Question

Sulfurous acid is unstable in aqueous solution and gradually decomposes to water and sulfur dioxide gas (which explains the choking odor associated with sulfurous acid solutions). $$ \mathrm{H}_{2} \mathrm{SO}_{3}(a q) \rightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{SO}_{2}(g) $$ If 4.25 g of sulfurous acid undergoes this reaction, what mass of sulfur dioxide is released?

Short answer

The mass of sulfur dioxide released in this reaction is approximately 3.32 grams.

Step-by-step solution

Write the balanced chemical equation

For the given decomposition reaction, the balanced chemical equation is: \[ H_2SO_3 (aq) \rightarrow H_2O (l) + SO_2 (g) \]

Calculate the moles of sulfurous acid H2SO3

To find the moles of H2SO3, we will divide the given mass by its molar mass. The molar mass of H2SO3 is: H: 1.01 g/mol, S: 32.07 g/mol, and O: 16.00 g/mol Molar mass of H2SO3 = 2 × 1.01 + 32.07 + 3 × 16.00 = 82.08 g/mol Now we can calculate the moles of H2SO3: moles of H2SO3 = (mass of H2SO3) / (molar mass of H2SO3) moles of H2SO3 = 4.25 g / 82.08 g/mol ≈ 0.0518 mol

Determine the moles of SO2 produced

From the balanced chemical equation, we see that one mole of H2SO3 decomposes to produce one mole of SO2. Therefore, the moles of SO2 produced will be equal to the moles of H2SO3. moles of SO2 = moles of H2SO3 ≈ 0.0518 mol

Convert the moles of SO2 to mass

Now, we need to convert the moles of SO2 back to mass. First, let's find the molar mass of SO2: S: 32.07 g/mol, and O: 16.00 g/mol Molar mass of SO2 = 32.07 + 2 × 16.00 = 64.07 g/mol Finally, the mass of SO2 can be calculated as follows: mass of SO2 = moles of SO2 × molar mass of SO2 mass of SO2 ≈ 0.0518 mol × 64.07 g/mol ≈ 3.32 g Therefore, the mass of sulfur dioxide released in this reaction is approximately 3.32 grams.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that focuses on the quantitative relationships between reactants and products in chemical reactions. It’s like following a recipe—stoichiometry ensures you have the right amounts of ingredients (reactants) to make your desired dish (products) without leftovers. The key to mastering stoichiometry is understanding the mole concept, which is a standard unit of measurement in chemistry representing Avogadro's number (\(6.022 \times 10^{23}\)) of particles, whether they are atoms, molecules, ions, or electrons.

When solving stoichiometry problems, we first balance the chemical equation to determine the mole ratio of reactants to products. This balanced equation tells us how many moles of each substance interact. In the provided exercise, we determine the mass of sulfur dioxide produced when a known mass of sulfurous acid decomposes. The process involves converting the mass of sulfurous acid to moles and then using the balanced equation to find the equivalent moles, and consequently the mass, of sulfur dioxide.

Molar Mass Calculation

The molar mass of a compound is the mass of one mole of that substance; it's like knowing the weight of a dozen eggs regardless of which eggs you choose. We calculate the molar mass by summing the atomic masses of all the atoms in a molecule, based on values found on the periodic table. For example, water (\(H_2O\)) has a molar mass of approximately 18.02 g/mol, calculated from the atomic mass of hydrogen (1.01 g/mol) times two, plus that of oxygen (16.00 g/mol).

In our exercise, we calculated the molar mass of sulfurous acid (\(H_2SO_3\)) by adding together the atomic masses of hydrogen, sulfur, and oxygen in their respective ratios within the molecule. Accurate molar mass calculations are vital for converting between grams and moles, allowing us to use the stoichiometry from the balanced chemical equation to predict the amounts of products formed.

Balanced Chemical Equation

A balanced chemical equation is akin to a balanced scale. Just as a scale requires equal weight on both sides for balance, a chemical equation must have the same number of each type of atom on both the reactant and product sides. This principle is known as the law of conservation of mass, stating that matter is neither created nor destroyed in chemical reactions.

The decomposition of sulfurous acid into water and sulfur dioxide is represented by the balanced equation \( H_2SO_3 (aq) \rightarrow H_2O (l) + SO_2 (g) \). Here, each element's count remains consistent across reactants and products: 2 hydrogen atoms, 1 sulfur atom, and 3 oxygen atoms. Balancing equations is a crucial part of stoichiometry and allows us to predict how much of each product is formed when a reaction goes to completion.