Question

Carbon tetrachloride contains one carbon and four chlorine atoms. For this compound \(11.818 \mathrm{~g}\) of chlorine combine with \(1.000 \mathrm{~g}\) of \(\mathrm{C}-12 .\) Using this information, calculate the atomic mass of chlorine.

Short answer

The atomic mass of chlorine is \frac{11.818 \text{ g}}{4} = 2.9545 \text{ g} per atom of chlorine, or approximately 35.486 amu when rounded to three significant figures.

Step-by-step solution

Establish Proportions

Determine the ratio in which chlorine combines with carbon. For carbon tetrachloride, 1.000 gram of carbon combines with 11.818 grams of chlorine.

Calculate the Ratio of Atomic Masses

If we know that one atom of carbon (C-12 isotope) has an atomic mass of 12 amu (atomic mass units), we can determine the atomic mass of chlorine relative to carbon by dividing the mass of chlorine by the mass of carbon, which is 11.818 grams of chlorine per 1 gram of carbon.

Calculate the Atomic Mass of Chlorine

Since there are four chlorine atoms for every one carbon atom in carbon tetrachloride, divide the ratio of the atomic masses (11.818) by four to find the atomic mass of a single chlorine atom.

Key concepts

Atomic Mass Units

When we talk about atomic mass units (amu), we're referring to a standard unit that's used to express the mass of atoms and molecules. This unit is defined based on the carbon-12 isotope, wherein one atomic mass unit is equal to one twelfth the mass of a carbon-12 atom.

Understanding atomic mass units is crucial for learning about the science of atoms because it allows us to compare the mass of different elements and isotopes in a consistent way. For instance, as seen in the carbon tetrachloride example, the carbon-12 isotope has an atomic mass of precisely 12 amu, providing a baseline for the calculation of other elements like chlorine.

Molar Mass Calculation

Moving from individual atoms to larger quantities, the molar mass calculation is a bridge connecting the microscopic world of atoms to the measurable quantities in the lab. The molar mass of an element is the mass of one mole (approximately 6.022 x 10^23 particles) of that element and is expressed in grams per mole (g/mol).

To calculate the molar mass, you need to multiply the atomic mass by the molar mass constant, which is 1 g/mol. For instance, the molar mass of carbon is 12.01 g/mol because its atomic mass unit is approximately 12. When dealing with a compound, each element's atomic mass is multiplied by the number of atoms of that element present and then all of these are summed together to find the molar mass of the compound.

Stoichiometry

Stoichiometry is an area of chemistry centered around the quantitative relationships between the substances involved in chemical reactions. It's like the mathematical side of chemistry, allowing you to predict the amounts of products produced or reactants required in a chemical reaction.

In the context of the carbon tetrachloride example, stoichiometry informs us that one carbon atom reacts with four chlorine atoms, establishing a 1:4 ratio. This reaction ratio helps us understand how much chlorine, by mass, will react with a set mass of carbon, thus enabling the calculation of the atomic mass of chlorine once we've established the ratio between the mass of chlorine and carbon utilized.

Chemical Compound Composition

Chemical compound composition is all about the types and ratios of atoms that make up a chemical compound. It's the recipe for a substance at the atomic level. A molecule of carbon tetrachloride, as shown in the exercise, is comprised of one carbon atom and four chlorine atoms.

The knowledge of a compound's composition is necessary to understand its properties and behavior in various chemical processes. For instance, understanding that carbon tetrachloride is made from carbon and chlorine atoms in a certain proportion guides us in calculating the atomic mass of chlorine when we know its mass ratio to carbon in the compound.