Determine Molecular Formula Of A Compound With Copper And Sulfur

Introduction

In chemistry, determining the molecular formula of a compound is a fundamental task that helps us understand its composition and properties. This article will delve into the process of finding the molecular formula of a compound with a molar mass of 159, which contains 39.62% copper (Cu) and 20.19% sulfur (S). By utilizing the given atomic masses (Cu = 63, S = 32, O = 16) and the percentage composition, we can systematically deduce the compound's molecular formula. Understanding the molecular formula is crucial as it provides insights into the number of atoms of each element present in a molecule of the compound. This information is essential for predicting the compound's chemical behavior, its interactions with other substances, and its role in various chemical reactions. The empirical formula, which represents the simplest whole-number ratio of atoms in a compound, is a key intermediate step in determining the molecular formula. Once the empirical formula is established, we can compare its formula mass to the molar mass of the compound to find the multiplier needed to obtain the molecular formula. This process involves several steps, including calculating the mass percentages, converting them to moles, finding the simplest mole ratio, and finally, determining the molecular formula. Let's embark on this step-by-step journey to unravel the molecular identity of our compound, ensuring a comprehensive understanding along the way. The ability to determine molecular formulas is not only vital for academic purposes but also holds significant importance in various industries, including pharmaceuticals, materials science, and environmental chemistry, where the precise knowledge of chemical compositions is paramount for research, development, and quality control.

Step 1: Calculate the Percentage of Oxygen

To begin determining the molecular formula, we first need to ascertain the percentage of oxygen (O) in the compound. Given that the compound contains only copper, sulfur, and oxygen, the percentages of these elements must add up to 100%. Therefore, we can calculate the percentage of oxygen by subtracting the percentages of copper and sulfur from 100%. This initial step is crucial as it completes the elemental composition data required for further calculations. Oxygen, being a highly reactive element, often combines with various metals and non-metals to form compounds with diverse properties. In this particular case, knowing the precise percentage of oxygen will enable us to determine its molar contribution in the compound and subsequently its stoichiometric relationship with copper and sulfur. The percentage calculation ensures that we have a complete picture of the compound's elemental makeup, which is a prerequisite for accurately determining its empirical and molecular formulas. This step underscores the importance of meticulous data collection and accurate calculations in chemistry, where even minor errors in elemental percentages can lead to significant discrepancies in the final formula. Therefore, we proceed with the calculation, ensuring that the result is consistent with the principles of mass conservation and elemental stoichiometry. The accuracy of this step will directly impact the reliability of subsequent calculations, emphasizing its critical role in the overall determination of the molecular formula.

Percentage of Oxygen = 100% - (Percentage of Copper + Percentage of Sulfur)

Percentage of Oxygen = 100% - (39.62% + 20.19%)

Percentage of Oxygen = 100% - 59.81%

Percentage of Oxygen = 40.19%

Step 2: Determine the Mole Ratio

With the percentages of all elements (copper, sulfur, and oxygen) now known, the next crucial step is to convert these percentages into moles. To do this, we assume that we have 100 grams of the compound. This assumption simplifies the calculation because the percentages directly translate into grams. For instance, 39.62% copper means we have 39.62 grams of copper in 100 grams of the compound. We then divide the mass of each element by its respective atomic mass to obtain the number of moles. This conversion is based on the fundamental principle that one mole of any element has a mass equal to its atomic mass in grams. The number of moles provides a quantitative measure of the amount of each element present in the compound, which is essential for determining the empirical formula. The atomic masses of copper, sulfur, and oxygen are approximately 63 g/mol, 32 g/mol, and 16 g/mol, respectively. By performing this conversion, we move from mass percentages to a molar ratio, which reflects the relative number of atoms of each element in the compound. This step is critical because chemical formulas are based on the number of atoms, not mass percentages. The mole concept serves as a bridge between the macroscopic world of grams and the microscopic world of atoms and molecules, allowing us to make quantitative connections between the mass of a substance and the number of particles it contains. Therefore, the accurate conversion of mass percentages to moles is a foundational step in the determination of the empirical and molecular formulas.

• Moles of Copper (Cu) = (39.62 g) / (63 g/mol) ≈ 0.629 moles
• Moles of Sulfur (S) = (20.19 g) / (32 g/mol) ≈ 0.631 moles
• Moles of Oxygen (O) = (40.19 g) / (16 g/mol) ≈ 2.512 moles

Step 3: Find the Simplest Whole Number Ratio

After calculating the moles of each element, the next critical step is to determine the simplest whole number ratio of these moles. This ratio will give us the empirical formula, which represents the smallest 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 approximately 0.629 (moles of copper). This normalization process helps to express the relative amounts of each element in the simplest terms, making it easier to identify the empirical formula. It is essential to perform this division accurately, as any error at this stage will propagate through the subsequent steps and lead to an incorrect empirical and, consequently, molecular formula. The resulting ratios may not be whole numbers initially, but they should be close enough that they can be rounded to the nearest whole number or multiplied by a common factor to obtain whole numbers. If the ratios are not close to whole numbers, we may need to multiply all ratios by a small integer to convert them into whole numbers. This step is a crucial bridge between the molar quantities we calculated and the whole-number subscripts in the empirical formula, reflecting the fundamental nature of chemical compounds as combinations of atoms in fixed, discrete ratios. By determining the simplest whole number ratio, we effectively distill the essential compositional information from the molar quantities, paving the way for the final determination of the compound's molecular identity.

• Ratio of Cu = (0.629 moles) / (0.629 moles) ≈ 1
• Ratio of S = (0.631 moles) / (0.629 moles) ≈ 1
• Ratio of O = (2.512 moles) / (0.629 moles) ≈ 4

Step 4: Determine the Empirical Formula

Based on the simplest whole number ratio calculated in the previous step, we can now deduce the empirical formula of the compound. The ratios of the elements (Cu:S:O) are approximately 1:1:4. This means that for every one atom of copper and one atom of sulfur, there are four atoms of oxygen in the simplest unit of the compound. The empirical formula, therefore, is CuSO₄. The empirical formula is a fundamental concept in chemistry, providing the simplest representation of the elemental composition of a compound. It serves as a crucial stepping stone towards determining the molecular formula, which gives the actual number of atoms of each element present in a molecule of the compound. Understanding the empirical formula is essential for characterizing unknown substances and for predicting their chemical properties and behavior. It is also vital in stoichiometry, where it is used to calculate the amounts of reactants and products involved in chemical reactions. The process of determining the empirical formula highlights the importance of accurate experimental data and precise calculations. Any errors in the initial percentage composition or in the subsequent mole calculations can lead to an incorrect empirical formula, underscoring the need for careful and methodical analysis. The empirical formula CuSO₄ suggests that the compound is likely an ionic compound, given the common valencies of copper, sulfur, and oxygen. This preliminary identification provides valuable insights into the compound's potential chemical reactivity and physical properties.

The empirical formula for the compound is CuSO₄.

Step 5: Calculate the Empirical Formula Mass

Having determined the empirical formula (CuSO₄), the next essential step is to calculate its formula mass. The formula mass is the sum of the atomic masses of all the atoms in the empirical formula. This calculation is crucial because it provides a reference point for determining the molecular formula. We use the given atomic masses of copper (Cu = 63), sulfur (S = 32), and oxygen (O = 16) to perform this calculation. The empirical formula mass represents the mass of the simplest repeating unit of the compound and is a key value in relating the empirical formula to the molar mass of the compound. This step underscores the significance of understanding atomic masses and their role in determining the mass of molecules and compounds. The accurate calculation of the empirical formula mass is a prerequisite for correctly determining the molecular formula, as any error here will propagate through the final calculation. The formula mass is expressed in atomic mass units (amu) or grams per mole (g/mol), and it provides a quantitative measure of the mass of the empirical unit. This calculation is not only a necessary step in determining the molecular formula but also reinforces the fundamental principles of stoichiometry and the conservation of mass in chemical compounds. By calculating the empirical formula mass, we establish a critical link between the empirical formula and the molar mass, paving the way for the final determination of the compound's molecular identity.

Empirical Formula Mass of CuSO₄ = (1 × Atomic mass of Cu) + (1 × Atomic mass of S) + (4 × Atomic mass of O)

Empirical Formula Mass of CuSO₄ = (1 × 63) + (1 × 32) + (4 × 16)

Empirical Formula Mass of CuSO₄ = 63 + 32 + 64

Empirical Formula Mass of CuSO₄ = 159

Step 6: Determine the Molecular Formula

The final step in determining the molecular formula involves comparing the empirical formula mass to the given molar mass of the compound. The molar mass (159) represents the mass of one mole of the compound, while the empirical formula mass (159) represents the mass of one empirical unit. By dividing the molar mass by the empirical formula mass, we obtain a whole number that indicates how many empirical units are present in one molecule of the compound. This multiplier is crucial for scaling up the empirical formula to the molecular formula, which accurately reflects the number of atoms of each element in a single molecule. In this case, the molar mass and the empirical formula mass are equal, which simplifies the process significantly. This equality implies that the empirical formula and the molecular formula are the same, meaning that the simplest ratio of atoms in the compound is also the actual ratio in a molecule. This outcome highlights the importance of the relationship between the empirical and molecular formulas, which are fundamental concepts in chemical stoichiometry. The molecular formula provides a complete and accurate representation of the compound's composition, which is essential for understanding its chemical properties and behavior. By determining the molecular formula, we finalize our analysis and gain a comprehensive understanding of the compound's molecular identity.

To find the molecular formula, we divide the molar mass by the empirical formula mass:

Multiplier = (Molar Mass) / (Empirical Formula Mass)

Multiplier = (159) / (159)

Multiplier = 1

Since the multiplier is 1, the molecular formula is the same as the empirical formula.

Conclusion

In conclusion, by meticulously following the steps outlined above, we have successfully determined the molecular formula of the compound. The initial step involved calculating the percentage of oxygen in the compound, followed by converting the percentages of each element to moles. We then found the simplest whole number ratio of the elements, which led us to the empirical formula. The empirical formula mass was calculated, and finally, by comparing the molar mass to the empirical formula mass, we determined the multiplier needed to obtain the molecular formula. In this specific case, the multiplier was 1, indicating that the empirical formula and the molecular formula are the same. Therefore, the molecular formula of the compound is CuSO₄. This process underscores the importance of systematic problem-solving in chemistry, where each step builds upon the previous one to arrive at a meaningful conclusion. The ability to determine molecular formulas is a fundamental skill for chemists, allowing them to identify and characterize unknown substances. The accurate determination of molecular formulas is crucial in various fields, including pharmaceuticals, materials science, and environmental chemistry, where the precise knowledge of chemical compositions is essential for research, development, and quality control. By mastering these techniques, we gain a deeper understanding of the molecular world and its fundamental principles.

The molecular formula for the compound is CuSO₄.