Question

125 grams of disulfur decafluoride contain (a) how many moles? (d) how many atoms of sulfur? (b) how many molecules? (e) how many atoms of fluorine? (c) how many total atoms?

Short answer

0.4919 moles, 5.92 \times 10^{23} atoms of sulfur, 2.96 \times 10^{23} molecules, 2.96 \times 10^{24} atoms of fluorine, 3.552 \times 10^{24} total atoms

Step-by-step solution

- Calculate moles of disulfur decafluoride (S₂F₁₀)

First, determine the molar mass of S₂F₁₀. Sulfur has an atomic mass of 32.06 g/mol and fluorine has an atomic mass of 19.00 g/mol.Calculate the molar mass as follows:\[ M_{\text{S₂F₁₀}} = 2 \times 32.06 \text{ g/mol} + 10 \times 19.00 \text{ g/mol} = 64.12 \text{ g/mol} + 190.00 \text{ g/mol} = 254.12 \text{ g/mol} \]Now, use the molar mass to calculate the number of moles:\[ \text{moles of S₂F₁₀} = \frac{125 \text{ g}}{254.12 \text{ g/mol}} \ = 0.4919 \text{ moles} \]

- Calculate the number of molecules

Use Avogadro's number (\(6.022 \times 10^{23}\)) to find the number of molecules from the number of moles calculated in Step 1.\[ \text{molecules of S₂F₁₀} = 0.4919 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \ = 2.96 \times 10^{23} \text{ molecules} \]

- Calculate the number of sulfur atoms

Since each molecule of S₂F₁₀ contains 2 sulfur (S) atoms, multiply the number of molecules by 2.\[ \text{atoms of S} = 2.96 \times 10^{23} \text{ molecules} \times 2 \ = 5.92 \times 10^{23} \text{ atoms of S} \]

- Calculate the number of fluorine atoms

Each molecule of S₂F₁₀ contains 10 fluorine (F) atoms, so multiply the number of molecules by 10.\[ \text{atoms of F} = 2.96 \times 10^{23} \text{ molecules} \times 10 \ = 2.96 \times 10^{24} \text{ atoms of F} \]

- Calculate the total number of atoms

Add the total number of sulfur atoms and fluorine atoms to get the total number of atoms.\[ \text{total atoms} = 5.92 \times 10^{23} \text{ atoms of S} + 2.96 \times 10^{24} \text{ atoms of F} \ = 3.552 \times 10^{24} \text{ atoms} \]

Key concepts

Molar Mass Calculation

The term 'molar mass' refers to the mass of a given substance (chemical element or compound) divided by the amount of substance. The molar mass is expressed in units of grams per mole (g/mol). It's crucial for converting between grams and moles. For example, the molar mass of disulfur decafluoride (S₂F₁₀) is calculated by adding the atomic masses of all the atoms in the molecule:
\[ M_{S₂F₁₀} = 2 \times 32.06 \text{ g/mol} + 10 \times 19.00 \text{ g/mol} = 254.12 \text{ g/mol} \] The value 254.12 g/mol represents the weight of one mole of S₂F₁₀ molecules. This molar mass helps convert the given mass (125 grams in this case) into moles, which is vital for further calculations in chemistry.

Avogadro's Number

Avogadro's number (6.022 \times 10^{23}) is a fundamental constant in chemistry that allows us to count particles like atoms and molecules in a given amount of substance. Specifically, it indicates the number of particles in one mole of substance. To find the number of molecules in our 125 grams of S₂F₁₀, we use the moles derived previously and multiply by Avogadro's number:
\[ \text{molecules of S₂F₁₀} = 0.4919 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} = 2.96 \times 10^{23} \] This result tells us that there are approximately 2.96 \times 10^{23} molecules in 125 grams of disulfur decafluoride.

Stoichiometry

Stoichiometry is the part of chemistry that studies the quantities of reactants and products in a chemical reaction. Here, it's used to determine the relationship between the quantities of different molecules and atoms in S₂F₁₀. By knowing the number of S₂F₁₀ molecules, we can figure out the number of constituent atoms. Each S₂F₁₀ molecule consists of 2 sulfur (S) atoms and 10 fluorine (F) atoms. For sulfur atoms:
\[ \text{atoms of S} = 2.96 \times 10^{23} \text{ molecules} \times 2 = 5.92 \times 10^{23} \text{ atoms of S} \] Similarly, for fluorine atoms:
\[ \text{atoms of F} = 2.96 \times 10^{23} \text{ molecules} \times 10 = 2.96 \times 10^{24} \text{ atoms of F} \]

Atoms Counting

Counting atoms in a compound involves knowing its chemical formula and applying stoichiometric principles. First, determine the number of molecules. Then, use the chemical formula to ascertain how many atoms of each element present per molecule. For disulfur decafluoride (S₂F₁₀), the total atom count for 125 grams is calculated by adding the number of sulfur and fluorine atoms:
\[ \text{total atoms} = 5.92 \times 10^{23} \text{ atoms of S} + 2.96 \times 10^{24} \text{ atoms of F} = 3.552 \times 10^{24} \text{ atoms} \] This shows the sum of all individual atoms within the given mass of the substance.

Chemical Formula

A chemical formula represents the types and numbers of atoms in a molecule of a compound. S₂F₁₀, the formula for disulfur decafluoride, tells us that each molecule contains 2 sulfur (S) atoms and 10 fluorine (F) atoms. Understanding chemical formulas is essential for calculating molar masses and stoichiometric ratios. It's a way to visualize the composition of a substance on an atomic level, which is fundamental for performing accurate chemical calculations such as the ones shown.
For example, knowing that the formula is S₂F₁₀ allowed us to break down our molecule to calculate the total number of each type of atom.