Problem 33 - Chemistry Matter and Change

Question

Calculate A can of chicken broth contains 450 \(\mathrm{mg}\) of sodium chloride in 240.0 \(\mathrm{g}\) of broth. What is the percent by mass of sodium chloride in the broth?

Step-by-Step Solution

Answer

The percent by mass of sodium chloride in the broth is approximately 0.1875%.

Step 1: Understanding the Problem

We need to find the percentage of sodium chloride (NaCl) in a can of chicken broth. We know that the mass of sodium chloride is 450 mg and the mass of the entire broth is 240 g. The percent by mass is calculated as \( \text{percent by mass} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100\% \).

Step 2: Convert Mass of Sodium Chloride

First, convert the mass of sodium chloride from milligrams (mg) to grams (g) because we need both masses in the same unit. We know 1 g = 1000 mg. Thus, \( 450\, \text{mg} = \frac{450}{1000} \, \text{g} = 0.45\, \text{g} \).

Step 3: Calculate Percent by Mass

Now, substitute the mass of sodium chloride and the mass of the broth into the percent by mass formula: \( \text{percent by mass} = \frac{0.45\, \text{g}}{240.0\, \text{g}} \times 100\% \).

Step 4: Solve the Equation

Perform the division: \( \frac{0.45}{240.0} \approx 0.001875 \). Multiply by 100 to convert to a percentage: \( 0.001875 \times 100 \approx 0.1875\% \).

Key Concepts

Understanding Sodium Chloride

Sodium chloride, commonly known as table salt, is a chemical compound with the formula \( \text{NaCl} \). It consists of sodium ions (a\(^+\)) and chloride ions (l\(^-\)), which are bonded together through ionic bonds. This compound is essential in various culinary and industrial applications. In the context of the chicken broth exercise, sodium chloride is used to enhance flavor and as a preservative.
It’s crucial to recognize how this compound's mass is used to calculate its concentration in a solution. As a solute in broth, measuring its precise mass helps in addressing health concerns related to sodium intake. Understanding its role and quantifying it accurately ensures that nutritional guidelines are met.

Mass Conversion Basics

Converting mass measurements between units is a fundamental skill in solving chemical calculations. In this exercise, we begin with sodium chloride measured in milligrams and need to convert it to grams to match the broth's measurement unit. The conversion factor to remember is that:

• 1 gram (g) = 1000 milligrams (mg)

To convert milligrams to grams, divide the mass in milligrams by 1000. So, in our case,

• \( 450 \, \text{mg} = \frac{450}{1000} \, \text{g} = 0.45 \, \text{g} \)

This conversion is not just a requirement for calculations but is also important for ensuring consistency across measurements.
Whether in culinary recipes or scientific experiments, precise conversions lead to accurate results. Next time you encounter a similar problem, make sure to check that all measurements are in the same unit before proceeding.

Chemical Calculations and Percent By Mass

After converting the mass, the next step is to perform a chemical calculation to find the percent by mass. The formula used is:\[\text{percent by mass} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100\%\]In this formula:

• The "mass of solute" refers to the substance whose concentration you wish to find—in this case, sodium chloride, which is 0.45 grams.
• The "mass of solution" is the total mass of the mixture or solution—in this exercise, 240.0 grams of chicken broth.

Substituting these values into the formula, we perform the calculation:

• Division: \( \frac{0.45}{240.0} \approx 0.001875 \)
• Conversion to a percentage: \( 0.001875 \times 100 \approx 0.1875\% \)

This calculation reveals the concentration of sodium chloride in the broth, which is important for dietary and culinary considerations. Understanding such chemical calculations helps students relate mathematical operations to real-world applications, making the complexities of chemistry both approachable and relevant.