Problem 144 - Introductory Chemistry Atoms First

Question

How many grams of sulfur hexafluoride would you need to have \(5.25 \times 10^{24}\) fluorine atoms?

Step-by-Step Solution

Answer

You would need 212 grams of sulfur hexafluoride to have \(5.25 \times 10^{24}\) fluorine atoms.

Step 1: Find the number of moles of fluorine atoms

To find the number of moles, we can use the formula: moles = atoms / (Avogadro's constant). Avogadro's constant is approximately \(6.022 \times 10^{23}\) atoms/mole. So for \(5.25 \times 10^{24}\) fluorine atoms, we have: moles of fluorine = \(\frac{5.25 \times 10^{24}}{6.022 \times 10^{23}}\) Calculate the number of moles of fluorine: moles of fluorine = \(8.717 \) moles

Step 2: Find the number of moles of sulfur hexafluoride

In sulfur hexafluoride (SF6), the ratio of sulfur to fluorine atoms is 1:6. Therefore, we can find the moles of sulfur hexafluoride by dividing the moles of fluorine by six: moles of sulfur hexafluoride = \(\frac{moles \ of \ fluorine}{6}\) moles of sulfur hexafluoride = \(\frac{8.717}{6}\) Calculate the number of moles of sulfur hexafluoride: moles of sulfur hexafluoride = \(1.453 \) moles

Step 3: Find the mass of sulfur hexafluoride in grams

To find the mass of sulfur hexafluoride in grams, we need to multiply the moles of sulfur hexafluoride by its molar mass. The molar mass of sulfur hexafluoride (SF6) is 32.07 g/mol (sulfur) + 6(18.998 g/mol) (fluorine) = 146.07 g/mol. mass of sulfur hexafluoride = moles of sulfur hexafluoride × molar mass mass of sulfur hexafluoride = \(1.453 \ moles \times 146.07 \ g/mol\) Calculate the mass of sulfur hexafluoride in grams: mass of sulfur hexafluoride = \(212 \ g\) So, you would need 212 grams of sulfur hexafluoride to have \(5.25 \times 10^{24}\) fluorine atoms.

Key Concepts

Avogadro's Constant

When dealing with the microscopic world of atoms and molecules, we use Avogadro's constant to bridge the gap between the very small and the everyday scales we are familiar with. Avogadro's constant, named after the scientist Amedeo Avogadro, is approximately \(6.022 \times 10^{23}\) entities per mole. It tells us how many atoms, ions, or molecules there are in one mole of a substance.

This constant is crucial for converting between the number of particles and the amount in moles. For instance, if a problem asks us how much of a substance is needed to have a certain number of particles, as in our sulfur hexafluoride example, we use Avogadro's constant to find out how many moles those particles amount to.

Molar Mass

Molar mass is another vital concept and is defined as the mass of one mole of a substance. The units for molar mass are grams per mole (g/mol). This value is unique for every substance, based on the atomic masses of the elements that make up the substance, as listed on the periodic table.

In the case of sulfur hexafluoride, we combine the molar masses of sulfur and fluorine to find its molar mass. Knowing the molar mass allows us to convert from moles to grams, which is precisely what we do to solve our problem. By multiplying the number of moles of sulfur hexafluoride by its molar mass, we can find the actual mass in grams required in the exercise.

Mole Concept

The mole concept is a cornerstone of chemistry that provides a way to count particles at the atomic level and relate them to mass which we can measure. One mole corresponds to Avogadro's constant number of particles, whether they're atoms, molecules, ions, or electrons.

Through this concept, we are able to take the vast number of fluorine atoms in our example and convert that number into a more manageable quantity - moles. This mole quantity then serves as a bridge to find out the grams of sulfur hexafluoride needed. It highlights the mole concept as a three-way connection between the number of particles we have, the moles that represent those particles, and the mass that corresponds to those moles.