Calculating Percent Composition Of Carbon In Glucose

In chemistry, understanding the composition of compounds is crucial. Percent composition is a way to express the relative mass of each element in a compound. It's a fundamental concept that helps us understand the properties and behavior of chemical substances. In this article, we will walk through the steps to calculate the percent composition of carbon in glucose ($C_6H_{12}O_6$). This calculation involves determining the molar mass of the compound and then finding the percentage of carbon by mass. This is a common type of problem in chemistry, and mastering it is essential for students and professionals alike. By understanding how to calculate percent composition, we can better analyze and interpret chemical formulas, which is critical in various fields, from medicine to materials science. The concepts discussed here provide a foundational understanding that can be applied to more complex chemical calculations and analyses, making it a vital skill for anyone studying or working in the sciences.

Percent composition by mass is the percentage of the total mass of a compound that is due to a particular element. To find this, we need to calculate the molar mass of the compound and the total mass contributed by the element in question. The formula for percent composition is:

$\text{Percent Composition} = (\frac{\text{Mass of element in 1 mole of compound}}{\text{Molar mass of compound}}) \times 100$

This calculation is essential in various fields, including chemistry, materials science, and environmental science, where knowing the precise composition of substances is crucial for accurate analysis and experimentation. For instance, in pharmaceutical chemistry, the correct percent composition of a drug is vital for its efficacy and safety. Similarly, in environmental science, understanding the composition of pollutants helps in devising effective remediation strategies. The percent composition not only tells us which elements are present in a compound but also in what proportion, providing a complete picture of the substance's makeup. This knowledge is foundational for understanding chemical reactions, predicting properties, and ensuring the accurate formulation of chemical products.

Our specific problem involves calculating the percent composition of carbon in glucose ($C_6H_{12}O_6$). Glucose is a simple sugar that serves as a primary source of energy for living organisms. Its chemical formula indicates that each molecule of glucose contains 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. To find the percent composition of carbon, we need to determine the molar mass of glucose and the total mass of carbon in one mole of glucose. This calculation will help us understand what proportion of glucose's mass is made up of carbon. Understanding the composition of glucose is not only important in chemistry but also in biology and nutrition, where glucose plays a central role in metabolic processes and energy production. By calculating its percent composition, we gain insight into the fundamental makeup of this essential molecule.

We are given the molar masses of the individual elements:

• Carbon (C) = 12.01 g/mol
• Hydrogen (H) = 1.0079 g/mol
• Oxygen (O) = 16.00 g/mol

These molar masses are crucial for calculating the molar mass of the entire glucose molecule. Each element contributes to the total mass based on its atomic weight and the number of atoms present in the molecule. Accurate molar masses are essential for precise stoichiometric calculations, which are the backbone of quantitative chemistry. The given values are standard atomic weights, which are experimentally determined and widely accepted. Using these values, we can accurately determine the molar mass of glucose and proceed with calculating the percent composition of carbon. This step is foundational for solving the problem and understanding the mass relationships within the glucose molecule.

Step 1: Calculate the Molar Mass of Glucose ($C_6H_{12}O_6$)

To calculate the molar mass of glucose ($C_6H_{12}O_6$), we need to sum the masses of all the atoms in the molecule. This involves multiplying the molar mass of each element by the number of atoms of that element in the formula and then adding these values together. For glucose, this means:

• 6 carbon atoms (6 * 12.01 g/mol)
• 12 hydrogen atoms (12 * 1.0079 g/mol)
• 6 oxygen atoms (6 * 16.00 g/mol)

The molar mass calculation is a fundamental step in stoichiometry, providing the basis for converting between mass and moles, which is essential for quantitative analysis in chemistry. The accurate calculation of molar mass is crucial for various applications, including preparing solutions, determining reaction yields, and analyzing chemical compositions. This step not only gives us the total mass of one mole of glucose but also lays the groundwork for understanding the proportional contributions of each element to the compound's mass. The molar mass serves as a conversion factor in many chemical calculations, making it a vital concept in chemistry.

So, the molar mass of glucose is:

$(6 \times 12.01) + (12 \times 1.0079) + (6 \times 16.00) = 72.06 + 12.0948 + 96.00 = 180.1548 \text{ g/mol}$

This calculation gives us the molar mass of glucose, which is approximately 180.15 g/mol. This value represents the mass of one mole of glucose molecules and is a crucial figure for subsequent calculations. The molar mass is determined by considering the atomic weights of each element present in the glucose molecule, taking into account the number of atoms of each element. This precise value is essential for various chemical calculations, including determining the amount of substance in a given mass and understanding the stoichiometry of chemical reactions involving glucose. The accurate determination of molar mass is a cornerstone of quantitative chemistry and is fundamental for understanding chemical relationships.

Step 2: Calculate the Mass of Carbon in 1 Mole of Glucose

Next, we need to find the total mass of carbon in one mole of glucose. Since there are 6 carbon atoms in a glucose molecule, we multiply the molar mass of carbon by 6:

$6 \times 12.01 \text{ g/mol} = 72.06 \text{ g/mol}$

This calculation gives us the total mass of carbon present in one mole of glucose. This value is a key component in determining the percent composition of carbon in glucose. By knowing the mass of carbon in one mole of the compound, we can compare it to the total molar mass of glucose and calculate the percentage. This step is crucial for understanding the contribution of carbon to the overall mass of the glucose molecule. The mass of carbon in one mole of glucose directly relates to the proportion of carbon in the compound, which is essential information for various applications, including nutritional analysis and chemical synthesis.

Step 3: Calculate the Percent Composition of Carbon

Now, we can calculate the percent composition of carbon in glucose using the formula:

$\text{Percent Composition} = (\frac{\text{Mass of carbon in 1 mole of glucose}}{\text{Molar mass of glucose}}) \times 100$

Plugging in the values we calculated:

$\text{Percent Composition} = (\frac{72.06 \text{ g/mol}}{180.1548 \text{ g/mol}}) \times 100$

$\text{Percent Composition} = 0.4000 \times 100$

$\text{Percent Composition} = 40.00 \%$

This calculation provides the final answer for the percent composition of carbon in glucose. The result, 40.00%, indicates the proportion of the total mass of glucose that is contributed by carbon. This percentage is a fundamental property of glucose and is essential for understanding its chemical characteristics. The percent composition calculation demonstrates the relative abundance of carbon within the molecule, which has implications for glucose's role in metabolic processes and its interactions with other substances. This result highlights the significance of carbon as a key element in the structure and function of glucose, a vital energy source for living organisms.

The percent composition of carbon in glucose ($C_6H_{12}O_6$) is 40.00 %, which corresponds to option D.

In this article, we successfully calculated the percent composition of carbon in glucose. This calculation involved several steps, including finding the molar mass of glucose, determining the mass of carbon in one mole of glucose, and then applying the percent composition formula. The result showed that carbon makes up 40% of glucose by mass. This exercise demonstrates the importance of understanding stoichiometry and molar mass calculations in chemistry. Percent composition is a fundamental concept that helps us understand the makeup of chemical compounds and their properties. Mastering these calculations is essential for anyone studying or working in the field of chemistry, as it provides a solid foundation for more advanced topics. The ability to accurately determine the percent composition of elements in compounds is crucial for various applications, including chemical analysis, pharmaceutical formulation, and materials science. By understanding these principles, we can better analyze and interpret chemical data, leading to more informed decisions and advancements in scientific research and applications.