Empirical Formula Calculation Step-by-Step Guide
The empirical formula represents the simplest whole-number ratio of atoms in a compound. Determining the empirical formula is a fundamental skill in chemistry, essential for identifying and characterizing chemical substances. In this comprehensive guide, we will walk you through the process of calculating the empirical formula, using a specific example to illustrate each step. This detailed exploration ensures a solid grasp of the underlying principles, making it easier to tackle similar problems with confidence. By understanding empirical formulas, chemists can deduce the fundamental composition of substances, which is crucial in various applications such as materials science, drug discovery, and environmental chemistry.
To begin, let's consider the question at hand: A 152.0 g sample of a compound contains 48.0 g of carbon ($C$), 8.0 g of hydrogen ($H$), and 96.0 g of oxygen ($O$). Our goal is to determine the empirical formula of this compound. This involves several key steps, each building upon the previous one to ultimately reveal the simplest ratio of elements present. The initial step is to convert the given masses of each element into moles. Moles provide a common unit that allows us to compare the relative amounts of different elements. This conversion is performed using the molar mass of each element, which can be found on the periodic table. Once we have the number of moles for each element, we can then identify the smallest mole value and divide each mole quantity by this value. This process normalizes the mole ratios, providing us with a set of simple ratios. If these ratios are not whole numbers, we must multiply them by a common factor to obtain whole numbers, ensuring that the final formula represents a realistic chemical composition. The whole-number ratios then serve as the subscripts in the empirical formula, giving us the simplest ratio of elements in the compound.
Step 1 Convert Grams to Moles
The first crucial step in determining the empirical formula is to convert the mass of each element from grams to moles. Moles are the standard unit of measurement for the amount of a substance in chemistry, and they allow us to compare the relative numbers of atoms of each element in the compound. To perform this conversion, we use the molar mass of each element, which can be found on the periodic table. The molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol).
For carbon ($C$), the molar mass is approximately 12.01 g/mol. To find the number of moles of carbon in the sample, we divide the mass of carbon (48.0 g) by its molar mass:
For hydrogen ($H$), the molar mass is approximately 1.008 g/mol. The number of moles of hydrogen is calculated as follows:
For oxygen ($O$), the molar mass is approximately 16.00 g/mol. The number of moles of oxygen is calculated as follows:
These calculations provide us with the number of moles of each element in the compound. The mole values represent the relative amounts of each element, but they are not yet in the simplest whole-number ratio. The next step involves normalizing these values to find that simplest ratio, which is essential for determining the empirical formula. This conversion to moles is a critical foundation for the subsequent steps, as it translates the given mass data into a form that can be directly related to the atomic composition of the compound. Ensuring accuracy in these initial calculations is vital for the final result.
Step 2 Determine the Simplest Mole Ratio
After converting the mass of each element to moles, the next step in determining the empirical formula is to find the simplest mole ratio. This involves identifying the smallest number of moles among the elements and dividing the number of moles of each element by this smallest value. This process normalizes the mole values, providing a set of ratios that represent the relative number of atoms in the simplest possible terms.
From the previous calculations, we have:
- Moles of Carbon ($C$): approximately 3.997 mol
- Moles of Hydrogen ($H$): approximately 7.937 mol
- Moles of Oxygen ($O$): 6.0 mol
Comparing these values, we see that the smallest number of moles is approximately 3.997 mol (Carbon). Now, we divide the number of moles of each element by this smallest value:
The resulting ratios are approximately 1 for carbon, 1.986 for hydrogen, and 1.501 for oxygen. These ratios indicate the relative number of atoms of each element in the compound. However, empirical formulas require whole numbers, so we need to convert these ratios into whole numbers. The next step addresses this conversion by multiplying the ratios by a common factor. This ensures that we maintain the proper proportions while expressing the formula in its simplest whole-number form.
Step 3 Convert to Whole Numbers
Having determined the initial mole ratios, the next crucial step in finding the empirical formula involves converting these ratios into whole numbers. Empirical formulas, by definition, represent the simplest whole-number ratio of atoms in a compound. The ratios obtained in the previous step might not be whole numbers, so we need to manipulate them to achieve integer values while maintaining their relative proportions. This usually involves multiplying all the ratios by a common factor.
From the previous step, we have the following mole ratios:
- Carbon ($C$): approximately 1
- Hydrogen ($H$): approximately 1.986
- Oxygen ($O$): approximately 1.501
The ratio for carbon is already a whole number (1), but the ratios for hydrogen (1.986) and oxygen (1.501) are not. We need to find a common factor that, when multiplied by these ratios, will yield whole numbers. Looking at the ratios, 1.501 suggests multiplying by 2, as 1.5 multiplied by 2 gives 3. Let's try multiplying all the ratios by 2:
- Carbon ($C$): $1 \times 2 = 2$
- Hydrogen ($H$): $1.986 \times 2 \approx 3.972 \approx 4$
- Oxygen ($O$): $1.501 \times 2 \approx 3$
After multiplying by 2, the ratios become approximately 2 for carbon, 4 for hydrogen, and 3 for oxygen. These values are now very close to whole numbers, and we can reasonably round 3.972 to 4. Thus, we have achieved the goal of converting the mole ratios into whole numbers. These whole-number ratios now represent the subscripts in the empirical formula, giving us the simplest ratio of elements in the compound.
With the whole-number ratios now established, we can finally determine the empirical formula of the compound. The whole-number ratios of the elements directly correspond to the subscripts in the empirical formula. These subscripts indicate the simplest ratio of atoms in the compound.
From the previous steps, we have found the following whole-number ratios:
- Carbon ($C$): 2
- Hydrogen ($H$): 4
- Oxygen ($O$): 3
These ratios tell us that for every 2 atoms of carbon, there are 4 atoms of hydrogen and 3 atoms of oxygen in the compound. Therefore, the empirical formula is formed by using these numbers as subscripts for the respective elements:
This formula represents the simplest whole-number ratio of carbon, hydrogen, and oxygen atoms in the compound. It does not necessarily indicate the actual number of atoms in a molecule of the compound (which would be represented by the molecular formula), but it provides the most basic proportion of elements. Understanding and calculating the empirical formula is crucial in chemistry for identifying and characterizing substances, and it forms the basis for further analysis and determination of molecular formulas. The process involves careful conversion of masses to moles, finding mole ratios, and converting those ratios to whole numbers, ultimately leading to the empirical formula.
Answer
Based on our calculations, the empirical formula of the compound is:
B. $C_2H_4O_3$
In conclusion, determining the empirical formula of a compound is a fundamental skill in chemistry that involves a series of logical steps. Starting from the given masses of the elements, we converted these masses to moles using the molar masses from the periodic table. This conversion is crucial because moles provide a common unit for comparing the amounts of different elements. Once we had the mole values, we identified the smallest one and divided all mole values by it. This normalization process gave us the initial mole ratios, which represent the relative number of atoms in the compound. However, since empirical formulas require whole numbers, we converted these ratios to whole numbers by multiplying them by a common factor, ensuring that we maintained the proper proportions. Finally, these whole-number ratios were used as subscripts to write the empirical formula, which represents the simplest whole-number ratio of atoms in the compound. This methodical approach ensures accuracy and clarity in determining the empirical formula. Understanding the principles behind each step is essential for tackling more complex chemical problems and for a deeper appreciation of chemical composition and stoichiometry. The ability to confidently determine empirical formulas is a cornerstone of chemical knowledge, allowing for the identification and characterization of a wide range of substances.
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