Chapter 9: Problem 100
Ethylene glycol, used for antifreeze, has the molecular formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\). Calculate the mass percent of each element in ethylene glycol.
Short Answer
Expert verified
The mass percentages of Carbon, Hydrogen, and Oxygen in ethylene glycol (\(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\)) are approximately 38.71%, 9.68%, and 51.61%, respectively.
Step by step solution
01
Find the molar mass of ethylene glycol
To find the molar mass of ethylene glycol, we need to multiply the number of each type of atom in the molecular formula by their respective atomic masses.
The molecular formula of ethylene glycol is \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\). Thus, it has 2 Carbon atoms, 6 Hydrogen atoms, and 2 Oxygen atoms.
The atomic masses of Carbon, Hydrogen, and Oxygen are approximately 12 g/mol, 1 g/mol, and 16 g/mol, respectively.
Now, we calculate the molar mass of ethylene glycol:
Molar Mass = (2 x 12) + (6 x 1) + (2 x 16) = 24 + 6 + 32 = 62 g/mol
02
Calculate the mass of each element in ethylene glycol
We can now determine the mass of each element in one mole of ethylene glycol by multiplying the number of each element times its respective molar mass.
Mass of Carbon = 2 atoms \(\times\) 12 g/mol = 24 g
Mass of Hydrogen = 6 atoms \(\times\) 1 g/mol = 6 g
Mass of Oxygen = 2 atoms \(\times\) 16 g/mol = 32 g
03
Calculate the mass percentage of each element in ethylene glycol
Finally, we find the mass percentage of each element in ethylene glycol by dividing the mass of each element by the molar mass of ethylene glycol and multiplying the result by 100.
Mass percentage of Carbon = (mass of Carbon / molar mass of ethylene glycol) \(\times\) 100 =
(24 g / 62 g/mol) \(\times\) 100 ≈ 38.71%
Mass percentage of Hydrogen = (mass of Hydrogen / molar mass of ethylene glycol) \(\times\) 100 =
(6 g / 62 g/mol) \(\times\) 100 ≈ 9.68%
Mass percentage of Oxygen = (mass of Oxygen / molar mass of ethylene glycol) \(\times\) 100 =
(32 g / 62 g/mol) \(\times\) 100 ≈ 51.61%
Thus, the mass percentages of Carbon, Hydrogen, and Oxygen in ethylene glycol are approximately 38.71%, 9.68%, and 51.61%, respectively.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Molar Mass Calculation
Understanding the molar mass of a substance is fundamental in chemistry. The molar mass signifies the weight of 1 mole (6.022 \( \times \) 10^23 particles) of a substance and is expressed in grams per mole (g/mol). To calculate the molar mass of a compound like ethylene glycol (\(C_{2}H_{6}O_{2}\)), you need to add up the atomic masses of all the atoms present in its molecular formula.
Let's take this step by step: First, identify the number of atoms of each element in the compound. For ethylene glycol, it's 2 Carbon (C) atoms, 6 Hydrogen (H) atoms, and 2 Oxygen (O) atoms. Then, use the standard atomic weights for these elements: Carbon is about 12 g/mol, Hydrogen is approximately 1 g/mol, and Oxygen sits at around 16 g/mol. Multiply the atomic mass of each element by the number of times that element appears in the molecule, and sum it all up. This gives us the molar mass of ethylene glycol, 62 g/mol.
Remember, precise knowledge of the molar mass is crucial, as it helps in converting moles to grams and vice versa, a necessary skill for quantitative analysis in chemistry.
Let's take this step by step: First, identify the number of atoms of each element in the compound. For ethylene glycol, it's 2 Carbon (C) atoms, 6 Hydrogen (H) atoms, and 2 Oxygen (O) atoms. Then, use the standard atomic weights for these elements: Carbon is about 12 g/mol, Hydrogen is approximately 1 g/mol, and Oxygen sits at around 16 g/mol. Multiply the atomic mass of each element by the number of times that element appears in the molecule, and sum it all up. This gives us the molar mass of ethylene glycol, 62 g/mol.
Remember, precise knowledge of the molar mass is crucial, as it helps in converting moles to grams and vice versa, a necessary skill for quantitative analysis in chemistry.
Chemical Formula
The chemical formula of a compound provides us with a wealth of information. It tells not only what elements are present but also the proportions in which the atoms are combined. This ratio is pivotal to understanding the compound's composition. In the case of ethylene glycol, the molecular formula is \(C_{2}H_{6}O_{2}\). This formula indicates that each molecule consists of 2 carbon atoms, 6 hydrogen atoms, and 2 oxygen atoms.
What's important here is that the chemical formula serves as the blueprint for the substance. It allows chemists to visualize the molecular structure, predict the behavior of the compound, and carry out various calculations, including the determination of the molar mass and percent composition. When studying chemistry, gaining familiarity with the interpretation of chemical formulas is an essential skill for understanding and explaining the properties of substances.
What's important here is that the chemical formula serves as the blueprint for the substance. It allows chemists to visualize the molecular structure, predict the behavior of the compound, and carry out various calculations, including the determination of the molar mass and percent composition. When studying chemistry, gaining familiarity with the interpretation of chemical formulas is an essential skill for understanding and explaining the properties of substances.
Percent Composition by Mass
The percent composition of a compound, expressed as mass percent, is simply the percentage by mass of each element in that compound. It gives you an idea of the relative masses of the elements in terms of the compound's total mass.
To calculate the mass percent, divide the mass of each element in a single molecule of the compound by the molar mass of the compound and then multiply by 100. This calculation was applied in our ethylene glycol example: The mass percent of Carbon, Hydrogen, and Oxygen were found to be approximately 38.71%, 9.68%, and 51.61%, respectively. These figures can be used to determine how much of each element is in any given quantity of the compound and is valuable when preparing solutions, analyzing empirical formulas, and in stoichiometric calculations.
It's also worth noting that for a compound, the sum of the mass percentages of all elements should equal to 100%. Anytime you perform such calculations, it's good practice to check that your calculated percentages add up to 100% as a verification step.
To calculate the mass percent, divide the mass of each element in a single molecule of the compound by the molar mass of the compound and then multiply by 100. This calculation was applied in our ethylene glycol example: The mass percent of Carbon, Hydrogen, and Oxygen were found to be approximately 38.71%, 9.68%, and 51.61%, respectively. These figures can be used to determine how much of each element is in any given quantity of the compound and is valuable when preparing solutions, analyzing empirical formulas, and in stoichiometric calculations.
It's also worth noting that for a compound, the sum of the mass percentages of all elements should equal to 100%. Anytime you perform such calculations, it's good practice to check that your calculated percentages add up to 100% as a verification step.