A substance \(\mathrm{X}_{2} Z\) has the composition (by mass) of \(40.0 \% \mathrm{X}\) and \(60.0 \% \mathrm{Z}\). What is the composition (by mass) of the compound \(\mathrm{XZ}_{2}\) ?

Understanding the mass ratio in a compound is crucial for various calculations in chemistry. The mass ratio represents how much of one substance is present compared to another within a compound. It's especially useful when we want to understand the proportions of elements in a molecule.

In the exercise, the mass ratio is determined directly from the given percentage composition. With X constituting 40% and Z 60% of the compound X₂Z, the initial mass ratio comes out as 40:60. Simplified, it turns into a ratio of 2:3, meaning for every two parts of X, there are three parts of Z. This ratio forms the basis for understanding the composition of other compounds involving the same elements.

When dealing with mass ratios, remember to simplify the ratios whenever possible. This simplification can make subsequent calculations more straightforward, as seen when this ratio is used to find the composition of XZ₂.

The percent composition by mass refers to the percentage by mass of each element in a compound. It's an expression of the mass fraction of each element presented as a percentage. This concept is fundamental in chemistry, as it helps us understand the makeup of substances and allows for the conversion between mass and moles of elements and compounds.

To calculate the percent composition, one simply divides the mass of the element in a mole of the compound by the mass of a mole of the compound and multiplies by 100%. In our exercise, after establishing the mass ratio of X to Z in XZ₂ as 1:3, we sum the parts, leading to four total parts, and assign percentages accordingly. We find that X makes up 25% (1 out of 4 parts) and Z makes up 75% (3 out of 4 parts) of the compound's mass.

This percent composition is a critical step that links the conceptual mass ratio to practical applications in stoichiometry and chemical analysis.

Stoichiometry is the section of chemistry that involves the calculation of reactants and products in chemical reactions. It builds upon the concepts of mass ratio and percent composition by mass to predict the outcomes of reactions. Stoichiometry is governed by the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction.

In practice, stoichiometry allows us to calculate things like how much reactant is needed to produce a desired amount of product, or what the yield of a reaction might be. In the context of the exercise, if we were to react X and Z to form XZ₂, we'd use the percent compositions and mass ratios we've calculated to ensure that reactants are mixed in the correct proportions.

Effective stoichiometry depends on a solid understanding of the relationships between the different elements and compounds involved in a reaction, highlighting the significance of the previous concepts in real-world applications.