Question

Sulfur hexafluoride, \(\mathrm{SF}_{6},\) is an extremely dense gas. How does its density compare with the density of air? Use a molar mass for air of \(29.0 \mathrm{~g} / \mathrm{mol}\).

Short answer

The density of SF6 is approximately 5.04 times greater than the density of air.

Step-by-step solution

Determine the Molar Mass of SF6

To calculate the molar mass of sulfur hexafluoride (SF6), we have to sum the atomic masses of sulfur and fluorine. Sulfur has an atomic mass of approximately 32.07 g/mol, and fluorine has an atomic mass of approximately 19.00 g/mol. Since there are six fluorine atoms, the calculation is:\[\text{Molar mass of } \text{SF}_6 = 32.07 \text{ g/mol (S)} + 6 \times 19.00 \text{ g/mol (F)} = 32.07 \text{ g/mol} + 114.00 \text{ g/mol} = 146.07 \text{ g/mol}.\]

Compare Densities Using Molar Masses

The density of a gas is proportional to its molar mass. Thus, we can compare the densities of SF6 and air by comparing their molar masses. The molar mass of air is given as 29.0 g/mol. The ratio of the densities is therefore equal to the ratio of the molar masses:\[\text{Density ratio} = \frac{\text{Molar mass of } \text{SF}_6}{\text{Molar mass of air}} = \frac{146.07 \text{ g/mol}}{29.0 \text{ g/mol}} \approx 5.04\]This indicates that SF6 is approximately 5.04 times denser than air.

Key concepts

Molar Mass Calculation

The molar mass calculation is a fundamental step in understanding properties such as density and reactivity of a compound. To calculate the molar mass of a compound, you sum the atomic masses of all the atoms in a molecule. In the case of sulfur hexafluoride (\(\text{SF}_6\), it consists of one sulfur atom and six fluorine atoms.

• Sulfur (S) has an atomic mass of approximately 32.07 g/mol.
• Fluorine (F) has an atomic mass of approximately 19.00 g/mol.

To find the molar mass, combine these values:
- Calculate the total mass of the fluorine atoms: \(6 \times 19.00 = 114.00\) g/mol.
- Add this to the molar mass of sulfur: \(32.07 + 114.00 = 146.07\) g/mol.
This means that the molar mass of \(\text{SF}_6\) is 146.07 g/mol, a crucial figure for further comparisons.

Sulfur Hexafluoride

Sulfur hexafluoride (\(\text{SF}_6\)) is an unusual gas with several interesting properties. One of its most significant characteristics is its high density, which results from its relatively large molar mass compared to other common gases.

• \(\text{SF}_6\) is composed of sulfur and fluorine, giving it a higher molar mass than many simple molecules.
• This factor contributes to its density—the essence of the exercise.

Furthermore, \(\text{SF}_6\) is known for being inert and non-toxic, often used in the electrical industry for insulation and in other applications for its ability to displace less dense gases.

Density Comparison

Density comparison is a useful method in chemistry to understand how heavy or light a gas is compared to another. The density of a gas directly correlates with its molar mass when conditions like temperature and pressure remain constant.
The concept becomes simple with the formula:
- Density (\(d\)) is proportional to Molar Mass (\(M\)):\[d \propto M\]For sulfur hexafluoride (\(\text{SF}_6\)), its significant molar mass of 146.07 g/mol makes it much denser than air, which has a molar mass of 29.0 g/mol.

• Formula for density ratio: \[\text{Density ratio} = \frac{\text{Molar mass of } \text{SF}_6}{\text{Molar mass of air}}\]
• Plug in the values: \(\frac{146.07}{29.0} \approx 5.04\)

Thus, \(\text{SF}_6\) is approximately 5.04 times denser than air, highlighting its physical heaviness in a simple, mathematical form.