Problem 5 - Prealgebra

Question

Solve each of the following problems by first restating it as one of the three basic percent problems of Section 7.2 . In each case, be sure to show the equation. Chemistry How much HCl (hydrochloric acid) is in a \(60-\) milliliter bottle that is marked \(75 \% \mathrm{HCl}\) ?

Step-by-Step Solution

Answer

There are 45 milliliters of HCl in the bottle.

Step 1: Restate the Problem as a Percent Problem

The problem asks us to find how much of a substance (HCl) is in a mixture that constitutes 75% of the total volume. Essentially, we need to find 75% of 60 mL.

Step 2: Write the Percent Equation

Use the percent equation to find the quantity of HCl: \[ \text{Amount of HCl} = \left( \dfrac{75}{100} \right) \times 60 \]

Step 3: Calculate 75% of the Total Volume

Perform the multiplication from the equation: \[ \text{Amount of HCl} = 0.75 \times 60 = 45 \]

Step 4: State the Final Answer

Upon calculating, we find that there are 45 milliliters of HCl in the bottle.

Key Concepts

Understanding the Percent Equation

The percent equation is an invaluable tool for solving a variety of problems involving percentages. It is used to express the relationship between the part, whole, and percentage. The basic form of the equation is:

• Part = (Percentage / 100) × Whole

This equation serves to find either the part or whole, depending on the given information. If you know the percentage and the whole, you can find the part, as illustrated in our problem about hydrochloric acid (HCl). This is particularly common in real-world applications, where understanding parts per whole is essential.
When solving percent problems, always convert the percentage to its decimal form by dividing by 100. For instance, 75% becomes 0.75. This conversion simplifies the calculations, as you can directly multiply the decimal by the whole to find the part. Remember, consistent practice with the percent equation confirms the concept and enhances speed and accuracy in solving such problems.

Chemistry Applications of Percent Problems

In chemistry, percentages are often used to express concentrations and compositions of substances. This is especially true when working with solutions, like our hydrochloric acid (HCl) problem. Chemists use percent concentration to describe how much solute is present in a given amount of solution.
For example, in our scenario, the label indicates 75% HCl in the bottle, which tells us that 75% of the entire solution is pure hydrochloric acid. By using the percent equation, you can determine exactly how much of that substance is present within the solution. This is critical when preparing solutions, as precise concentrations are needed to achieve the desired chemical reactions or results.
By understanding how to calculate the part using the percent equation, you can effectively manage and manipulate concentrations, ensuring successful chemical experiments and procedures.

Solving Basic Percent Problems

Basic percent problems consist of three main types, where one of the elements (part, whole, or percentage) is missing, and the other two are given. Mastering these types of problems is crucial for handling more complex calculations in various fields, including finance, chemistry, and everyday life.

• Finding the Part: Use Part = (Percentage / 100) × Whole. This is used when you need to find out a component of a total, such as 75% of 60 mL in our example, which resulted in finding 45 mL of HCl.
• Finding the Whole: Use Whole = (Part × 100) / Percentage. This is useful when you know the part and the percentage, but need the total amount.
• Finding the Percentage: Use Percentage = (Part / Whole) × 100. This helps when you know the part and whole but need to find the percentage.

When solving percent problems, breaking them down into one of these three basic formats ensures clarity and precision. Be sure to practice each type to become efficient in identifying and solving different percentage issues.