The question at hand requires us to calculate the formula weight of potassium dichromate, which has the chemical formula K₂Cr₂O₇. This calculation is fundamental in chemistry, particularly in stoichiometry, where the molar mass of compounds is crucial for converting between mass and moles. To accurately determine the formula weight, we must consider the atomic weights of each element present in the compound and their respective quantities.
Potassium dichromate (K₂Cr₂O₇) is an orange-red crystalline solid that is widely used as an oxidizing agent in various laboratory and industrial applications. It is an ionic compound, comprising potassium ions (K⁺) and dichromate ions (Cr₂O₇²⁻). The formula weight, also known as the molar mass, is the sum of the atomic weights of all the atoms in the chemical formula. To calculate this, we need to reference the periodic table for the atomic weights of each element involved: potassium (K), chromium (Cr), and oxygen (O).
Firstly, let's identify the atomic weights:
- Potassium (K) has an atomic weight of approximately 39.10 amu.
- Chromium (Cr) has an atomic weight of approximately 52.00 amu.
- Oxygen (O) has an atomic weight of approximately 16.00 amu.
Now, we account for the number of atoms of each element in the chemical formula K₂Cr₂O₇:
- There are two potassium (K) atoms.
- There are two chromium (Cr) atoms.
- There are seven oxygen (O) atoms.
Next, we multiply the atomic weight of each element by the number of atoms present in the compound:
- For potassium: 2 atoms × 39.10 amu/atom = 78.20 amu
- For chromium: 2 atoms × 52.00 amu/atom = 104.00 amu
- For oxygen: 7 atoms × 16.00 amu/atom = 112.00 amu
Finally, we sum these values to obtain the formula weight of K₂Cr₂O₇:
Formula weight = (2 × 39.10) + (2 × 52.00) + (7 × 16.00) = 78.20 + 104.00 + 112.00 = 294.20 amu
Thus, the formula weight of potassium dichromate (K₂Cr₂O₇) is approximately 294.20 amu. This value is very close to one of the provided options, allowing us to confidently select the correct answer.
Therefore, considering the options provided, the correct answer is:
- E. 294.18
This detailed calculation ensures accuracy and provides a clear understanding of how to determine the formula weight of chemical compounds. This is a crucial skill in chemistry, as it is the basis for many quantitative analyses and stoichiometric calculations.
Step-by-Step Calculation of Potassium Dichromate Formula Weight
Calculating the formula weight, also known as the molar mass, of a compound is a fundamental skill in chemistry. For potassium dichromate (K₂Cr₂O₇), this calculation involves summing the atomic weights of each element in the compound, multiplied by the number of atoms of that element present in the formula. This process is critical for various stoichiometric calculations and chemical analyses. Let’s break down the steps to ensure a clear and accurate calculation.
1. Identify the Chemical Formula
The chemical formula for potassium dichromate is K₂Cr₂O₇. This formula indicates that each molecule of the compound contains two potassium atoms (K), two chromium atoms (Cr), and seven oxygen atoms (O). Understanding the formula is the first step in accurately calculating the formula weight.
2. Determine the Atomic Weights of Each Element
To find the atomic weights, we refer to the periodic table. The atomic weight is typically listed below the element's symbol. For the elements in potassium dichromate, the atomic weights are approximately:
- Potassium (K): 39.10 amu (atomic mass units)
- Chromium (Cr): 52.00 amu
- Oxygen (O): 16.00 amu
These values are essential for the subsequent calculations. Precise atomic weights ensure the accuracy of the final formula weight.
3. Multiply the Atomic Weight by the Number of Atoms
Next, we multiply the atomic weight of each element by the number of atoms present in the chemical formula. This step accounts for the total contribution of each element to the compound's mass:
- Potassium (K): 2 atoms × 39.10 amu/atom = 78.20 amu
- Chromium (Cr): 2 atoms × 52.00 amu/atom = 104.00 amu
- Oxygen (O): 7 atoms × 16.00 amu/atom = 112.00 amu
By performing these multiplications, we determine the mass contribution of each element in the compound.
4. Sum the Values to Obtain the Formula Weight
Finally, we sum the values obtained in the previous step to calculate the total formula weight of potassium dichromate:
Formula weight of K₂Cr₂O₇ = (2 × 39.10) + (2 × 52.00) + (7 × 16.00) = 78.20 + 104.00 + 112.00 = 294.20 amu
Therefore, the formula weight of potassium dichromate (K₂Cr₂O₇) is approximately 294.20 amu. This value represents the mass of one mole of K₂Cr₂O₇ and is crucial for various chemical calculations.
Summary
The formula weight of potassium dichromate (K₂Cr₂O₇) is calculated by summing the atomic weights of its constituent elements, each multiplied by the number of atoms present in the formula. Following the steps outlined above ensures an accurate determination of the compound's molar mass. This calculation is not only a fundamental skill in chemistry but also a practical tool for quantitative analysis and stoichiometric problem-solving. The accurate formula weight, 294.20 amu, aligns closely with option E, 294.18, confirming the correct answer.
Applications and Importance of Formula Weight in Chemistry
Formula weight, also known as molar mass, is a crucial concept in chemistry with wide-ranging applications. It serves as a bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and kilograms that we can measure in the laboratory. Understanding and accurately calculating formula weight is essential for various chemical calculations, experiments, and industrial processes. In this section, we delve into the applications and importance of formula weight in chemistry, particularly in the context of potassium dichromate (K₂Cr₂O₇).
1. Stoichiometry and Chemical Reactions
Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. The formula weight is the foundation of stoichiometric calculations. It allows chemists to convert between mass (grams) and moles, which is necessary for balancing chemical equations and predicting the amounts of reactants and products involved in a reaction. For instance, in any reaction involving potassium dichromate, knowing its formula weight (approximately 294.20 g/mol) allows us to determine how many grams of K₂Cr₂O₇ are needed to react with a specific amount of another substance, or how much product will be formed from a given amount of K₂Cr₂O₇.
2. Solution Preparation
In chemistry, many reactions and experiments are conducted in solutions. The formula weight is crucial for preparing solutions of specific concentrations, such as molar solutions (moles per liter) or molal solutions (moles per kilogram). To prepare a solution of a known molarity, one must first calculate the mass of the solute needed using its formula weight. For example, if a chemist needs to prepare a 1.0 M solution of potassium dichromate, they would use the formula weight to determine that 294.20 grams of K₂Cr₂O₇ are required per liter of solution. Accurate solution preparation is vital for reproducible and reliable experimental results.
3. Chemical Analysis and Quantitative Determination
Formula weight plays a significant role in chemical analysis, particularly in techniques such as titrations and gravimetric analysis. In titrations, a solution of known concentration (the titrant) is used to determine the concentration of an unknown solution (the analyte). The formula weight of the titrant and analyte are essential for calculating the stoichiometry of the reaction and accurately determining the concentration of the unknown solution. In gravimetric analysis, a substance is converted into a product of known composition, which is then weighed. The formula weight of the product is used to calculate the amount of the original substance in the sample. For example, potassium dichromate can be used in redox titrations, and its formula weight is crucial for calculating the results of these titrations.
4. Industrial Applications
In industrial chemistry, formula weight is indispensable for the large-scale production of chemicals and materials. Chemical engineers rely on formula weights to determine the quantities of raw materials needed, calculate product yields, and optimize chemical processes. Potassium dichromate, for instance, is used in various industrial applications, including as an oxidizing agent, in the production of pigments, and in the tanning of leather. Accurate knowledge of its formula weight is essential for cost-effective and efficient industrial processes.
5. Research and Development
In research and development, formula weight is a fundamental parameter in the synthesis and characterization of new compounds. When synthesizing a new compound, chemists use stoichiometry and formula weights to calculate the amounts of reactants needed and predict the theoretical yield of the product. The formula weight is also used in the characterization of the synthesized compound, such as in elemental analysis, to verify its purity and composition. The development of new materials and pharmaceuticals often relies on precise stoichiometric calculations, making formula weight an indispensable tool.
Conclusion
The formula weight is a cornerstone concept in chemistry, essential for a wide array of applications from basic stoichiometric calculations to complex industrial processes and research endeavors. Its importance lies in its ability to connect the microscopic and macroscopic worlds, allowing chemists to accurately measure, manipulate, and understand chemical substances and reactions. Whether preparing solutions, conducting titrations, or synthesizing new compounds, the formula weight remains a vital tool for chemists and chemical engineers worldwide. The accurate calculation of formula weight, such as that for potassium dichromate (K₂Cr₂O₇), ensures precision and reliability in all chemical endeavors.
Common Mistakes to Avoid When Calculating Formula Weight
Calculating formula weight, or molar mass, is a fundamental skill in chemistry, yet it is prone to errors if certain precautions are not taken. Accuracy in this calculation is crucial for various applications, including stoichiometry, solution preparation, and quantitative analysis. To ensure correct results, it is important to be aware of common mistakes and how to avoid them. This section highlights some of these pitfalls and provides guidance on best practices for calculating formula weight.
1. Incorrectly Identifying the Chemical Formula
One of the most basic yet significant errors is misidentifying the chemical formula of the compound. The chemical formula dictates the number of atoms of each element present in a molecule or formula unit, and any mistake here will propagate through the entire calculation. For example, potassium dichromate has the formula K₂Cr₂O₇. If one were to incorrectly write it as KCrO₄ or any other variation, the calculated formula weight would be drastically wrong. Always double-check the chemical formula before proceeding with any calculations. This can be done by referring to reliable sources such as textbooks, chemical databases, or reputable online resources.
2. Using Incorrect Atomic Weights
The atomic weights of elements are the foundation of formula weight calculations. These values are obtained from the periodic table, and it is essential to use accurate and up-to-date atomic weights. Using outdated or rounded-off values can lead to significant errors, especially for compounds with heavy elements or a large number of atoms. For instance, the atomic weight of potassium (K) is approximately 39.10 amu, chromium (Cr) is approximately 52.00 amu, and oxygen (O) is approximately 16.00 amu. Always use the most precise atomic weights available, typically found in the most recent periodic tables or chemical databases, to minimize errors in your calculations.
3. Failing to Account for All Atoms in the Formula
Another common mistake is failing to account for the correct number of atoms of each element in the chemical formula. This often occurs when dealing with compounds containing polyatomic ions or hydrates. For example, in potassium dichromate (K₂Cr₂O₇), there are two potassium atoms, two chromium atoms, and seven oxygen atoms. If one were to overlook any of these numbers, the final formula weight would be incorrect. It is crucial to meticulously count the number of atoms of each element and ensure that they are correctly incorporated into the calculation. Using a systematic approach, such as writing down each element and its quantity before multiplying by the atomic weight, can help prevent this error.
4. Arithmetic Errors
Simple arithmetic errors, such as mistakes in multiplication or addition, can easily occur during the calculation process. Even if the correct chemical formula and atomic weights are used, an arithmetic error will lead to an incorrect formula weight. To minimize these errors, it is advisable to perform calculations carefully and double-check each step. Using a calculator can reduce the likelihood of manual calculation errors. Additionally, writing down intermediate steps clearly can help in identifying and correcting any mistakes made along the way.
5. Confusing Formula Weight with Atomic Weight
It is important to distinguish between formula weight and atomic weight. Atomic weight refers to the mass of a single atom of an element, whereas formula weight refers to the mass of one mole of a compound or molecule. Confusing these terms can lead to incorrect calculations and misunderstandings. For example, the atomic weight of potassium is approximately 39.10 amu, but the formula weight of potassium dichromate (K₂Cr₂O₇) is approximately 294.20 amu. Always be clear about what you are calculating and ensure you are using the appropriate values and concepts.
Conclusion
Calculating formula weight is a critical skill in chemistry, and avoiding common mistakes is essential for accurate results. These mistakes include misidentifying the chemical formula, using incorrect atomic weights, failing to account for all atoms in the formula, making arithmetic errors, and confusing formula weight with atomic weight. By being aware of these potential pitfalls and following best practices, such as double-checking formulas, using precise atomic weights, and carefully performing calculations, you can minimize errors and ensure the accurate determination of formula weights. This accuracy is vital for stoichiometry, solution preparation, chemical analysis, and a wide range of other chemical applications.