Problem 78 - Chemistry Matter and Change

Question

A 100 -g sample of an unknown salt contains 64 g of chlorine. What is the percent by mass of chlorine in the compound?

Step-by-Step Solution

Answer

The percent by mass of chlorine in the compound is 64%.

Step 1: Identify the Total Mass

The problem states that the total mass of the unknown salt sample is 100 g.

Step 2: Identify the Mass of the Component

The mass of chlorine in the sample is given as 64 g.

Step 3: Use the Percent by Mass Formula

The formula for percent by mass is \( \text{Percent by Mass} = \left( \frac{\text{Mass of Component}}{\text{Total Mass}} \right) \times 100 \).

Step 4: Substitute the Values

Substitute the values into the formula: \( \text{Percent by Mass} = \left( \frac{64}{100} \right) \times 100 \).

Step 5: Perform the Calculation

Calculate \( \left( \frac{64}{100} \right) \times 100 = 64 \).

Key Concepts

Understanding the Mass of a Component

When we discuss the mass of a component in chemistry, it refers to the weight of a particular element or part within a larger compound. For example, if you have a mixture or a chemical compound, the mass of a component would be the specific weight of an element in the entire mixture.
In our given problem, the component we are focusing on is chlorine. The mass of chlorine is given as 64 grams. Understanding this value is crucial because it helps us calculate how much of the compound is composed of chlorine. Identifying the mass is the first step in determining the percent composition by mass of a compound.

Determining the Total Mass

The total mass in a chemistry problem refers to the entire weight of a substance or sample you are analyzing. It includes all components within the substance or mixture. In our problem, the total mass of the unknown salt compound is given as 100 grams.
This is significant because knowing the total mass allows us to find the proportion of each individual component related to the whole. It acts as the denominator when calculating percent by mass, serving as the reference against which the component's mass is compared.

Applying the Percent by Mass Formula

To determine the percent by mass, it's essential to use the correct formula. The percent by mass tells us how much of each component is present in every 100 grams of the substance. It uses the formula: \[ \text{Percent by Mass} = \left( \frac{\text{Mass of Component}}{\text{Total Mass}} \right) \times 100 \]With this formula, you can easily find the percent composition of any component if you know its mass and the total mass of the compound. This formula is straightforward and directly applicable once you identify the necessary values for the mass of the component and the total mass.

Carrying Out the Calculation Steps

Let's take a look at the steps involved in calculating the percent by mass. It helps to break it down into clear stages:

• Step 1: Identify Values. Gather the necessary values: mass of the component (64 grams for chlorine) and total mass (100 grams for the salt compound).
• Step 2: Apply the Formula. Use the percent by mass formula: \( \text{Percent by Mass} = \left( \frac{64}{100} \right) \times 100 \).
• Step 3: Calculate. Perform the arithmetic. Divide 64 by 100 to get 0.64, then multiply by 100.

When you complete the calculation, you find that the percent by mass of chlorine in the compound is 64%. This methodical approach ensures accuracy and understanding, making computation straightforward and intuitive.