Determining Molecular Formula Of A Hydrocarbon Compound

Jul 10, 2025 by ADMIN 56 views

Unveiling the Molecular Formula of a Hydrocarbon Compound: A Step-by-Step Guide

#mainkeyword Determining the molecular formula of an unknown compound is a fundamental task in chemistry. This article will guide you through a detailed, step-by-step solution to find the molecular formula of a compound containing only carbon and hydrogen, given its elemental composition and molar mass. We'll break down the problem, providing clear explanations and calculations, ensuring you grasp every concept along the way. This comprehensive approach aims to equip you with the skills to tackle similar problems confidently and effectively.

Problem Statement

We are tasked with finding the mainkeyword molecular formula of a compound composed solely of carbon and hydrogen. We know that it is 85.6% carbon by mass, and it has a molar mass of 70 g/mol. The multiple-choice options provided are:

A. $CH_2$ B. $C_5H_{10}$ C. $C_5H_5$ D. $C_4H_{21}$

Step 1: Calculate the Mass Percent of Hydrogen

Since the compound contains only carbon and hydrogen, the percentages of these two elements must add up to 100%. We are given that carbon constitutes 85.6% of the compound's mass. Therefore, we can calculate the percentage of hydrogen as follows:

% Hydrogen = 100% - % Carbon % Hydrogen = 100% - 85.6% % Hydrogen = 14.4%

This initial calculation is crucial as it sets the stage for determining the relative amounts of each element within the compound. Understanding the mass percentages allows us to proceed to the next step: converting these percentages into grams, which will then allow us to determine the mole ratios.

Step 2: Assume a 100g Sample and Convert Percentages to Grams

To simplify calculations, let's assume we have a 100g sample of the compound. This assumption makes it straightforward to convert percentages into grams. The mass of carbon in the sample is 85.6g, and the mass of hydrogen is 14.4g. This conversion is a common technique in stoichiometry problems because it allows us to work with tangible masses, which we can then convert to moles using molar masses.

By assuming a 100g sample, we effectively transform the percentages into masses, making the subsequent calculations much easier to handle. This is a standard practice and a valuable tool in your problem-solving arsenal.

Step 3: Convert Grams to Moles

To determine the empirical formula, we need to convert the mass of each element to moles. We use the molar masses of carbon (approximately 12.01 g/mol) and hydrogen (approximately 1.01 g/mol) for this conversion.

Moles of Carbon = (Mass of Carbon) / (Molar Mass of Carbon) Moles of Carbon = 85.6 g / 12.01 g/mol Moles of Carbon ≈ 7.13 moles

Moles of Hydrogen = (Mass of Hydrogen) / (Molar Mass of Hydrogen) Moles of Hydrogen = 14.4 g / 1.01 g/mol Moles of Hydrogen ≈ 14.26 moles

Converting grams to moles is a crucial step because it allows us to compare the relative number of atoms of each element in the compound. The mole is the SI unit for the amount of a substance, and it directly relates to the number of particles (atoms, molecules, etc.). This conversion is essential for determining the simplest whole-number ratio of the elements, which is the basis of the empirical formula.

Step 4: Determine the Empirical Formula

The empirical formula represents the simplest whole-number ratio of atoms in the compound. To find this ratio, we divide the number of moles of each element by the smallest number of moles calculated. In this case, the smallest number of moles is 7.13 (moles of carbon).

Ratio of Carbon = (Moles of Carbon) / 7.13 Ratio of Carbon = 7.13 / 7.13 Ratio of Carbon ≈ 1

Ratio of Hydrogen = (Moles of Hydrogen) / 7.13 Ratio of Hydrogen = 14.26 / 7.13 Ratio of Hydrogen ≈ 2

Therefore, the empirical formula of the compound is $CH_2$ . This means that for every carbon atom, there are two hydrogen atoms in the simplest ratio. The empirical formula is a crucial stepping stone to finding the mainkeyword molecular formula, as it provides the basic building block of the compound's structure.

Step 5: Calculate the Molar Mass of the Empirical Formula

To find the mainkeyword molecular formula, we need to compare the molar mass of the empirical formula with the given molar mass of the compound (70 g/mol). The molar mass of the empirical formula ( $CH_2$ ) is calculated by adding the atomic masses of one carbon atom and two hydrogen atoms:

Molar Mass of $CH_2$ = (1 × Molar Mass of Carbon) + (2 × Molar Mass of Hydrogen) Molar Mass of $CH_2$ = (1 × 12.01 g/mol) + (2 × 1.01 g/mol) Molar Mass of $CH_2$ ≈ 14.03 g/mol

This calculation is necessary to determine how many empirical formula units make up one molecule of the compound. By comparing the empirical formula mass to the given molar mass, we can find the multiplier needed to convert the empirical formula to the mainkeyword molecular formula.

Step 6: Determine the Multiplication Factor

We divide the given molar mass of the compound (70 g/mol) by the molar mass of the empirical formula (14.03 g/mol) to find the multiplication factor:

Multiplication Factor = (Molar Mass of Compound) / (Molar Mass of Empirical Formula) Multiplication Factor = 70 g/mol / 14.03 g/mol Multiplication Factor ≈ 5

This factor tells us how many times the empirical formula unit is repeated in the actual molecule. It's a critical value because it allows us to scale up the empirical formula to the mainkeyword molecular formula, which represents the actual number of atoms of each element in a single molecule of the compound.

Step 7: Calculate the Molecular Formula

Multiply the subscripts in the empirical formula ( $CH_2$ ) by the multiplication factor (5) to obtain the mainkeyword molecular formula:

$C_{1×5}H_{2×5} = C_5H_{10}$

Therefore, the mainkeyword molecular formula of the compound is $C_5H_{10}$ . This means that each molecule of the compound contains 5 carbon atoms and 10 hydrogen atoms. This final step synthesizes all the previous calculations and provides the definitive answer to the problem.

Step 8: Verify the Answer

Let's verify our answer by calculating the molar mass of $C_5H_{10}$ :

Molar Mass of $C_5H_{10}$ = (5 × Molar Mass of Carbon) + (10 × Molar Mass of Hydrogen) Molar Mass of $C_5H_{10}$ = (5 × 12.01 g/mol) + (10 × 1.01 g/mol) Molar Mass of $C_5H_{10}$ = 60.05 g/mol + 10.1 g/mol Molar Mass of $C_5H_{10}$ ≈ 70.15 g/mol

This result is very close to the given molar mass of 70 g/mol, confirming that our calculated mainkeyword molecular formula is correct. This step is crucial for ensuring the accuracy of our result and for solidifying our understanding of the problem-solving process. Always verify your answer if possible, as it provides a valuable check on your calculations and reasoning.

Conclusion

Through a systematic, step-by-step approach, we have successfully determined that the mainkeyword molecular formula of the compound is $C_5H_{10}$ . This process involved converting percentages to masses, masses to moles, finding the empirical formula, and then using the molar mass to find the mainkeyword molecular formula. This methodology is applicable to a wide range of similar problems in chemistry. Understanding these steps and practicing them will build your confidence and skill in solving chemical formulas. Option B, $C_5H_{10}$ , is the correct answer.