Question

What is the molecular mass of \(\mathrm{UF}_{6}\) ? What is the molar mass of \(\mathrm{UF}_{6}\) ? (Chapter 10\()\)

Short answer

The molecular mass of \(\mathrm{UF}_{6}\) is 352 amu, and the molar mass is 352 g/mol.

Step-by-step solution

Find the atomic masses of Uranium (U) and Fluorine (F)

To find the molecular mass of \(\mathrm{UF}_{6}\), we first need the atomic masses of the elements involved. - For Uranium (U), the atomic mass is approximately 238 amu (atomic mass units). - For Fluorine (F), the atomic mass is approximately 19 amu.

Calculate the molecular mass of \(\mathrm{UF}_{6}\)

Now that we know the atomic masses of Uranium and Fluorine, we can calculate the molecular mass of \(\mathrm{UF}_{6}\). We do this by multiplying the atomic mass of each element by the number of atoms in the molecule and then adding the products together. $$ \text{Molecular mass of }\mathrm{UF}_{6} = (\text{Atomic mass of U}) + 6 \times (\text{Atomic mass of F}) $$ Let's plug in the atomic masses we found in Step 1: $$ \text{Molecular mass of }\mathrm{UF}_{6} = (238) + 6 \times (19) $$ Now, perform the multiplication and addition: $$ \text{Molecular mass of }\mathrm{UF}_{6} = 238 + 114 = 352\text{ amu} $$ So the molecular mass of \(\mathrm{UF}_{6}\) is 352 amu.

Find the molar mass of \(\mathrm{UF}_{6}\)

The molar mass of a substance is essentially the same as its molecular mass, but it is expressed in grams per mole (g/mol) instead of atomic mass units (amu). In this case, the molar mass of \(\mathrm{UF}_{6}\) is equal to its molecular mass: 352 g/mol. So, the molar mass of \(\mathrm{UF}_{6}\) is 352 g/mol.

Key concepts

Atomic Mass Units

In the world of chemistry, one important building block is understanding atomic mass units (amu). This term refers to a standard unit of mass that quantifies the weight of atoms or molecules. Specifically, one atomic mass unit is defined as one twelfth of the mass of a carbon-12 atom. It's a very tiny unit of measurement since atoms are incredibly small.

When we say, for example, that Uranium (U) has an atomic mass of approximately 238 amu, it means that one atom of Uranium is 238 times heavier than one twelfth of the mass of a carbon-12 atom. This is important for calculating molecular masses, as you can effectively tally up the weight of each atom multiplied by its occurrence in the molecule.

Mole Concept

To understand the mole concept, imagine you have a large collection of anything—pens, for instance. It's cumbersome to count each pen if you want to express a large quantity. Instead, you could use a term like 'dozen' to represent 12 of them. Chemistry has a similar concept but on a much larger scale, called a 'mole'.

A mole represents Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities (atoms, molecules, etc.). This huge number is used because atoms and molecules are exceedingly small. This concept allows chemists to work with manageable numbers when they deal with the massive number of atoms in even the smallest sample.

Molar Mass

The concept of molar mass is connected to both the atomic mass units and the mole concept. It's the mass of one mole of a substance. The numerical value of molar mass in grams per mole (g/mol) is equal to the molecular mass in atomic mass units. This is because the mole is defined such that one mole of carbon-12 atoms has a mass of exactly 12 grams.

Therefore, when we say the molar mass of \(\mathrm{UF}_{6}\) is 352 g/mol, we're stating that if you had Avogadro's number of \(\mathrm{UF}_{6}\) molecules, it would weigh 352 grams. This concept is essential for chemists when they want to measure out amounts of substances for reactions, as it bridges the macroscopic world we can weigh to the atomic scale of substances.