Problem 21 - Chemistry Matter and Change

Question

If 3.5 g of element X reacts with 10.5 g of element Y to form the compound X Y, what is the percent by mass of element X in the compound? The percent by mass of element Y?

Step-by-Step Solution

Answer

The percent by mass of element X in the compound XY is approximately 25%, and the percent by mass of element Y is approximately 75%.

Step 1: 1. Find the total mass of the compound

The total mass of the compound is the sum of the masses of elements X and Y. Add the masses of element X (3.5 g) and element Y (10.5 g) to find the total mass: Total Mass = Mass of X + Mass of Y

Step 2: 2. Calculate the percent by mass of element X

To find the percent by mass of element X, divide the mass of element X by the total mass of the compound and then multiply by 100 to convert the fraction to percentage: Percent by mass of X = (Mass of X / Total Mass) * 100 Plug in the values and calculate the percent by mass of element X: Percent by mass of X = (3.5 / (3.5 + 10.5)) * 100

Step 3: 3. Calculate the percent by mass of element Y

To find the percent by mass of element Y, divide the mass of element Y by the total mass of the compound and then multiply by 100 to convert the fraction to percentage: Percent by mass of Y = (Mass of Y / Total Mass) * 100 Plug in the values and calculate the percent by mass of element Y: Percent by mass of Y = (10.5 / (3.5 + 10.5)) * 100

Step 4: 4. Find the percent by mass of elements X and Y

Now that we have the formulas for each element, let's calculate their percent by mass: Percent by mass of X = (3.5 / (3.5 + 10.5)) * 100 ≈ 25% Percent by mass of Y = (10.5 / (3.5 + 10.5)) * 100 ≈ 75% The percent by mass of element X in the compound XY is approximately 25%, and the percent by mass of element Y is approximately 75%.

Key Concepts

Percent by Mass

Percent by mass, also known as mass percent, is a way to express the concentration of an element in a compound. It's calculated by dividing the mass of the element by the total mass of the compound and multiplying the result by 100. This tells us what fraction of the compound's mass is made up of that specific element.
For instance, in a compound formed by the reaction of 3.5 grams of element X with 10.5 grams of element Y, the mass of the entire compound is 14.0 grams.

• Mass of X: 3.5 grams
• Mass of Y: 10.5 grams
• Total mass: 14.0 grams

To find the percent by mass of each element, we simply use the formula: \[\text{Percent by mass} = \left( \frac{\text{mass of the element}}{\text{total mass of the compound}} \right) \times 100\] This gives about 25% for X and 75% for Y, indicating how each contributes to the total mass.

Chemical Reaction

A chemical reaction occurs when substances, known as reactants, change to form new substances, called products. In this context, element X and element Y react to form a new compound XY. This means that the atoms of X and Y combine in a specific ratio and rearrange to create the compound.
Such reactions follow the law of conservation of mass, indicating that mass is neither lost nor gained during the chemical change. So, in our example where 3.5 grams of X combine with 10.5 grams of Y, the new compound must have the same combined mass, which is 14.0 grams. This ensures that all the mass from the reactants is accounted for in the product.

Mass Calculation

Mass calculation involves determining the total mass of a compound by adding up the masses of the individual elements that form the compound. In our exercise, we first calculate the total mass by summing the masses of element X (3.5 grams) and element Y (10.5 grams). This is straightforward and results in a total mass of 14.0 grams.
This kind of calculation is crucial because it provides the basis for further calculations such as percent by mass. By knowing the total mass, we can easily determine how much each element contributes to the total mass as a percentage, thereby helping us understand the composition of the compound.

Element Composition

Element composition refers to the proportion of each element in a compound. It's vital in chemistry because it tells us about the make-up and properties of the compound. The composition is expressed in terms of mass percent of each element within the compound.
In our scenario, with a compound of element X and Y, the calculation of percent by mass provides insight into how the two elements combine to form the compound. A composition of 25% X and 75% Y means that in every 100 grams of compound XY, 25 grams are X and 75 grams are Y.
This understanding of element composition helps in predicting the properties, behavior, and uses of the compound in various applications.