Question

Complete the table. \(\begin{array}{llll}\text { Compound } & \text { Mass } & \text { Moles } & \begin{array}{l}\text { Number of } \\ \text { Molecules }\end{array} \\\ \mathrm{H}_{2} \mathrm{O} & 112 \mathrm{lg} & \- & \- \\ \mathrm{N}_{2} \mathrm{O} & 6.33 \mathrm{~g} & \- & \- \\ \mathrm{SO}_{2} & \- & 2.44 & \- \\\ \mathrm{CH}_{2} \mathrm{Cl}_{2} & \- & 0.0643 & -\end{array}\)

Short answer

Moles of H2O: 6.22; Moles of N2O: 0.144; Mass of SO2: 156.32 g; Mass of CH2Cl2: 6.48 g. Number of molecules for each can be calculated using their respective moles times Avogadro's number.

Step-by-step solution

Calculate Moles of H2O

Use the molar mass of H2O to convert the given mass to moles. The molar mass of H2O (water) is approximately 18.015 g/mol. Moles of H2O = mass (g) / molar mass (g/mol) = 112 g / 18.015 g/mol.

Calculate Number of Molecules of H2O

Use Avogadro's number to convert moles to molecules. Avogadro's number is 6.022 x 10^23 molecules/mol. Number of molecules = moles x Avogadro's number.

Calculate Moles of N2O

Use the molar mass of N2O to convert the given mass to moles. The molar mass of N2O is approximately 44.013 g/mol. Moles of N2O = mass (g) / molar mass (g/mol) = 6.33 g / 44.013 g/mol.

Calculate Number of Molecules of N2O

Use the same method from Step 2. Number of molecules = moles x Avogadro's number.

Calculate Mass of SO2

First, find the molar mass of SO2. The molar mass of SO2 is approximately 64.066 g/mol. Mass of SO2 = moles x molar mass = 2.44 mol x 64.066 g/mol.

Calculate Number of Molecules of SO2

Use the moles of SO2 and Avogadro's number as in Steps 2 and 4. Number of molecules = moles x Avogadro's number.

Calculate Mass of CH2Cl2

Find the molar mass of CH2Cl2: C (12.011 g/mol) + 2H (1.008 g/mol each) + 2Cl (35.453 g/mol each), and then multiply the molar mass by the moles. Mass = moles x molar mass.

Calculate Number of Molecules of CH2Cl2

Again, use the moles of CH2Cl2 and Avogadro's number as in the previous steps. Number of molecules = moles x Avogadro's number.

Key concepts

Understanding Molar Mass

Molar mass is a vital concept in chemistry, defined as the mass of one mole of a substance. It acts as a bridge between the microscopic world of molecules and the macroscopic world we can measure. An important note is that the molar mass has units of grams per mole (g/mol) and it's numerically equivalent to the atomic or molecular mass when expressed in atomic mass units (u or amu).

For example, water (H₂O) has a molar mass of approximately 18.015 g/mol which is calculated by adding the mass of two hydrogen atoms (1.008 g/mol each) to the mass of one oxygen atom (15.999 g/mol). Simplifying this concept and using rounded atomic masses can greatly aid in understanding, especially when quickly estimating molar masses for calculations.

Exploring Avogadro's Number

Avogadro's number, named after the scientist Amedeo Avogadro, is another cornerstone of chemistry, representing the number of particles in one mole of a substance. This constant is approximately 6.022 x 10²³ particles/mol. It's essential for translating between the amount of moles and the actual number of atoms or molecules.

Understanding Avogadro's number is like knowing that a dozen refers to twelve items; it's a specific quantity that allows chemists to work with usable numbers when dealing with the incredibly large number of atoms and molecules in even a small sample of material.

Converting Mass to Moles

To convert mass to moles, one must utilize the molar mass as a conversion factor. The process involves dividing the mass of a substance (in grams) by its molar mass (in grams per mole). The formula looks like this: Moles = Mass / Molar Mass.

This simple ratio allows us to move from the tangible mass of a substance to the abstract number of moles, a key step in countless chemical calculations. Keep in mind, precise measurements are important, so always use the exact molar mass and mass values when performing these conversions in practice.

Calculating Number of Molecules

Once we've achieved moles from the previous conversion, we can calculate the number of molecules by multiplying the moles by Avogadro's number. The formula is: Number of molecules = Moles x Avogadro's number.

This step finalizes the concept of moving from a weighed substance to understanding exactly how many individual molecules we're dealing with. It is a powerful tool used in stoichiometry to predict the outcomes of chemical reactions, such as how much product can be expected from a certain amount of reactants.