What Is The Percent Composition Of A 16.75 G Sample Of A Compound Containing 14.02 G Oxygen And 2.73

What Is The Percent Composition Of A 16.75 G Sample Of A Compound Containing 14.02 G Oxygen And 2.73

Understanding the percent composition of a chemical compound is fundamental in chemistry, as it provides insight into the relative amounts of each element within a sample. In this article, we will explore how to determine the percent composition of a 16.75 g sample of a compound that contains 14.02 g of oxygen and 2.73 g of another element—likely a metal or non-metal depending on the compound's nature. By the end of this guide, you'll have a comprehensive understanding of how to calculate percent composition, its significance, and its applications in various chemical analyses.

What Is Percent Composition in Chemistry?

Percent composition refers to the percentage by mass of each element in a compound. It allows chemists to understand the elemental makeup and deduce the empirical formula of a compound. This information is crucial in various fields, including pharmaceuticals, materials science, and chemical manufacturing, where precise knowledge of molecular composition influences the synthesis, quality control, and reaction mechanisms.

Key Points About Percent Composition:

• It is expressed as a percentage.


• Calculated using the mass of each element divided by the total mass of the compound.


• Essential for determining empirical and molecular formulas.

Given Data and Objective

Let's first clarify the data provided:

• Total mass of the sample: 16.75 g


• Mass of oxygen in the sample: 14.02 g


• Mass of the other element (let's denote it as element X): 2.73 g

Our goal is to find the percent composition of each element in the sample, primarily focusing on:

• Percent of oxygen


• Percent of element X

Additionally, we can verify the total percentage sum and discuss implications.

Step-by-Step Calculation of Percent Composition

To determine the percent composition, we'll follow these steps:

1. Identify the masses of each element.


2. Calculate the percentage of each element by dividing its mass by the total sample mass.


3. Express the result as a percentage.

Let's perform these calculations.

1. Masses of Elements

• Oxygen: 14.02 g
• Element X: 2.73 g
• Total: 16.75 g (given, but also verify sum)

Check if the sum of the masses of oxygen and element X equals the total:

14.02 g + 2.73 g = 16.75 g

Yes, it matches the total sample mass, confirming the data's consistency.

2. Calculating Percentages

Percent of Oxygen:

\[
\% \text{Oxygen} = \left( \frac{\text{Mass of Oxygen}}{\text{Total Mass}} \right) \times 100
\]

\[
= \left( \frac{14.02\, \text{g}}{16.75\, \text{g}} \right) \times 100 \approx 83.69\%
\]

Percent of Element X:

\[
\% \text{Element X} = \left( \frac{\text{Mass of Element X}}{\text{Total Mass}} \right) \times 100
\]

\[
= \left( \frac{2.73\, \text{g}}{16.75\, \text{g}} \right) \times 100 \approx 16.31\%
\]

Summary:

| Element | Mass (g) | Percent Composition (%) |
|-------------|----------|-------------------------|
| Oxygen | 14.02 | 83.69 |
| Element X | 2.73 | 16.31 |

The total of these percentages sums to approximately 100%, confirming the calculations' correctness.

Interpreting the Percent Composition Data

Knowing that oxygen constitutes about 83.69% of the sample indicates that oxygen is the predominant element in this compound. Conversely, element X makes up roughly 16.31%. This information can be used to determine the empirical formula of the compound, which reflects the simplest whole-number ratio of the elements.

Determining the Empirical Formula

The empirical formula provides the ratio of moles of elements in a compound. To derive it:

1. Convert the masses into moles by dividing by atomic masses.


2. Find the simplest whole-number ratio of these moles.

Let's proceed with this process, assuming element X is a specific element, such as carbon, nitrogen, or a metal. For illustration, suppose element X is nitrogen (atomic mass approximately 14.01 g/mol). The atomic mass of oxygen is approximately 16.00 g/mol.

Calculating Moles of Each Element

Oxygen:

\[
n_{\text{O}} = \frac{14.02\, \text{g}}{16.00\, \text{g/mol}} \approx 0.876\, \text{mol}
\]

Element X (assuming nitrogen):

\[
n_{\text{X}} = \frac{2.73\, \text{g}}{14.01\, \text{g/mol}} \approx 0.195\, \text{mol}
\]

Finding the Mole Ratio

Divide each by the smallest number of moles:

Smallest mole value: 0.195 mol (element X)

Oxygen:

\[
\frac{0.876}{0.195} \approx 4.49 \approx 4.5
\]

Element X:

\[
\frac{0.195}{0.195} = 1
\]

The ratio is approximately 4.5:1 for oxygen to element X, which suggests multiplying both by 2 to obtain whole numbers:

• Oxygen: 4.5 × 2 = 9


• Element X: 1 × 2 = 2

Thus, the empirical formula ratio is roughly \(\text{X}2\text{O}9\). Since molecular formulas are typically represented with whole numbers, this might be simplified further or used to determine the molecular formula if molar mass data is available.

Note: If element X is different, the atomic mass used should correspond accordingly.

Applications and Significance of Percent Composition

Understanding percent composition serves multiple purposes in chemistry:

• Formulating compounds: Helps in deducing empirical and molecular formulas.


• Quality Control: Ensures the correct elemental makeup in pharmaceuticals and materials.


• Reaction Analysis: Determines which elements are involved and in what proportions.


• Environmental Monitoring: Assesses pollutant composition.


• Educational Purposes: Fundamental in teaching stoichiometry and chemical calculations.

Additional Considerations and Practical Tips

• Purity of Sample: Ensure the sample is pure; impurities can skew results.


• Accurate Measurements: Use precise scales and proper measurement techniques.


• Atomic Masses: Use the most current atomic weights for calculations.


• Molecular vs. Empirical: Empirical formulas are based on simplest ratios; molecular formulas depend on molar mass.

Conclusion

Calculating the percent composition of a compound provides valuable insight into its elemental makeup, aiding in further chemical analysis and synthesis endeavors. For the given sample containing 14.02 g oxygen and 2.73 g of another element in a total mass of 16.75 g, the percent composition is approximately 83.69% oxygen and 16.31% of the other element. These calculations not only help in understanding the compound's structure but also form the foundation for determining empirical and molecular formulas, which are crucial in various scientific and industrial applications.

By mastering the steps involved in percent composition calculations, chemists can accurately analyze substances, verify purity, and design compounds with desired properties. Whether working in a laboratory, manufacturing plant, or academic setting, understanding these fundamental concepts enhances your ability to interpret chemical data effectively.

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Remember: Always double-check your data, use precise atomic weights, and consider the context of your analysis when applying percent composition calculations to real-world chemical problems.