Question

How is the mass percent of elements in a compound different for a \(1.0-\mathrm{g}\) sample versus a \(100 .-\mathrm{g}\) sample versus a \(1-\mathrm{mol}\) sample of the compound?

Short answer

The mass percent of elements in a compound remains constant regardless of the sample size (1.0-g, 100-g, or 1-mol) because it is a relative measure based on the ratio of the mass of each element to the total mass of the compound. It is an inherent property of the compound and does not depend on the amount of compound present.

Step-by-step solution

Understand the concept of mass percent of an element in a compound

In a compound, the mass percent of an element is the ratio of the mass of that element to the total mass of the compound, expressed as a percentage. Mass percent of an element (X) in a compound = \(\frac{mass\:of\:element\:X}{total\:mass\:of\:the\:compound}\) × 100

Mass percent of elements in a 1.0-g sample of a compound

No matter the size of the sample, the mass percent of each element in a compound remains the same, as it is a relative measure. So, if we have a 1.0-g sample of a compound, the mass percent of the elements in that compound would remain unchanged as compared to any other sample size.

Mass percent of elements in a 100-g sample of a compound

Similarly, for a 100-g sample of the compound, the mass percent of each element would still be the same. The total mass of each element in the sample will be increased, but since the mass of the compound also increases proportionally, the mass percent will remain the same.

Mass percent of elements in a 1-mol sample of a compound

For a 1-mol sample of a compound, we need to calculate the molar mass of the compound. The molar mass of a compound is calculated by summing the molar masses of each element present in the compound according to their stoichiometric proportions. Once we have the molar mass of the compound, we can convert it to grams using Avogadro's number (1 mol = 6.022 × 10^23 particles) and the mass percent of each element will still hold true, as it is an inherent property of the compound and not dependent on the sample size. In conclusion, no matter the sample size (1.0-g, 100-g, or 1-mol), the mass percent of elements in a compound remains constant, as it is a relative measure and does not depend on the amount of compound present.

Key concepts

Mass Percent Calculation

The math behind mass percent calculation is succinct yet profound. In essence, it hinges on a simple ratio that compares the mass of a particular element to the total mass of the compound it is a part of, and then this ratio is converted into a percentage. A critical realization is that this measure is unaffected by the quantity of the substance you're dealing with.

Here’s the formula again for clarity:
\[\text{Mass percent of element X} = \left( \frac{\text{mass of element X}}{\text{total mass of the compound}} \right) \times 100\]Suppose you have a compound that contains 30 grams of hydrogen and 120 grams of oxygen. Regardless of whether you have 1 gram or 100 grams of this compound, the mass percent of hydrogen will always be \(\frac{30}{30 + 120} \times 100 = 20\%\).This is a cornerstone concept in chemistry that enables consistent calculations across different sample sizes. To provide more clarity and facilitate deeper understanding, imagine shopping for oranges by the bag. Whether you buy one bag or ten, the proportion of oranges to the total contents of a bag stays the same. Mass percent echoes this concept on a molecular level.

When calculating mass percent, always express your final answer with appropriate unit labels and note that mass percent does not change with sample size, which can be a common source of confusion.

Molar Mass

Molar mass, the next step in our exploration, is the weight of one mole of a substance typically expressed in grams per mole (g/mol). It reflects the collective weight of the atoms comprising the molecule, considering the number of each type of atom multiplied by their respective atomic weights.

To find the molar mass, you would do the following:\[\text{Molar Mass of compound} = (\text{Number of atoms of 1st element} \times \text{Atomic weight of 1st element}) + ... + (\text{Number of atoms of nth element} \times \text{Atomic weight of nth element})\]Suppose we're looking at water (H2O). You would calculate its molar mass by adding the atomic weights of two hydrogens (2 x 1.008 g/mol) and one oxygen (15.999 g/mol), yielding approximately 18.015 g/mol for the molar mass of water.

Why is this measure important?

• It helps in determining the number of molecules in a given sample, essential in reactions and calculations.
• It provides a bridge from the microscopic world of atoms to the macroscopic world we can measure in the lab.

In practice, the molar mass is indispensable for converting between mass and moles, a frequent task in stoichiometry.

Stoichiometry

The core of stoichiometry lies in the relationships between substances as they engage in chemical reactions. It's a mathematical approach to predicting product outcomes, quantifying reactants, and balancing the scales of chemical equations.

Stoichiometry hinges on the law of conservation of mass, where the total mass of reactants equals the total mass of products, and it employs the concept of molar ratios from the balanced chemical equation. For example, the reaction of hydrogen gas with oxygen gas to form water can be represented as:\[2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}\]This indicates that 2 moles of hydrogen react with 1 mole of oxygen to produce 2 moles of water.

In practical terms, if you start with 10 moles of hydrogen, stoichiometry allows you to determine how much oxygen is needed and how much water will form as a result. It’s like a recipe where you need to know the exact amount of each ingredient in order to get your desired product - except the 'ingredients' are elements and compounds! It’s precisely this quantitative nature of stoichiometry that makes it so powerful, both for theoretical predictions and empirical work in the lab.

Grasping stoichiometry is vital since it paves the way for predicting the outcomes of reactions, determining limiting reactants, and executing various calculations in chemistry with precision and confidence.