Question

Laundry bleach is a solution of sodium hypochlorite (NaClO). To determine the hypochlorite (ClO \(^{-}\) ) content of bleach (which is responsible for its bleaching action), sulfide ion is added in basic solution. The balanced equation for the reaction is $$ \mathrm{ClO}^{-}(a q)+\mathrm{S}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{Cl}^{-}(a q)+\mathrm{S}(s)+2 \mathrm{OH}^{-}(a q) $$ The chloride ion resulting from the reduction of HClO is precipitated as \(\mathrm{AgCl}\). When \(50.0 \mathrm{~mL}\) of laundry bleach \(\left(d=1.02 \mathrm{~g} / \mathrm{cm}^{3}\right)\) is treated as described above, \(4.95 \mathrm{~g}\) of \(\mathrm{AgCl}\) is obtained. What is the mass percent of \(\mathrm{NaClO}\) in the bleach?

Short answer

Answer: The mass percent of NaClO in the bleach is 5.04%.

Step-by-step solution

Calculate moles of AgCl formed

First, we need to calculate the number of moles of AgCl formed. We can do this using the mass of AgCl formed (4.95 g) and the molar mass of AgCl (143.32 g/mol). Moles of AgCl = (4.95 g) / (143.32 g/mol) = 0.0345 mol

Determine stoichiometric ratio

The balanced chemical equation shows the stoichiometric ratio between AgCl and NaClO: ClO^- (aq) + S^2- (aq) + H2O → Cl^- (aq) + S (s) + 2 OH^- (aq). We can see that the ratio of AgCl to NaClO is 1:1. Therefore, the number of moles of NaClO in the bleach is equal to the moles of AgCl formed.

Calculate moles of NaClO

Since the stoichiometric ratio between AgCl and NaClO is 1:1, the moles of NaClO in the bleach is equal to the moles of AgCl formed: Moles of NaClO = 0.0345 mol

Calculate the mass of NaClO

Now we will calculate the mass of NaClO present in the bleach using its molar mass (74.44 g/mol). Mass of NaClO = (0.0345 mol) * (74.44 g/mol) = 2.57 g

Determine the mass percent of NaClO

Next, we need to calculate the mass of the bleach. We can do this using the volume and density of the bleach. Mass of bleach = (50.0 mL) * (1.02 g/cm^3) * (1 cm^3/1 mL) = 51.0 g Now that we have both the mass of NaClO (2.57 g) and the mass of the bleach (51.0 g), we can find the mass percent of NaClO: Mass percent of NaClO = (Mass of NaClO / Mass of bleach) * 100 = (2.57 g / 51.0 g) * 100 = 5.04 % The mass percent of NaClO in the bleach is 5.04%.

Key concepts

Chemical Reactions and Stoichiometry

In chemistry, a chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Understanding these reactions is critical in various fields, including environmental science, pharmacology, and materials science. To study chemical reactions, stoichiometry comes into play, which is essentially the math behind chemistry. It provides the quantitative relation between reactants and products in a chemical reaction.

When balancing chemical equations, it's important to understand the conservation of mass. This principle states that atoms are neither created nor destroyed during a chemical reaction, which means the number of atoms for each element must be the same on both sides of the equation. By using stoichiometry, we can calculate necessary quantities such as moles, mass, and volume, and relate these to the quantities of other substances in the reaction.

Let's consider the reaction where sodium hypochlorite (NaClO) reacts with sulfide ions in a basic solution. The balanced chemical equation provided allows us to determine the stoichiometric ratios needed to calculate the mass percent composition of NaClO in a solution—this kind of calculation is an indispensable skill in chemical analysis.

Molar Mass Calculation

The molar mass of a substance is the mass per mole of its entities, which could be atoms, molecules, or formula units, depending on the substance in question. The molar mass is typically expressed in grams per mole (g/mol), and its calculation is central to stoichiometry.

For a compound, the molar mass is calculated by adding the molar masses of the individual elements that make up the compound, adjusted by their respective amounts in the molecular formula. For example, the molar mass of silver chloride (AgCl) is determined by adding the molar mass of silver and the molar mass of chlorine. If you need to find the number of moles of a compound from a given mass, you divide the mass of the substance by its molar mass, allowing you to transition from mass to moles and vice versa. This is a fundamental step in solving various types of quantitative problems in chemistry.

Mass Percent Composition

Understanding the mass percent composition of a compound is a key aspect of analytical chemistry. Mass percent indicates the concentration of a particular substance within a mixture or solution. It is defined as the mass of a component divided by the total mass of the mixture, multiplied by 100%.

Calculating mass percent can tell you how much of a specific compound, such as sodium hypochlorite in bleach, is present in a mixture. For instance, in the example given, we used stoichiometry to determine the moles of NaClO, converted these moles to mass, and then compared this mass to the total mass of the bleach solution. The final calculation gave us the mass percentage of NaClO in the bleach.

This type of calculation is critical when preparing solutions for chemical reactions or evaluating product purity. The ability to calculate mass percent is also essential in formulating products such as pharmaceuticals, where precise concentrations can be critical to the efficacy of a drug.