Problem 21 - Chemistry Matter and Change

Question

If 3.5 \(\mathrm{g}\) of element \(\mathrm{X}\) reacts with 10.5 \(\mathrm{g}\) of element \(\mathrm{Y}\) to form the compound \(\mathrm{XY},\) what is the percent by mass of element \(\mathrm{X}\) in the compound? The percent by mass of element \(\mathrm{Y}\) ?

Step-by-Step Solution

Answer

Element X: 25% by mass; Element Y: 75% by mass.

Step 1: Calculate Total Mass of Compound

First, find the total mass of the compound by summing the masses of elements X and Y. Total mass = mass of X + mass of Y = 3.5 g + 10.5 g = 14 g.

Step 2: Calculate Percent by Mass of Element X

The percent by mass of element X is calculated by dividing the mass of X by the total mass of the compound, then multiplying by 100. \[ \text{Percent by mass of X} = \left(\frac{3.5}{14}\right) \times 100 = 25\% \]

Step 3: Calculate Percent by Mass of Element Y

Similarly, calculate the percent by mass of element Y by dividing the mass of Y by the total mass of the compound, then multiplying by 100. \[ \text{Percent by mass of Y} = \left(\frac{10.5}{14}\right) \times 100 = 75\% \]

Key Concepts

Mass of Compound

The mass of a compound is fundamental to understanding its composition. Imagine you have a cake. To know the full size of the cake, you need to weigh it as a whole before you cut it into slices. Similarly, when elements combine to form a compound, knowing the total mass helps us understand what portions each element contributes.

In the case of the compound XY, we add the masses of element X and element Y to find out how heavy the compound is altogether. Here, the math is simple:

• Mass of X = 3.5 g
• Mass of Y = 10.5 g
• Total mass of compound = 3.5 g + 10.5 g = 14 g

With a total mass of 14 grams, you now have the foundational piece of information to figure out the composition in terms of percentage of each element in the compound.

Percent by Mass

Percent by mass is like finding out how much of the chocolate in your cake is influenced by cocoa. It's about figuring out the concentration of each ingredient. By calculating the percent by mass, you grasp how much of each element is present relative to the whole compound.

The formula is straightforward:

• Take the mass of the element of interest
• Divide it by the total mass of the compound
• Multiply by 100 to convert the ratio into a percentage

This calculation gives you a clearer picture of the compound’s composition, allowing you to compare how much of each ingredient (or element) makes up the substance.

Element X

Considering element X in our compound, we want to determine its portion of the total mass. Knowing how much of element X is in the compound helps paint a clearer picture of its contribution.

For element X:

• We first calculate: \( \frac{3.5}{14} \) giving us the fractional presence of X in the compound
• Next, multiply by 100: \( \frac{3.5}{14} \times 100 = 25\% \)

This tells us that element X makes up 25% of the total compound's mass. Understanding this helps us see whether element X is a major or minor component based on the percentage.

Element Y

Element Y plays its own role within the compound. We can uncover its significance by calculating its percentage by mass. This tells us how much of the compound is made up specifically by Y.

For element Y:

• Calculate: \( \frac{10.5}{14} \) to express the fraction that Y contributes
• Then multiply by 100: \( \frac{10.5}{14} \times 100 = 75\% \)

This calculation reveals that element Y comprises 75% of the compound's total mass. Knowing the percentage of each element not only deepens our understanding of the compound but also allows us to assess the dominance of one element over another.