Mass Of 2.01 X 10^23 Formula Units Of CoSO4 Calculation And Explanation
In chemistry, stoichiometry is a crucial concept that deals with the quantitative relationships between reactants and products in chemical reactions. One of the fundamental calculations in stoichiometry involves converting between the number of formula units (or molecules) of a substance and its mass. This conversion relies on the concept of the mole, which is the SI unit for the amount of substance. One mole contains Avogadro's number (approximately 6.022 x 10^23) of entities, such as atoms, molecules, or formula units. This article will provide a detailed, step-by-step approach to calculating the mass of 2.01 x 10^23 formula units of cobalt(II) sulfate (CoSO4), utilizing the provided molar mass and Avogadro's number.
The problem presents a scenario where we need to determine the mass of a specific quantity of cobalt(II) sulfate (CoSO4). We are given that we have 2.01 x 10^23 formula units of CoSO4. To solve this, we'll use the molar mass of CoSO4 (154.99 g/mol) and Avogadro's number (6.02 x 10^23 formula units/mol) as conversion factors. The molar mass serves as the bridge between grams and moles, while Avogadro's number connects the number of formula units to moles. Understanding these relationships is crucial for accurately converting between different units in chemical calculations. The key here is to convert formula units to moles and then moles to grams, using the appropriate conversion factors. This process ensures that we can accurately determine the mass of the given quantity of CoSO4.
To calculate the mass of 2.01 x 10^23 formula units of CoSO4, we follow a two-step process:
Step 1: Convert Formula Units to Moles
First, we need to convert the given number of formula units to moles. We use Avogadro's number (6.02 x 10^23 formula units/mol) as a conversion factor. The conversion is set up as follows:
Moles of CoSO4 = (Number of Formula Units) / (Avogadro's Number)
Substituting the given values:
Moles of CoSO4 = (2.01 x 10^23 formula units) / (6.02 x 10^23 formula units/mol)
Calculating this gives us:
Moles of CoSO4 ≈ 0.334 moles
This step is crucial because it transforms the number of discrete units into a more chemically relevant unit—the mole. The mole concept allows us to relate microscopic entities (like formula units) to macroscopic quantities (like grams), which are easily measurable in a laboratory setting. By dividing the given number of formula units by Avogadro's number, we find the equivalent amount in moles, which serves as the basis for the next conversion.
Step 2: Convert Moles to Grams
Next, we convert moles of CoSO4 to grams using the molar mass of CoSO4 (154.99 g/mol). The molar mass is the mass of one mole of a substance and serves as the conversion factor between moles and grams. The conversion is set up as follows:
Mass of CoSO4 = (Moles of CoSO4) x (Molar Mass of CoSO4)
Substituting the values we have:
Mass of CoSO4 = (0.334 moles) x (154.99 g/mol)
Calculating this gives us:
Mass of CoSO4 ≈ 51.8 g
This final step converts the amount of CoSO4 from moles to grams, providing the answer in a unit of mass that is commonly used and easily measurable. By multiplying the number of moles by the molar mass, we determine the mass of the substance. This step completes the conversion process, giving us the final answer to the problem.
The Mole Concept
The mole is a fundamental unit in chemistry, representing a specific number of particles (atoms, molecules, ions, etc.). One mole is defined as the amount of substance containing the same number of entities as there are atoms in 12 grams of carbon-12. This number, known as Avogadro's number, is approximately 6.022 x 10^23. The mole concept is essential because it provides a bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and kilograms, which we can measure in the laboratory.
The mole allows chemists to count atoms and molecules by weighing substances. Instead of dealing with individual atoms, which are incredibly tiny, we work with moles, which represent manageable quantities. This concept simplifies stoichiometric calculations and allows for accurate measurement and prediction of chemical reactions. The mole is the cornerstone of quantitative chemistry, enabling the precise formulation and execution of experiments.
Avogadro's Number
Avogadro's number (approximately 6.022 x 10^23) is the number of entities (atoms, molecules, ions, or formula units) in one mole of a substance. It is a critical constant in chemistry, linking the macroscopic and microscopic scales. Avogadro's number is used to convert between the number of particles and the amount in moles, and vice versa. It allows us to relate the number of discrete entities to the molar quantity, which is essential for stoichiometric calculations.
Avogadro's number was named in honor of the Italian scientist Amedeo Avogadro, whose hypothesis that equal volumes of gases at the same temperature and pressure contain the same number of molecules laid the groundwork for the concept. This constant is not just a number; it represents a fundamental connection between the number of particles and the amount of substance. It is crucial for converting between moles and the actual number of atoms, molecules, or formula units in a sample.
Molar Mass
The molar mass of a substance is the mass of one mole of that substance, expressed in grams per mole (g/mol). It is numerically equal to the atomic or molecular weight of the substance, but with units of g/mol. For example, the molar mass of CoSO4 is 154.99 g/mol, meaning that one mole of CoSO4 weighs 154.99 grams. The molar mass serves as a conversion factor between the mass of a substance and the number of moles.
To calculate the molar mass of a compound, you sum the atomic masses of all the atoms in the chemical formula. The atomic masses are obtained from the periodic table. Molar mass is an indispensable tool in chemistry, enabling the conversion between mass and moles, and is vital for preparing solutions of specific concentrations and performing stoichiometric calculations. The accuracy of molar mass values is critical for the precision of chemical experiments and analyses.
While the step-by-step method outlined above is straightforward, there are alternative approaches to solving this problem. One such method involves using a single combined conversion factor. This approach can streamline the calculation and reduce the number of steps involved.
Using a Single Conversion Factor
Instead of converting formula units to moles and then moles to grams, we can combine these two steps into a single conversion. We set up a single equation using both Avogadro's number and the molar mass as conversion factors:
Mass of CoSO4 = (Number of Formula Units) x (1 mol / 6.02 x 10^23 formula units) x (Molar Mass in g/mol)
Substituting the given values:
Mass of CoSO4 = (2.01 x 10^23 formula units) x (1 mol / 6.02 x 10^23 formula units) x (154.99 g/mol)
This single equation combines the two conversion steps, directly converting formula units to grams. Calculating this gives us:
Mass of CoSO4 ≈ 51.8 g
This method condenses the calculation into a single step, which can be more efficient for those comfortable with setting up complex conversion factors. It also minimizes the potential for rounding errors by performing the calculation in one continuous operation. However, it's important to ensure that the units cancel correctly to arrive at the desired unit (grams).
Dimensional Analysis
Another way to approach this problem is using dimensional analysis, a problem-solving method that ensures the correct units are used throughout the calculation. In dimensional analysis, you set up the problem so that the units you don't want cancel out, leaving you with the units you need. This method is particularly useful in chemistry and physics for complex unit conversions.
For our problem, we start with the given number of formula units and multiply by conversion factors until we arrive at grams:
2. 01 x 10^23 formula units CoSO4 x (1 mol CoSO4 / 6.02 x 10^23 formula units CoSO4) x (154.99 g CoSO4 / 1 mol CoSO4)
Notice how the units
