Problem 10 - Chemistry Matter and Change

Question

You have 1500.0 g of a bleach solution. The percent by mass of the solute sodium hypochlorite (NaOCl) is 3.62\(\%\) . How many grams of NaOCl are in the solution?

Step-by-Step Solution

Answer

There are \(54.3\) grams of NaOCl in the 1500 g bleach solution with a mass percentage of \(3.62\%\).

Step 1: Convert the mass percentage into decimal form

To find out the grams of NaOCl in the solution, we first need to convert the given mass percentage (3.62%) into decimal form. To do this, divide the percentage value by 100. Decimal form of mass percentage = 3.62% / 100

Step 2: Calculate the mass of NaOCl in the solution

Now that we have the decimal form of the mass percentage, we can find the mass (in grams) of NaOCl in the solution by multiplying the decimal form of the mass percentage by the total mass of the bleach solution. Mass of NaOCl (grams) = Decimal form of mass percentage * Total mass of bleach solution

Step 3: Plug in the values and solve

Plug in the values from Steps 1 and 2 into the formula and solve for the mass of NaOCl (grams). Mass of NaOCl (grams) = (3.62 / 100) * 1500.0 Mass of NaOCl (grams) = 0.0362 * 1500.0 Mass of NaOCl (grams) = 54.3 grams There are 54.3 grams of NaOCl in the bleach solution.

Key Concepts

Sodium Hypochlorite

Sodium hypochlorite is a chemical compound with the formula NaOCl. It is commonly known as the active ingredient in bleach. This compound is made up of sodium (Na), oxygen (O), and chlorine (Cl) elements. Sodium hypochlorite acts as a disinfectant and sanitizing agent commonly found in household bleach. It is effective at removing stains and killing bacteria or viruses in water. Understanding the role of sodium hypochlorite in bleach helps us appreciate its presence and effects in cleaning and disinfection purposes.

Bleach Solution

A bleach solution is a mixture containing a certain percentage of sodium hypochlorite dissolved in water. The primary purpose of this solution is to sanitize and whiten surfaces and fabrics. Commercial bleach solutions commonly contain about 3% to 6% sodium hypochlorite by mass. The percentage indicates how much of the entire solution is made up of the solute, which in this case is sodium hypochlorite. This soapy solution is effective in household cleaning but must be used with care to prevent harm or damage due to its corrosive nature.

Solute Mass Determination

Solute mass determination in a solution involves calculating the mass of the dissolved substance, known as the solute. In the context of our bleach solution, the solute is sodium hypochlorite. To determine the mass of the solute:

• Convert the given mass percentage into a decimal by dividing by 100.
• Multiply the decimal by the total mass of the solution.

For example, with a 1500 g bleach solution containing 3.62% sodium hypochlorite:

• Convert 3.62% to 0.0362.
• Multiply 0.0362 by the total mass (1500g) to find the mass of the solute.
• Resulting in 54.3 grams of NaOCl in the solution.

Percent Composition

Percent composition is a concept used to express the amount of each component within a mixture as a percentage of the total. In the case of the bleach solution, percent composition helps us know exactly how much sodium hypochlorite is in the solution compared with the total mass. The calculation is straightforward:

• Divide the solute mass by the total mass of the solution and multiply by 100 to obtain a percentage.

For example, if we know there are 54.3 grams of NaOCl in a 1500 g solution, you can confirm the percentage by calculating:

• \( \frac{54.3}{1500} \times 100 = 3.62\% \)

This reinforces the given mass percentage of sodium hypochlorite initially specified in the bleach solution.