Problem 80 - Chemistry The Science in Context

Question

Toxic chromate can be precipitated from an aqueous solution by bubbling \(\mathrm{SO}_{2}\) through the solution. How many grams of \(\mathrm{SO}_{2}\) are required to treat \(3.0 \times 10^{8} \mathrm{L}\) of \(0.050 \mathrm{mM} \mathrm{CrO}_{4}^{-} ?\) $$\begin{aligned} &2 \mathrm{CrO}_{4}^{2-}(a q)+3 \mathrm{SO}_{2}(g)+4 \mathrm{H}^{+}(a q) \rightarrow\\\ &\mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3}(s)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \end{aligned}$$

Step-by-Step Solution

Answer

Answer: 1.44 x 10⁹ grams

Step 1: Calculate moles of CrO₄²⁻

To begin with, we will convert the concentration of the chromate solution (0.050 mM) and its volume (3.0 x 10⁸ L) into moles: Moles of CrO₄²⁻ = (0.050 mM x (1 mol / 1000 mmol)) x (3.0 x 10⁸ L) Moles of CrO₄²⁻ = (5.0 x 10⁻² mol/m³) x (3.0 x 10⁸ m³) Moles of CrO₄²⁻ = 1.5 x 10⁷ mol

Step 2: Calculate moles of SO₂

Next, we will use stoichiometric ratios to determine the moles of SO₂ required to react with the given moles of CrO₄²⁻. According to the balanced equation: 2 moles of CrO₄²⁻ + 3 moles of SO₂ → ... Thus, we can use the stoichiometric ratio (2:3) to find the moles of SO₂ needed: Moles of SO₂ = (3 moles SO₂ / 2 moles CrO₄²⁻) x 1.5 x 10⁷ moles CrO₄²⁻ Moles of SO₂ = (3/2) x 1.5 x 10⁷ moles Moles of SO₂ = 2.25 x 10⁷ moles

Step 3: Calculate mass of SO₂

Finally, we will convert the moles of SO₂ calculated in step 2 to grams, using its molar mass. The molar mass of SO₂ is 32 g/mol (S) + 2 × 16 g/mol (O) = 64 g/mol. Mass of SO₂ = moles of SO₂ × molar mass of SO₂ Mass of SO₂ = 2.25 x 10⁷ moles × 64 g/mol Mass of SO₂ = 1.44 x 10⁹ g Therefore, 1.44 x 10⁹ grams of SO₂ gas are required to treat 3.0 x 10⁸ L of 0.050 mM CrO₄²⁻ solution.

Key Concepts

Molecular Stoichiometry

Molecular stoichiometry is a critical concept in chemistry that involves the quantitative relationship between reactants and products in a chemical reaction. It follows the law of conservation of mass which states that matter cannot be created or destroyed in a chemical reaction. Therefore, the amount of reactants consumed must equal the amount of products formed.

In practice, molecular stoichiometry allows us to calculate how much of a reactant is needed to completely react with another substance, or how much product will be produced from given amounts of reactants. The balanced chemical equation provides the stoichiometric coefficients, which represent the molar ratios of the substances involved.

For example, in the exercise given, the balanced equation shows a 2:3 relationship between chromate ions and sulfur dioxide. This ratio means that for every 2 moles of chromate ions, 3 moles of sulfur dioxide gas are required for complete reaction. Understanding these ratios is essential for calculating the precise quantities needed for a reaction, which is indispensable in both laboratory and industrial settings where accuracy is paramount.

Chemical Precipitation

Chemical precipitation is a process that occurs when a solid (the precipitate) forms in a solution due to a chemical reaction, and then separates from the solution. It is commonly used in wastewater treatment processes to remove contaminants, such as toxic metal ions, from water.

Precipitation reactions are usually represented by a solid product in a chemical equation, indicated by the letter 's' following the chemical formula. Various factors such as temperature, concentration, and the presence of other ions can affect the solubility of substances and whether or not precipitation will occur.

In the given problem, toxic chromate ions are precipitated by bubbling sulfur dioxide, SO₂, into the aqueous solution, which leads to the formation of a solid compound, chromium sulfate. This solid can then be removed from the solution, effectively reducing the concentration of chromate from the water. This practical application of chemical precipitation is not only important for understanding the chemical processes involved but also for its environmental applications in removing harmful substances from water.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance. It is a bridge between the mass scale and the atomic scale; since the molar mass of an element is numerically equal to its atomic weight as listed on the periodic table, but expressed in units of grams per mole (g/mol).

Various compounds have their unique molar masses, which are found by summing the atomic masses of all the atoms in a molecule of that compound. For instance, in the exercise, the molar mass of sulfur dioxide (SO₂) is calculated by adding the atomic mass of sulfur (32 g/mol) to the atomic mass of two oxygen atoms (2×16 g/mol), totaling 64 g/mol. Knowing the molar mass allows us to convert between mass and moles of a substance, which is a necessary step in stoichiometric calculations.

Having the correct molar mass is crucial when performing stoichiometric calculations in chemistry. A wrong value could lead to incorrect amounts of substances used or produced in a chemical reaction, which in professional settings could mean failed experiments or industrial processes. In our exercise, by using the molar mass, we could calculate the exact mass of SO₂ gas required to treat the chromate solution.