Question

Calculate the number of moles of sulfur atoms present in each of the following samples. a. \(2.01 \mathrm{g}\) of sodium sulfate b. \(2.01 \mathrm{g}\) of sodium sulfite c. \(2.01 \mathrm{g}\) of sodium sulfide d. \(2.01 \mathrm{g}\) of sodium thiosulfate, \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\)

Short answer

The number of moles of sulfur atoms in each sample are: a. \(1.39 \times 10^{-2} \: \mathrm{moles}\) in sodium sulfate b. \(1.59 \times 10^{-2} \: \mathrm{moles}\) in sodium sulfite c. \(2.57 \times 10^{-2} \: \mathrm{moles}\) in sodium sulfide d. \(2.55 \times 10^{-2} \: \mathrm{moles}\) in sodium thiosulfate

Step-by-step solution

Determine the molar mass of the compounds

Using the periodic table or a molar mass calculator, find the molar mass of the four compounds involved: a. Sodium sulfate (Na2SO4) has a molar mass of \(2(22.99) + 32.07 + 4(16)\) = \(144.06 \: \mathrm{g/mol}\). b. Sodium sulfite (Na2SO3) has a molar mass of \(2(22.99) + 32.07 + 3(16)\) = \(126.06 \: \mathrm{g/mol}\). c. Sodium sulfide (Na2S) has a molar mass of \(2(22.99) + 32.07\) = \(78.05 \: \mathrm{g/mol}\). d. Sodium thiosulfate (Na2S2O3) has a molar mass of \(2(22.99) + 2(32.07) + 3(16)\) = \(158.12 \: \mathrm{g/mol}\).

Calculate the moles of compound

To calculate the number of moles of each compound, divide the given mass (2.01 g) by the molar mass of that compound: a. Moles of sodium sulfate = \(\frac{2.01 \: \mathrm{g}}{144.06 \: \mathrm{g/mol}}\) b. Moles of sodium sulfite = \(\frac{2.01 \: \mathrm{g}}{126.06 \: \mathrm{g/mol}}\) c. Moles of sodium sulfide = \(\frac{2.01 \: \mathrm{g}}{78.05 \: \mathrm{g/mol}}\) d. Moles of sodium thiosulfate = \(\frac{2.01 \: \mathrm{g}}{158.12 \: \mathrm{g/mol}}\)

Calculate the number of moles of sulfur atoms

Now, multiply the number of moles of each compound by the number of sulfur atoms present in one mole of that compound: a. Moles of sulfur atoms in sodium sulfate = \(\frac{2.01 \: \mathrm{g}}{144.06 \: \mathrm{g/mol}} \times 1\) b. Moles of sulfur atoms in sodium sulfite = \(\frac{2.01 \: \mathrm{g}}{126.06 \: \mathrm{g/mol}} \times 1\) c. Moles of sulfur atoms in sodium sulfide = \(\frac{2.01 \: \mathrm{g}}{78.05 \: \mathrm{g/mol}} \times 1\) d. Moles of sulfur atoms in sodium thiosulfate = \(\frac{2.01 \: \mathrm{g}}{158.12 \: \mathrm{g/mol}} \times 2\) The resulting number of moles are: a. \(1.39 \times 10^{-2} \: \mathrm{moles}\) of sulfur in sodium sulfate b. \(1.59 \times 10^{-2} \: \mathrm{moles}\) of sulfur in sodium sulfite c. \(2.57 \times 10^{-2} \: \mathrm{moles}\) of sulfur in sodium sulfide d. \(2.55 \times 10^{-2} \: \mathrm{moles}\) of sulfur in sodium thiosulfate

Key concepts

Molar Mass

The molar mass of a compound is an essential concept in chemistry. It allows us to understand how different elements combine and react in measurable quantities. Molar mass is the mass of one mole of a given substance, expressed in grams per mole (g/mol). To calculate this, we sum up the atomic masses of all atoms present in the molecule. These atomic masses are obtained from the periodic table.

Suppose we have sodium sulfate, with the formula \(\text{Na}_2\text{SO}_4\). Sodium (Na) has an atomic mass of approximately 22.99 amu (atomic mass units), sulfur (S) weighs about 32.07 amu, and oxygen (O) is around 16 amu. To get the molar mass of sodium sulfate, multiply the number of each type of atom by its atomic mass and sum them up:

• Sodium: \(2 \times 22.99 = 45.98 \text{ g/mol}\)
• Sulfur: \(1 \times 32.07 = 32.07 \text{ g/mol}\)
• Oxygen: \(4 \times 16 = 64 \text{ g/mol}\)

Adding these gives \(144.06 \text{ g/mol}\). Understanding molar mass helps in converting between mass and moles, which is crucial for stoichiometric calculations in chemistry.

Sulfur Atoms

Sulfur atoms are an integral part of many chemical compounds, particularly those involving sodium, due to sulfur's versatile chemical properties. In the given exercise, you need to calculate the number of moles of sulfur atoms in various sodium compounds. The number of sulfur atoms per formula unit determines the total moles of sulfur you will calculate.

Each compound in the exercise contains sulfur in different proportions:

• Sodium sulfate (\(\text{Na}_2\text{SO}_4\)): Contains one sulfur atom per formula unit.
• Sodium sulfite (\(\text{Na}_2\text{SO}_3\)): Also contains one sulfur atom per formula unit.
• Sodium sulfide (\(\text{Na}_2\text{S}\)): Contains one sulfur atom per formula unit.
• Sodium thiosulfate (\(\text{Na}_2\text{S}_2\text{O}_3\)): Contains two sulfur atoms per formula unit.

When calculating moles of sulfur atoms, multiply the moles of the compound by the number of sulfur atoms per molecule. For example, sodium thiosulfate contributes double the moles of sulfur than compounds with a single sulfur atom per formula unit due to its two sulfur atoms.

Sodium Compounds

Sodium compounds, such as sodium sulfate, sodium sulfite, sodium sulfide, and sodium thiosulfate, are essential in various chemical processes and industrial applications. These compounds often involve the combination of sodium with other elements like sulfur and oxygen.

Sodium itself is highly reactive, especially with water, making it crucial to understand its behavior in compounds. Here's a brief overview:

• Sodium sulfate (\(\text{Na}_2\text{SO}_4\)): Often used in detergents and paper manufacturing.
• Sodium sulfite (\(\text{Na}_2\text{SO}_3\)): Commonly used as a preservative and in the paper industry.
• Sodium sulfide (\(\text{Na}_2\text{S}\)): Utilized in leather production and as an additive in water treatment.
• Sodium thiosulfate (\(\text{Na}_2\text{S}_2\text{O}_3\)): Used in photography and as a medical treatment for cyanide poisoning.

Understanding these compounds' compositions, including their molar masses and sulfur content, is vital for their effective use in various chemical applications. Calculations involving these compounds often require understanding their complete chemical formula and the interaction of sodium with other elements.