Question

Given that the molar mass of carbon tetrachloride, \(\mathrm{CCl}_{4},\) is \(153.8 \mathrm{g},\) calculate the mass in grams of 1 molecule of \(\mathrm{CCl}_{4}\).

Short answer

The mass in grams of one molecule of carbon tetrachloride (CCl4) is \(2.56 \times 10^{-22}\: \mathrm{g}\).

Step-by-step solution

Write down the given information

We have the following information given in the exercise: - Molar mass of CCl4: 153.8 g/mol - Avogadro's number: \(6.022 \times 10^{23}\) molecules/mol

Set up the conversion factor

We are trying to find the mass in grams of one molecule of CCl4. We can set up the conversion factor as follows: $$ \frac{153.8 \mathrm{g}}{1 \mathrm{mol}} \times \frac{1 \mathrm{mol}}{6.022 \times 10^{23} \mathrm{molecules}} $$ The units of moles cancel out, leaving us with the conversion factor in terms of grams per molecule.

Calculate the mass of one molecule of CCl4

Multiply the conversion factor to find the mass in grams of one molecule of CCl4: $$ \frac{153.8 \mathrm{g}}{1 \mathrm{mol}} \times \frac{1 \mathrm{mol}}{6.022 \times 10^{23} \mathrm{molecules}} = \frac{153.8 \mathrm{g}}{6.022 \times 10^{23} \mathrm{molecules}} $$ Now, divide 153.8 by \(6.022 \times 10^{23}\): $$ \frac{153.8 \mathrm{g}}{6.022 \times 10^{23} \mathrm{molecules}} = 2.56 \times 10^{-22} \mathrm{g} $$ So, the mass in grams of one molecule of carbon tetrachloride (CCl4) is \(2.56 \times 10^{-22}\: \mathrm{g}\).

Key concepts

Avogadro's Number

Avogadro's Number is a cornerstone concept in chemistry, named after the scientist Amedeo Avogadro. It represents the number of atoms, ions, or molecules contained in one mole, which is a standard unit in chemistry for measuring large quantities of very small particles. Avogadro's number is approximately \(6.022 \times 10^{23}\) units per mole. This huge number helps bridge the microscopic scale of atoms and molecules with the macroscopic amounts we can actually measure in a laboratory.
Understanding Avogadro's number is essential when you deal with converting between moles and actual numbers of molecules. For instance, if you need to determine how many individual molecules are present in a given amount of substance in moles, you simply multiply by Avogadro's number. Similarly, if you are given the number of particles, you can divide by Avogadro's number to convert them into moles.
It's important to be comfortable using this number because it frequently appears in chemical calculations, particularly when relating molar mass to molecular mass. It's the key to transforming the abstract concept of a mole into measurable data.

Conversion Factor

A conversion factor is critical in scientific calculations. It's a tool used to convert quantities from one unit of measurement to another. The magic of conversion factors is how they allow us to carry out conversions without altering the value of what we're measuring.
In the case of carbon tetrachloride's molar mass calculation, we used a conversion factor to transform the units from grams per mole to grams per molecule. This was achieved using the conversion factor: \[\frac{153.8 \, \text{g}}{1 \, \text{mol}} \times \frac{1 \, \text{mol}}{6.022 \times 10^{23} \, \text{molecules}}\]
By carefully setting up this conversion factor, we allowed the mole units to cancel out, resulting in a direct conversion to grams per molecule. It's all about ensuring units are correctly aligned for accurate conversion.
Using conversion factors correctly requires understanding the relationship between the units. Once you master this skill, solving chemistry problems becomes much easier and helps avoid errors.

Carbon Tetrachloride

Carbon tetrachloride, known by the formula \(\mathrm{CCl}_{4}\), is a fascinating compound used in this exercise. It is a clear, heavy, and toxic liquid with a distinct sweet smell. Historically, carbon tetrachloride was used as a refrigerant and cleaning agent. However, due to its environmental effects and potential health hazards, its use is now limited.
The molar mass of carbon tetrachloride is 153.8 grams per mole. This number is key when you want to calculate the mass of single molecules, as demonstrated earlier. Knowing the molar mass allows you to find the relationship between a sample in grams and its corresponding amount in moles, guiding us to use the conversion factor appropriately.
Additionally, understanding substances like carbon tetrachloride from a molecular level enhances your grasp of chemical reactions and compounds' properties. Being aware of the characteristics of such compounds can also be critical when discussing environmental concerns or occupational safety.