Problem 43 - Chemistry Matter and Change

Question

A sample of sodium sulfite \(\left(\mathrm{Na}_{2} \mathrm{SO}_{3}\right)\) has a mass of 2.25 \(\mathrm{g}\) a. How many Nat ions are present? b. How many \(\mathrm{SO}_{3}^{2-}\) ions are present? c. What is the mass in grams of one formula unit of \(\mathrm{Na}_{2} \mathrm{SO}_{3} ?\)

Step-by-Step Solution

Answer

a. \(2.17 \times 10^{22}\) Na⁺ ions are present b. \(1.08 \times 10^{22}\) SO₃²⁻ ions are present c. The mass of one formula unit of Na₂SO₃ is \(2.08 \times 10^{-22}\) g.

Step 1: Calculate the moles of Na₂SO₃

First, we need to find the molar mass of Na₂SO₃, which is the sum of the atomic masses of the constituent elements. Molar mass of Na₂SO₃ = (2 x Atomic mass of Na) + (1 x Atomic mass of S) + (3 x Atomic mass of O) Molar mass of Na₂SO₃ = (2 x 22.99 g/mol) + (1 x 32.07 g/mol) + (3 x 16.00 g/mol) = 45.98 + 32.07 + 48 = 125.05 g/mol Now, we can calculate the moles of Na₂SO₃ in the sample using the given mass and the molar mass: moles of Na₂SO₃ = mass of Na₂SO₃ / molar mass of Na₂SO₃ moles of Na₂SO₃ = 2.25 g / 125.05 g/mol = 0.018 mol

Step 2: Calculate the moles of Na⁺ and SO₃²⁻ ions

Now, we can find the moles of Na⁺ and SO₃²⁻ ions using the mole ratios of the compound. Mole ratio of Na⁺ to Na₂SO₃ = 2:1 Mole ratio of SO₃²⁻ to Na₂SO₃ = 1:1 moles of Na⁺ = moles of Na₂SO₃ x (2/1) = 0.018 mol x 2 = 0.036 mol moles of SO₃²⁻ = moles of Na₂SO₃ x (1/1) = 0.018 mol x 1 = 0.018 mol

Step 3: Find the number of ions

Next, we can find the number of ions using Avogadro's number, which is approximately 6.022 x 10²³ particles per mole. Number of Na⁺ ions = moles of Na⁺ x Avogadro's number Number of Na⁺ ions = 0.036 mol x 6.022 x 10²³ ions/mol = 2.17 x 10²² ions Number of SO₃²⁻ ions = moles of SO₃²⁻ x Avogadro's number Number of SO₃²⁻ ions = 0.018 mol x 6.022 x 10²³ ions/mol = 1.08 x 10²² ions

Step 4: Calculate the mass of one formula unit of Na₂SO₃

First, find the mass of one mole of Na₂SO₃, which is equal to its molar mass: Mass of one mole of Na₂SO₃ = 125.05 g/mol Now, divide this mass by Avogadro's number to find the mass of one formula unit: Mass of one formula unit of Na₂SO₃ = mass of one mole of Na₂SO₃ / Avogadro's number Mass of one formula unit of Na₂SO₃ = 125.05 g/mol / 6.022 x 10²³ formula units/mol = 2.08 x 10⁻²² g So the answers are: a. 2.17 x 10²² Na⁺ ions are present b. 1.08 x 10²² SO₃²⁻ ions are present c. The mass of one formula unit of Na₂SO₃ is 2.08 x 10⁻²² g.

Key Concepts

Molar Mass Calculation

Understanding how to calculate molar mass is critical for mastering stoichiometry, which is the study of the quantitative relationships in chemical reactions. The molar mass is the mass of one mole of a substance, typically measured in grams per mole (g/mol). It is numerically equal to the average atomic mass of the substance but expressed in grams.

For instance, to calculate the molar mass of sodium sulfite (\( \text{Na}_2 \text{SO}_3 \)), you would sum the molar masses of all the atoms in the molecule. Each sodium (Na) atom has a molar mass of about 22.99 g/mol, sulfur (S) has 32.07 g/mol, and oxygen (O) has 16.00 g/mol. So, for \( \text{Na}_2 \text{SO}_3 \), you would calculate as follows:\[ \text{Molar mass of } \text{Na}_2 \text{SO}_3 = (2 \times 22.99) + (1 \times 32.07) + (3 \times 16.00) = 125.05 \text{ g/mol} \]
In practical terms, this means that 1 mole of \( \text{Na}_2 \text{SO}_3 \) weighs 125.05 grams. This value is central to converting between grams and moles, which is a foundational step in stoichiometry.

Avogadro's Number

A concept that's as fundamental as molar mass calculation in stoichiometry is Avogadro's number. It allows chemists to count particles by weighing them. Avogadro's number, usually denoted as \( 6.022 \times 10^{23} \), is the number of atoms, ions, or molecules in one mole of a substance.

For example, when we say there are \( 0.036 \) moles of sodium ions (\( \text{Na}^+ \)) in a sample, we can use Avogadro's number to find out exactly how many ions that corresponds to:\[ \text{Number of } \text{Na}^+ \text{ ions} = 0.036 \text{ moles} \times 6.022 \times 10^{23} \text{ ions/mole} \]This allows us to understand the scale of chemical reactions and calculate specific amounts of substances needed in laboratory settings or industrial processes.

Chemical Formula Units

The term 'chemical formula unit' refers to the simplest ratio of atoms present in an ionic compound that still reflects the composition of that substance. For sodium sulfite (\( \text{Na}_2 \text{SO}_3 \)), one formula unit consists of two sodium ions and one sulfite ion (\( \text{SO}_3^{2-} \)).

Knowing the composition of one formula unit allows chemists to compute the mass of that unit by dividing the molar mass by Avogadro's number, which results in the mass of the individual formula unit. So, for \( \text{Na}_2 \text{SO}_3 \), the calculation would be:\[ \text{Mass of one formula unit of } \text{Na}_2 \text{SO}_3 = \frac{125.05 \text{ g/mol}}{6.022 \times 10^{23} \text{ formula units/mol}} \]The result is the incredibly small mass of a single formula unit, helping us comprehend the minuscule scale at which chemical phenomena occur.