Determining Empirical Formula Of Compound With Na, C, And O

Introduction: Understanding Empirical Formulas

In the fascinating realm of chemistry, one of the fundamental concepts is the empirical formula. This formula represents the simplest whole-number ratio of atoms of each element present in a compound. Determining the empirical formula is a crucial step in characterizing a substance and understanding its composition. This article delves into a specific problem, problem 23 of 26, which challenges us to find the empirical formula of a compound containing sodium (Na), carbon (C), and oxygen (O). We are given the molar amounts of each element and tasked with unraveling the mystery of their simplest combination. Understanding this process is vital for anyone studying chemistry, as it lays the groundwork for more complex stoichiometric calculations and compound identification. The ability to decipher the empirical formula from molar ratios is a cornerstone skill in the chemist's toolkit. This article will not only walk you through the solution to this specific problem but also reinforce the underlying principles, ensuring you can confidently tackle similar challenges in the future. We will explore each step meticulously, highlighting the logic behind the calculations and emphasizing the importance of accuracy in chemical stoichiometry.

Problem Statement: Deciphering the Compound's Composition

The core of this problem lies in deciphering the composition of a compound. We are presented with a compound that contains three essential elements: sodium (Na), carbon (C), and oxygen (O). The challenge is that we don't know the exact number of atoms of each element in the compound's formula. Instead, we are provided with the molar amounts of each element present: 1.06 mol of Na, 0.528 mol of C, and 1.59 mol of O. Molar amounts are a chemist's way of quantifying the number of atoms or molecules, using the concept of the mole, which represents a fixed number of particles (Avogadro's number, approximately 6.022 x 10^23). These molar amounts hold the key to unlocking the compound's empirical formula. The empirical formula, as mentioned earlier, provides the simplest whole-number ratio of the elements in the compound. Our mission is to convert these seemingly disparate molar amounts into a clear, concise chemical formula. This conversion involves a series of steps, including finding the smallest whole-number ratio by dividing by the smallest mole value and, if necessary, multiplying by a factor to obtain integers. By carefully following this process, we can reveal the hidden composition of the compound and express it in its most fundamental form.

Solution Breakdown: Step-by-Step Calculation

To solve this problem and determine the empirical formula, we embark on a step-by-step journey that transforms the given molar amounts into the simplest whole-number ratio. The first crucial step involves recognizing the given information: we have 1.06 moles of Na, 0.528 moles of C, and 1.59 moles of O. These values represent the relative amounts of each element in the compound, but they are not yet in a format that directly translates to the empirical formula. The next step is to normalize these molar amounts by dividing each by the smallest molar amount present. This crucial step provides a relative ratio between the elements. In this case, 0.528 moles of carbon is the smallest amount. Dividing each molar amount by 0.528, we get: Na: 1.06 / 0.528 ≈ 2.01, C: 0.528 / 0.528 = 1, O: 1.59 / 0.528 ≈ 3.01. These resulting numbers, 2.01, 1, and 3.01, represent the approximate ratio of Na, C, and O atoms in the compound. However, empirical formulas require whole numbers, so the final step involves rounding these values to the nearest whole number. In this case, 2.01 rounds to 2, 1 remains 1, and 3.01 rounds to 3. Thus, the simplest whole-number ratio of Na:C:O is 2:1:3, which directly translates to the empirical formula.

Detailed Calculation Steps

To reiterate the calculation steps with even greater clarity, let's delve into the nitty-gritty details. We begin with the molar amounts: 1.06 mol Na, 0.528 mol C, and 1.59 mol O. The primary objective is to convert these molar amounts into a ratio that represents the subscripts in the empirical formula. To achieve this, we identify the smallest molar amount, which is 0.528 mol of C. Dividing each molar amount by 0.528 mol serves as the normalization process, effectively setting the ratio relative to carbon. For sodium, we have 1.06 mol Na / 0.528 mol ≈ 2.0075. For carbon, it's straightforward: 0.528 mol C / 0.528 mol = 1. For oxygen, we calculate 1.59 mol O / 0.528 mol ≈ 3.0114. At this stage, we have the ratios 2.0075:1:3.0114 for Na:C:O. However, since empirical formulas demand whole numbers, we round these values to the nearest whole numbers. 2.0075 becomes 2, 1 remains 1, and 3.0114 rounds to 3. This rounding gives us the whole-number ratio of 2:1:3, which directly corresponds to the subscripts in the empirical formula. This meticulous step-by-step calculation ensures accuracy and eliminates ambiguity in determining the empirical formula.

Final Result: The Empirical Formula Unveiled

After carefully executing the calculations, we arrive at the final result: the empirical formula of the compound. The simplest whole-number ratio of Na:C:O is 2:1:3. This ratio translates directly into the empirical formula, which is Na2CO3. This formula signifies that, in the simplest representation of the compound, there are two sodium atoms, one carbon atom, and three oxygen atoms. It's important to recognize that the empirical formula represents the simplest ratio, not necessarily the actual molecular formula of the compound. The molecular formula could be a multiple of the empirical formula (e.g., Na4C2O6), but without further information, the empirical formula is the most accurate representation we can derive from the given data. The empirical formula Na2CO3 is commonly known as sodium carbonate, a widely used chemical compound with various applications, including in the production of glass, detergents, and as a food additive. Thus, by meticulously analyzing the molar amounts of each element, we have successfully determined the empirical formula of the compound, shedding light on its fundamental composition.

Conclusion: Significance of Empirical Formula Determination

In conclusion, solving problem 23 of 26 has provided a valuable exercise in determining the empirical formula of a compound. We started with the molar amounts of each element—sodium, carbon, and oxygen—and systematically transformed this data into the simplest whole-number ratio, ultimately revealing the empirical formula as Na2CO3. This process highlights the significance of empirical formulas in chemistry. Empirical formulas serve as a foundational concept for understanding the composition of chemical compounds. They provide the most basic representation of the ratio of elements within a compound, acting as a crucial stepping stone for further chemical analysis and calculations. The ability to determine empirical formulas is essential for identifying unknown substances, predicting chemical reactions, and understanding the stoichiometry of compounds. Furthermore, this exercise reinforces the importance of careful calculations and attention to detail in chemistry. From dividing by the smallest molar amount to rounding to the nearest whole number, each step plays a critical role in achieving an accurate result. Mastering the techniques involved in empirical formula determination equips chemists with a powerful tool for unraveling the mysteries of the molecular world. The knowledge gained from this problem can be applied to a wide range of chemical contexts, making it a vital skill for any aspiring chemist.

Answer

The correct answer is B. Na2CO3.