$ gas at STP, we first convert volume to moles:
$\text{Moles} = \frac{5.60 \text{ L}}{22.4 \text{ L/mol}} = 0.250 \text{ mol}$.
Next, convert moles to molecules of $\text{O}_2$:
$\text{Molecules of O}_2 = 0.250 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} = 1.5055 \times 10^{23} \text{ molecules}$.
Since each $\text{O}_2$ molecule contains two oxygen atoms, the total number of oxygen atoms is:
$\text{Atoms} = 1.5055 \times 10^{23} \text{ molecules} \times 2 = 3.011 \times 10^{23} \text{ atoms}$.
Rounding to 3 significant figures, the result is $3.01 \times 10^{23} \text{ atoms O}$.

Solving Molecules to Mass: NaCl

Given $3.01 \times 10^{24}$ formula units of $\text{NaCl}$, we first find the molar mass:
$\text{Na} = 22.990 \text{ g/mol}$, $\text{Cl} = 35.453 \text{ g/mol}$.
$\text{Molar mass of NaCl} = 22.990 + 35.453 = 58.443 \text{ g/mol}$.
Convert formula units to moles:
$\text{Moles} = \frac{3.01 \times 10^{24} \text{ units}}{6.022 \times 10^{23} \text{ units/mol}} \approx 4.99834 \text{ mol}$.
Finally, convert moles to mass:
$\text{Mass} = 4.99834 \text{ mol} \times 58.443 \text{ g/mol} \approx 292.09 \text{ g}$.
Reporting to 3 significant figures, the mass is $\boxed{292 \text{ g}}$.

Examples

Mole conversions are essential in real-world chemical manufacturing. For example, a pharmaceutical company producing a medication must calculate exactly how many grams of an active ingredient (like salt) are needed to ensure a specific number of molecules are present in a dose, guaranteeing the safety and efficacy of the treatment. Mastering these conversions ensures that chemical reactions are performed with the exact stoichiometric amounts required for quality control and efficiency.