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 of one molecule of carbon tetrachloride (CCl4) is approximately \( 2.56 \times 10^{-22} \mathrm{~g} \).

Step-by-step solution

Find the mass of one mole of CCl4

The molar mass of CCl4 is given as 153.8 g/mol. This means that one mole of CCl4 has a mass of 153.8 grams.

Using Avogadro's number to find the number of molecules in one mole

Avogadro's number is the number of entities (atoms, molecules, etc.) in one mole of a substance. In this case, we want to find the number of CCl4 molecules in one mole. Avogadro's number is equal to 6.022 x 10^23 entities per mole. Therefore, there are 6.022 x 10^23 molecules of CCl4 in one mole.

Calculate the mass of one molecule of CCl4

In order to find the mass of one CCl4 molecule, we can use the mass of one mole of CCl4 and the number of molecules in one mole. We can set up the equation as follows: Mass of one molecule of CCl4 = (Mass of one mole of CCl4) / (Number of CCl4 molecules in one mole) Let's plug in the given values: Mass of one molecule of CCl4 = \( \frac{153.8 \mathrm{~g}}{6.022 \times 10^{23} \mathrm{~molecules}} \)

Calculate the mass of one molecule of CCl4

Now, we can simply divide the mass of one mole of CCl4 by the number of molecules in one mole to get the mass of one molecule of CCl4: Mass of one molecule of CCl4 = \( \frac{153.8 \mathrm{~g}}{6.022 \times 10^{23} \mathrm{~molecules}} \) ≈ \( 2.5558 \times 10^{-22} \mathrm{~g} \) Thus, the mass of one molecule of carbon tetrachloride (CCl4) is approximately \( 2.56 \times 10^{-22} \mathrm{~g} \).

Key concepts

What is Carbon Tetrachloride?

Carbon tetrachloride, with the chemical formula \( \mathrm{CCl}_{4} \), is a compound consisting of one carbon atom bonded to four chlorine atoms. This colorless and dense liquid is often used as a solvent in organic chemistry and was once commonly used as a cleaning agent. However, due to its potential health hazards, its usage has decreased over time.
Carbon tetrachloride plays an important role in various calculations in chemistry due to its well-defined molar mass, which aids in converting between moles and grams. This conversion is essential for understanding chemical reactions and determining the quantities of each substance involved. Understanding carbon tetrachloride's composition helps in calculating its molecular mass, which further assists by contributing to larger concepts such as stoichiometry and material balance in chemical engineering.

Understanding Avogadro's Number

Avogadro's number, which is \( 6.022 \times 10^{23} \) entities per mole, acts as a bridge between the atomic scale and the scale we use in everyday measurements. It signifies the number of atoms, molecules, ions, or other basic units present in one mole of a substance. This fixed constant allows chemists to easily convert between the mass of a substance and the number of molecules or atoms it contains.
In practical terms, Avogadro's number helps us to relate measurable quantities, like grams, to the nanoscale world of molecular entities. For example, knowing that one mole of carbon tetrachloride corresponds to \( 6.022 \times 10^{23} \) molecules gives a clear quantitative understanding of how many individual molecules comprise a measurable sample.

• This concept is crucial for quantitative analysis in chemistry,
• it simplifies the complex calculations involved in determining precise molecular interactions, and
• it is foundational in the study of gases through Avogadro's law, which relates the volume of gas to the number of molecules.

How to Calculate Molecular Mass

Molecular mass calculation involves determining the mass of a single molecule of a substance, often expressed in atomic mass units (amu) or grams per mole (g/mol). For a compound like carbon tetrachloride, that means adding up the atomic masses of all the atoms in the molecule.
Here’s a simplified process for calculating molecular mass:

• Add the atomic masses of each element present, considering how many atoms of each element are in the molecule.
• The atomic mass of carbon is approximately 12 amu, and the atomic mass of chlorine is approximately 35.5 amu.
• For \( \mathrm{CCl}_4 \), the calculation would be: \( 12 \mathrm{~amu~(C)} + 4 \times 35.5 \mathrm{~amu~(Cl)} = 153.8 \mathrm{~amu} \).
• This total is the molecular mass of carbon tetrachloride.

Knowing the molecular mass is essential for further calculations, such as converting between the mass of a sample and the number of molecules it contains, which is where Avogadro's number comes into play.
Understanding molecular mass helps in translating lab-scale observations and reactions into meaningful chemical insights, making it a cornerstone of chemistry studies.