Question

How is the mass percent of elements in a compound different for a 1.0-g sample versus a 100.-g sample versus a 1-mole sample of the compound?

Short answer

The mass percent of elements in a compound remains the same regardless of the sample size (1.0 g, 100 g, or 1-mole). This is because the ratio of individual elements' masses to the total mass of the compound remains constant. Mass percent can be calculated as: \[\frac{\text{mass of element}}{\text{total mass of compound}} \times 100\% .\]

Step-by-step solution

Determine the molar mass of the compound

First, we need to determine the molar mass of the compound. Molar mass is the sum of the atomic masses of all the elements present in the compound. For element A and B, the atomic masses are given by 'm_A' (mass of A in g/mol) and 'm_B' (mass of B in g/mol). So, the molar mass of the compound A_x B_y = x * m_A + y * m_B.

Mass percent of elements in a 1.0-g sample

For a 1.0-g sample of the compound, the mass of element A present in the sample is given by (x * m_A) / (x * m_A + y * m_B) * 1.0 g. Similarly, the mass of element B present in the sample is given by (y * m_B) / (x * m_A + y * m_B) * 1.0 g. Now, calculate the mass percent of elements A and B by dividing their respective masses in the sample by the total mass (1.0 g) and multiplying by 100.

Mass percent of elements in a 100.-g sample

Similarly, for a 100.-g sample, the mass of element A present in the sample is given by (x * m_A) / (x * m_A + y * m_B) * 100 g and the mass of element B present in the sample is given by (y * m_B) / (x * m_A + y * m_B) * 100 g. Calculate the mass percent of elements A and B by dividing their masses in the sample by the total mass (100 g) and multiplying by 100.

Mass percent of elements in a 1-mole sample

To find the mass percent in a 1-mole sample, first find the mass of a 1-mole sample of the compound. The mass of one mole of the compound equals its molar mass, which is x * m_A + y * m_B. Now, calculate the mass percent of elements A and B by dividing their masses in the 1-mole sample by the total mass (x * m_A + y * m_B) and multiplying by 100.

Compare the results

Compare the mass percentages of elements A and B in the 1.0-g, 100.-g, and 1-mole samples. In all cases, the mass percentage for each element should remain the same, as the ratio of individual elements' masses to the total mass of the compound remains constant.

Key concepts

Molar Mass

Understanding molar mass is essential when working with chemical compounds. Molar mass is the total mass of one mole of a substance, and it's calculated by summing the atomic masses of all the atoms in its chemical formula. For example, if a compound is made of elements A and B, its molar mass is determined by the formula:

• \[ \text{Molar mass of } A_x B_y = x \times m_A + y \times m_B \]

where \( m_A \) and \( m_B \) are the atomic masses of elements A and B, respectively, given in grams per mole (g/mol). Knowing the molar mass helps convert between grams and moles, an essential practice in chemistry.

Atomic Mass

Atomic mass is the mass of an individual atom of an element, typically expressed in atomic mass units (amu). It's the weighted average of all naturally occurring isotopes of that element. In chemical calculations, the atomic mass is crucial for determining the molar mass, as it provides the basic building block for summing the masses of different elements in a compound.
For instance, if element A has an atomic mass of 12 amu and element B has 16 amu, these values will directly influence the molar mass of a compound containing these elements. Atomic masses are key to measuring and interpreting chemical compositions accurately.

Sample Size Comparison

It's interesting to observe that the mass percent of elements in a compound remains constant, regardless of the sample size. Whether you have a 1.0-g, 100-g, or 1-mole sample of the compound, the mass percent does not change.
This consistency occurs because the ratio of each element’s mass to the total mass of the compound is fixed. For example:

• In a 1.0-g sample, you calculate the mass percent by dividing the individual mass of each element by 1.0 g.
• In a 100-g sample, the division is by 100 g, but the result is the same because both the numerator and denominator scale equally.
• In a 1-mole sample, the molar mass serves as the total mass, but the same ratio holds.

This invariability is a fundamental principle in chemistry and highlights the relative proportions that define a compound.

Chemical Composition

Chemical composition refers to the types and amounts of elements that make up a substance. It provides insight into a compound's unique characteristics and physical properties.
For instance, the chemical composition of a compound with general formula \( A_x B_y \) is determined by the presence and amount of elements A and B. These amounts define how elements are bonded together and dictate the compound's molar mass.

• Molecular formulas depict the exact number of each type of atom and enable calculation of the molar and mass percentages.
• Empirical formulas provide the simplest ratio between the elements.

Understanding chemical composition is crucial for predicting reactions and properties in materials science, biology, and preserving the consistency of results in analytics.

Elemental Analysis

Elemental analysis is a technique used to determine the elemental composition of a compound—basically, identifying 'what's in there' and 'how much of it.' This type of analysis informs scientists about the quantity of each element in a sample, which is critical for tasks like confirming chemical formulas or identifying unknown substances.
There are various methods for elemental analysis, such as:

• Quantitative elemental analysis, measuring precise amounts.
• Qualitative analysis, which might only identify presence without amounts.

These techniques are central to fields such as pharmaceuticals, environmental science, and material engineering where knowledge of chemical composition and purity is crucial.