Determining Hydrocarbon Molecular Formula A Step-by-Step Guide
1) When 58g of a hydrocarbon is burned, 176g of carbon dioxide and 90g of water are formed. The relative density of the substance in air is 4. Determine the molecular formula of the hydrocarbon.
2) Find the molecular formula of the hydrocarbon, the mass fraction of carbon in which is:
1. Introduction: Unveiling Hydrocarbon Composition
In the realm of organic chemistry, hydrocarbons form the very backbone of a vast array of compounds. These molecules, composed solely of carbon and hydrogen atoms, exhibit diverse structures and properties, playing crucial roles in energy production, industrial processes, and even biological systems. Determining the molecular formula of a hydrocarbon is a fundamental task in chemical analysis, providing essential information about its composition and structure. In this comprehensive guide, we will delve into the step-by-step process of elucidating the molecular formula of a hydrocarbon, using a practical example to illustrate the concepts involved. Mastering this skill is vital for students, researchers, and anyone seeking a deeper understanding of organic chemistry. Let's embark on this journey of unraveling the molecular mysteries of hydrocarbons.
The quest to identify a hydrocarbon's molecular formula begins with a meticulous analysis of its combustion products. When a hydrocarbon undergoes complete combustion, it reacts with oxygen to produce carbon dioxide (CO2) and water (H2O). The masses of these products, carefully measured in the laboratory, serve as crucial clues to the hydrocarbon's elemental composition. By employing stoichiometric principles, we can convert these masses into moles, revealing the relative amounts of carbon and hydrogen atoms within the molecule. The density of the hydrocarbon vapor, often expressed relative to air, provides additional information about its molecular weight, further narrowing down the possibilities. This initial stage of analysis lays the foundation for determining the empirical formula, the simplest whole-number ratio of elements in the compound. However, the empirical formula is just the first step; to unveil the true molecular formula, we must consider the molecular weight and its relationship to the empirical formula mass. This involves a methodical approach, combining experimental data with chemical principles to arrive at an accurate representation of the hydrocarbon's molecular structure. Through careful calculations and logical deductions, we can decipher the molecular formula, unlocking valuable insights into the compound's identity and properties. This intricate process highlights the power of analytical chemistry in revealing the hidden composition of matter.
Ultimately, the determination of a hydrocarbon's molecular formula is a testament to the precision and analytical prowess of chemistry. It's not merely about crunching numbers; it's about understanding the fundamental relationships between elements and molecules. The journey from combustion data to molecular formula involves a thoughtful application of chemical principles, a keen eye for detail, and a methodical approach to problem-solving. The ability to perform this analysis is a cornerstone of organic chemistry, allowing scientists to identify unknown compounds, predict their behavior, and even design new molecules with specific properties. As we delve into the intricacies of this process, remember that each step is a piece of the puzzle, contributing to the final, complete picture of the hydrocarbon's identity. So, let's sharpen our pencils, ignite our analytical minds, and embark on this exciting exploration of molecular formulas.
2. Problem 1: Determining the Molecular Formula from Combustion Data and Relative Density
2.1. Problem Statement
When 58 grams of a hydrocarbon are combusted, 176 grams of carbon dioxide (CO2) and 90 grams of water (H2O) are produced. The relative density of the substance with respect to air is 4. Determine the molecular formula of the hydrocarbon.
2.2. Solution
2.2.1. Step 1: Calculate the moles of CO2 and H2O
To begin, we need to convert the masses of the combustion products, CO2 and H2O, into moles. This conversion utilizes the molar masses of these compounds. The molar mass of CO2 is calculated as (12.01 g/mol for carbon + 2 * 16.00 g/mol for oxygen) = 44.01 g/mol. Similarly, the molar mass of H2O is (2 * 1.01 g/mol for hydrogen + 16.00 g/mol for oxygen) = 18.02 g/mol. Dividing the given masses by their respective molar masses yields the number of moles: Moles of CO2 = 176 g / 44.01 g/mol ≈ 4 moles Moles of H2O = 90 g / 18.02 g/mol ≈ 5 moles These values provide the foundation for determining the carbon and hydrogen content in the original hydrocarbon. The number of moles of CO2 directly corresponds to the number of moles of carbon in the hydrocarbon, while the moles of water provide the hydrogen content. This initial step is crucial for establishing the stoichiometry of the combustion reaction and ultimately, the hydrocarbon's molecular formula. Accurate calculation of moles is paramount, as it directly impacts the subsequent steps and the final result. Therefore, careful attention to detail and proper use of molar masses are essential for a successful analysis.
2.2.2. Step 2: Determine the moles of C and H in the hydrocarbon
From the mole calculations of CO2 and H2O, we can deduce the moles of carbon (C) and hydrogen (H) in the original hydrocarbon. Each mole of CO2 contains one mole of carbon, so the hydrocarbon contained 4 moles of carbon. Similarly, each mole of H2O contains two moles of hydrogen, meaning the hydrocarbon contained 5 moles H2O * 2 moles H/mole H2O = 10 moles of hydrogen. This direct relationship between the combustion products and the constituent elements of the hydrocarbon is a cornerstone of this analytical method. The conservation of mass dictates that all the carbon in the CO2 and all the hydrogen in the H2O must have originated from the hydrocarbon fuel. Therefore, the molar ratios of CO2 and H2O directly reflect the molar ratios of carbon and hydrogen in the original molecule. This step is critical for establishing the empirical formula, which represents the simplest whole-number ratio of elements in the compound. By accurately determining the moles of C and H, we lay the groundwork for constructing the empirical formula and ultimately, the molecular formula of the unknown hydrocarbon. The clarity and precision in this step are essential for avoiding errors and ensuring the correct identification of the hydrocarbon.
2.2.3. Step 3: Calculate the empirical formula
With the moles of carbon and hydrogen determined, we can now calculate the empirical formula of the hydrocarbon. The empirical formula represents the simplest whole-number ratio of atoms in a compound. To find this ratio, we divide the moles of each element by the smallest number of moles. In this case, we have 4 moles of carbon and 10 moles of hydrogen. Dividing both by 4 (the smaller value) gives us a ratio of 1 carbon to 2.5 hydrogens. Since empirical formulas require whole numbers, we multiply both subscripts by 2 to obtain the whole-number ratio: C2H5. This C2H5 represents the empirical formula of the hydrocarbon. It signifies that for every two carbon atoms, there are five hydrogen atoms in the simplest repeating unit of the molecule. However, it is crucial to remember that the empirical formula may not be the same as the molecular formula, which represents the actual number of atoms in a molecule. The empirical formula provides a starting point for determining the molecular formula, and further information, such as the molecular weight, is needed to complete the picture. The accurate determination of the empirical formula is a crucial step in the overall process, as it forms the basis for the final molecular formula determination.
2.2.4. Step 4: Determine the molecular weight of the hydrocarbon
The problem states that the relative density of the hydrocarbon with respect to air is 4. This information is crucial for determining the molecular weight of the hydrocarbon. Relative density is defined as the ratio of the density of the substance to the density of a reference substance, in this case, air. The average molecular weight of air is approximately 29 g/mol. Therefore, the molecular weight of the hydrocarbon can be calculated by multiplying the relative density by the molecular weight of air: Molecular weight = Relative density * Molecular weight of air Molecular weight = 4 * 29 g/mol = 116 g/mol This calculated molecular weight is a critical piece of information, as it allows us to bridge the gap between the empirical formula and the true molecular formula. The molecular weight represents the mass of one mole of the hydrocarbon molecules, while the empirical formula mass represents the mass of one mole of the simplest repeating unit. By comparing these two values, we can determine how many empirical formula units are present in a single molecule of the hydrocarbon. This step is essential for resolving any ambiguity arising from the empirical formula and arriving at the unique molecular formula that accurately represents the hydrocarbon's composition. Therefore, the accurate determination of the molecular weight using the relative density is a key step in the overall process.
2.2.5. Step 5: Calculate the molecular formula
Now, we have the empirical formula (C2H5) and the molecular weight (116 g/mol). To determine the molecular formula, we need to find the ratio between the molecular weight and the empirical formula mass. The empirical formula mass is calculated as (2 * 12.01 g/mol for carbon + 5 * 1.01 g/mol for hydrogen) ≈ 29 g/mol. Dividing the molecular weight by the empirical formula mass gives us the number of empirical formula units in the molecule: n = Molecular weight / Empirical formula mass n = 116 g/mol / 29 g/mol = 4 This result indicates that the molecular formula is four times the empirical formula. Therefore, we multiply the subscripts in the empirical formula (C2H5) by 4 to obtain the molecular formula: C8H20. This C8H20 represents the actual number of carbon and hydrogen atoms in a single molecule of the hydrocarbon. The molecular formula provides a complete and accurate representation of the hydrocarbon's composition, allowing us to identify the compound and predict its properties. This final step in the calculation process demonstrates the power of combining experimental data (combustion analysis, relative density) with stoichiometric principles to unveil the molecular structure of an unknown compound. The accurate determination of the molecular formula is the culmination of a series of careful calculations and logical deductions, highlighting the elegance and precision of chemical analysis.
2.3. Answer
The molecular formula of the hydrocarbon is C8H20.
3. Problem 2: Determining the Molecular Formula from Mass Percentage of Carbon
3.1. Problem Statement
Find the molecular formula of a hydrocarbon in which the mass fraction of carbon is 82.76% and the relative molecular weight is 58.
3.2. Solution
3.2.1. Step 1: Determine the mass percentage of hydrogen
In any hydrocarbon, the only elements present are carbon and hydrogen. Therefore, the mass percentages of carbon and hydrogen must add up to 100%. Given that the mass percentage of carbon is 82.76%, we can calculate the mass percentage of hydrogen by subtracting the carbon percentage from 100%: Mass percentage of hydrogen = 100% - Mass percentage of carbon Mass percentage of hydrogen = 100% - 82.76% = 17.24% This simple subtraction is a crucial first step, as it provides the complete elemental composition of the hydrocarbon in terms of mass percentages. Knowing the mass percentages of both carbon and hydrogen allows us to determine the ratio of atoms in the compound and ultimately, the empirical and molecular formulas. This step highlights the fundamental principle of conservation of mass, ensuring that all elements present in the compound are accounted for. The accurate determination of the hydrogen mass percentage is essential for the subsequent calculations and the final determination of the hydrocarbon's molecular formula.
3.2.2. Step 2: Calculate the mole ratio of C and H
To determine the mole ratio of carbon and hydrogen, we need to convert the mass percentages into moles. This conversion requires dividing the mass percentage of each element by its respective atomic weight. The atomic weight of carbon is approximately 12.01 g/mol, and the atomic weight of hydrogen is approximately 1.01 g/mol. Let's assume we have 100 grams of the hydrocarbon. This simplifies the calculations, as the mass percentages directly translate to grams. Moles of carbon = (Mass of carbon / Atomic weight of carbon) = (82.76 g / 12.01 g/mol) ≈ 6.89 moles Moles of hydrogen = (Mass of hydrogen / Atomic weight of hydrogen) = (17.24 g / 1.01 g/mol) ≈ 17.07 moles These mole values represent the relative amounts of carbon and hydrogen atoms in the hydrocarbon. To express this relationship in the simplest whole-number ratio, we proceed to the next step, where we determine the empirical formula. Accurate conversion of mass percentages to moles is a critical step in the process, as it forms the basis for establishing the stoichiometry of the compound and ultimately, its molecular formula. Careful attention to atomic weights and proper calculation techniques are essential for ensuring the accuracy of the results.
3.2.3. Step 3: Determine the empirical formula
Now that we have the moles of carbon (6.89 moles) and hydrogen (17.07 moles), we can determine the empirical formula. The empirical formula represents the simplest whole-number ratio of atoms in a compound. To find this ratio, we divide the moles of each element by the smallest number of moles. In this case, we divide both values by 6.89: Ratio of C = 6.89 moles / 6.89 moles = 1 Ratio of H = 17.07 moles / 6.89 moles ≈ 2.48 Since we need whole numbers for the empirical formula, we can round 2.48 to 2.5. To eliminate the decimal, we multiply both subscripts by 2, resulting in an empirical formula of C2H5. This C2H5 signifies that for every two carbon atoms, there are five hydrogen atoms in the simplest repeating unit of the molecule. However, it's important to remember that the empirical formula may not be the same as the molecular formula, which represents the actual number of atoms in a molecule. The empirical formula serves as a stepping stone towards determining the molecular formula, and additional information, such as the molecular weight, is needed to complete the picture. The accurate determination of the empirical formula is a crucial step in the overall process, as it lays the foundation for the final molecular formula determination.
3.2.4. Step 4: Calculate the molecular formula
We have the empirical formula (C2H5) and the relative molecular weight (58). To determine the molecular formula, we need to find the ratio between the molecular weight and the empirical formula mass. The empirical formula mass is calculated as (2 * 12.01 g/mol for carbon + 5 * 1.01 g/mol for hydrogen) ≈ 29 g/mol. Dividing the molecular weight by the empirical formula mass gives us the number of empirical formula units in the molecule: n = Molecular weight / Empirical formula mass n = 58 g/mol / 29 g/mol = 2 This result indicates that the molecular formula is two times the empirical formula. Therefore, we multiply the subscripts in the empirical formula (C2H5) by 2 to obtain the molecular formula: C4H10. This C4H10 represents the actual number of carbon and hydrogen atoms in a single molecule of the hydrocarbon. The molecular formula provides a complete and accurate representation of the hydrocarbon's composition, allowing us to identify the compound and predict its properties. This final step in the calculation process demonstrates the power of combining compositional data (mass percentage) with molecular weight information to unveil the molecular structure of an unknown compound. The accurate determination of the molecular formula is the culmination of a series of careful calculations and logical deductions, highlighting the elegance and precision of chemical analysis.
3.3. Answer
The molecular formula of the hydrocarbon is C4H10.
4. Conclusion: The Significance of Molecular Formulas
In conclusion, determining the molecular formula of a hydrocarbon is a cornerstone skill in chemistry, providing essential insights into the composition and structure of these fundamental compounds. By combining experimental data, such as combustion analysis results or mass percentages, with stoichiometric principles and molecular weight information, we can unravel the molecular makeup of these compounds. The examples presented illustrate the methodical approach required, involving careful calculations, logical deductions, and a thorough understanding of chemical concepts.
The molecular formula is far more than just a collection of symbols and subscripts; it is a powerful representation of a molecule's identity and its potential to interact with other substances. It serves as a blueprint for understanding a compound's properties, predicting its behavior in chemical reactions, and even designing new molecules with specific functions. In essence, the ability to determine molecular formulas empowers us to decipher the language of molecules, opening doors to a deeper understanding of the chemical world around us.
From the simplest hydrocarbons to the most complex organic molecules, the molecular formula remains a crucial piece of information. It is a fundamental concept that underpins countless applications in chemistry, from the development of new materials to the synthesis of life-saving drugs. Mastering the techniques for determining molecular formulas is therefore an invaluable skill for any aspiring chemist, researcher, or anyone seeking to explore the fascinating realm of molecular structure and composition.
In the grand tapestry of chemistry, hydrocarbons hold a prominent position, serving as the building blocks of countless organic compounds. Their molecular formulas are the key to unlocking their secrets, allowing us to understand their properties, predict their behavior, and harness their potential for various applications. As we continue to explore the vast landscape of chemical knowledge, the ability to determine molecular formulas will undoubtedly remain a cornerstone skill, guiding us towards new discoveries and a deeper appreciation of the molecular world.