Chapter 4: Problem 102
The elemental mass percent composition of ascorbic acid (vitamin C) is 40.92% C, 4.58% H, and 54.50% O. Determine the empirical formula of ascorbic acid.
Short Answer
Expert verified
The empirical formula of ascorbic acid is \(C_3H_4O_3\).
Step by step solution
01
Calculate Moles of Each Element
First, assume a 100 g sample of ascorbic acid to work with percentages easily. Convert the mass percent of each element to moles by dividing by the atomic mass of each element. For Carbon (C), \(\frac{40.92 \text{ g}}{12.01 \text{ g/mol}} = 3.409 \text{ moles}\). For Hydrogen (H), \(\frac{4.58 \text{ g}}{1.008 \text{ g/mol}} = 4.545 \text{ moles}\). For Oxygen (O), \(\frac{54.50 \text{ g}}{16.00 \text{ g/mol}} = 3.406 \text{ moles}\).
02
Determine the Simplest Whole Number Ratio
Divide the number of moles of each element by the smallest number of moles calculated in Step 1 to get the simplest whole number ratio. For Carbon: \(\frac{3.409}{3.406} \approx 1\), for Hydrogen: \(\frac{4.545}{3.406} \approx 1.336\), and for Oxygen: \(\frac{3.406}{3.406} = 1\).
03
Convert to Whole Numbers
To convert the ratio for Hydrogen to a whole number, we can multiply all ratios by the same factor. Multiplying all by 3 gives the ratios: Carbon is 3 (since 1 times 3 is 3), Hydrogen is 4 (since 1.336 times 3 is approximately 4) and Oxygen is 3 (since 1 times 3 is 3).
04
Write the Empirical Formula
The empirical formula is determined by the ratio of atoms derived in Step 3. For ascorbic acid, the empirical formula is \(C_3H_4O_3\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Elemental Mass Percent Composition
Understanding the elemental mass percent composition is crucial when we dive into the world of chemistry, particularly when determining an unknown compound's empirical formula. This concept involves calculating the percentage by mass of each element present in a compound. Imagine an intricate dance where the weights of the individual dancers represent the elements, and the whole dance floor represents the compound. The mass percent of each dancer tells us how much they contribute to the total performance.
Take ascorbic acid, for example. It contains 40.92% carbon (C), 4.58% hydrogen (H), and 54.50% oxygen (O). This information is the first vital clue to unlock the compound's empirical formula. By starting with a common base of 100 grams, which simplifies our calculations, we convert these percentages into a tangible amount of substance using moles, the standard unit for amount of substance in chemistry. This is akin to converting the percentage of each dancer's contribution to the number of steps they take.
Take ascorbic acid, for example. It contains 40.92% carbon (C), 4.58% hydrogen (H), and 54.50% oxygen (O). This information is the first vital clue to unlock the compound's empirical formula. By starting with a common base of 100 grams, which simplifies our calculations, we convert these percentages into a tangible amount of substance using moles, the standard unit for amount of substance in chemistry. This is akin to converting the percentage of each dancer's contribution to the number of steps they take.
Stoichiometry
Stoichiometry is like the mathematical choreographer of the chemical world. It's a section of chemistry that deals with the quantitative relationships, or ratios, between reactants and products in a chemical reaction. In the context of empirical formula determination, stoichiometry allows us to balance the scales between different elements, ensuring we can move from moles to actual atoms and create a balanced depiction of the chemical entity in question.
In the case of ascorbic acid, after determining the moles of each element, we employ stoichiometry to deduce the simplest whole number ratios of these atoms. This step is like finding the rhythm in music—each beat corresponds to the presence of an element in the compound. By comparing each element's rhythm, or mole ratio, we identify the simplest consistent pattern that the dance follows, providing a foundational step to uncovering the empirical formula.
In the case of ascorbic acid, after determining the moles of each element, we employ stoichiometry to deduce the simplest whole number ratios of these atoms. This step is like finding the rhythm in music—each beat corresponds to the presence of an element in the compound. By comparing each element's rhythm, or mole ratio, we identify the simplest consistent pattern that the dance follows, providing a foundational step to uncovering the empirical formula.
Molecular Formula
The molecular formula takes the dance of elements to the next level—it shows the exact number of atoms of each element in a molecule but scaled up from the empirical formula. Think of it as the expanded script for our dance performance, detailing every move and step, rather than just the basic choreography. The molecular formula is a multiple of the empirical formula, and to grasp its true form, additional information such as the molar mass of the compound is required.
For ascorbic acid, the molecular formula could be the same as the empirical formula, or it could be a multiple, revealing a more complex arrangement between atoms. This is where understanding the empirical formula is essential, as it acts as the building block for deciphering the more intricate molecular formula.
For ascorbic acid, the molecular formula could be the same as the empirical formula, or it could be a multiple, revealing a more complex arrangement between atoms. This is where understanding the empirical formula is essential, as it acts as the building block for deciphering the more intricate molecular formula.
Chemical Composition
Finally, the chemical composition is the overarching description of what our chemical dance is made of. It encompasses both the qualitative and quantitative aspects, essentially providing a full list of dancers and how much space they occupy on the dance floor. In terms of a compound like ascorbic acid, the chemical composition encompasses the types of atoms present (C, H, and O), their relative amounts, and how they are bonded together.
The empirical formula we derive is a vital component of this overall composition. With the empirical formula being the simplest ratio of the elements, it's like a snapshot of the larger picture, offering a glimpse at the fundamental structure of the compound. This view is foundational for anyone studying chemistry, as it provides a basis from which further properties and behaviors of the compound can be explored and understood.
The empirical formula we derive is a vital component of this overall composition. With the empirical formula being the simplest ratio of the elements, it's like a snapshot of the larger picture, offering a glimpse at the fundamental structure of the compound. This view is foundational for anyone studying chemistry, as it provides a basis from which further properties and behaviors of the compound can be explored and understood.