Calculating The Mass Of 5.66 Moles Of XY4 A Chemistry Guide
In the realm of chemistry, determining the mass of a given quantity of a substance is a fundamental concept. This article delves into the process of calculating the mass of 5.66 moles of a hypothetical molecule, $XY_4$, where the molar masses of elements X and Y are provided as 17.091 g/mol and 2.708 g/mol, respectively. We will meticulously walk through the steps involved, ensuring a comprehensive understanding of the underlying principles.
Understanding Moles and Molar Mass
Before we delve into the calculations, let's establish a firm grasp of the key concepts involved: moles and molar mass. A mole is a unit of measurement that represents a specific number of particles, precisely 6.022 x 10^23 particles, also known as Avogadro's number. Molar mass, on the other hand, is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). The molar mass of a compound is the sum of the atomic masses of all the atoms present in its chemical formula.
The relationship between moles, mass, and molar mass is elegantly captured in the following equation:
Mass = Moles x Molar Mass
This equation forms the cornerstone of our calculations, allowing us to seamlessly convert between the amount of a substance in moles and its corresponding mass in grams.
Determining the Molar Mass of $XY_4$
Our first crucial step is to calculate the molar mass of the hypothetical molecule, $XY_4$. To achieve this, we need to consider the atomic masses of elements X and Y, which are given as 17.091 g/mol and 2.708 g/mol, respectively. The chemical formula, $XY_4$, indicates that each molecule of the compound contains one atom of element X and four atoms of element Y.
Therefore, the molar mass of $XY_4$ can be calculated as follows:
Molar mass of XY4 = (1 x Molar mass of X) + (4 x Molar mass of Y)
Molar mass of XY4 = (1 x 17.091 g/mol) + (4 x 2.708 g/mol)
Molar mass of XY4 = 17.091 g/mol + 10.832 g/mol
Molar mass of XY4 = 27.923 g/mol
Thus, the molar mass of the hypothetical molecule, $XY_4$, is determined to be 27.923 g/mol. This value signifies that one mole of $XY_4$ weighs 27.923 grams.
Calculating the Mass of 5.66 Moles of $XY_4$
Now that we have established the molar mass of $XY_4$, we can proceed to calculate the mass of 5.66 moles of this compound. We will employ the fundamental equation we discussed earlier:
Mass = Moles x Molar Mass
In this case, we have:
- Moles = 5.66 moles
- Molar Mass = 27.923 g/mol
Substituting these values into the equation, we get:
Mass = 5.66 moles x 27.923 g/mol
Mass = 157.985 g
Therefore, the mass of 5.66 moles of the hypothetical molecule, $XY_4$, is approximately 157.985 grams. When we consider significant figures, this value rounds to approximately 158 grams.
Analyzing the Answer Choices
Now, let's compare our calculated mass with the provided answer choices:
A. 0.202 g B. 158 g C. $1.5 imes 10^{-22} g$ D. $5.45 imes 10^{24} g$
By comparing our result of approximately 158 grams with the answer choices, it becomes evident that option B, 158 g, is the correct answer. The other options deviate significantly from our calculated value and can be confidently eliminated.
Conclusion
In conclusion, we have successfully calculated the mass of 5.66 moles of the hypothetical molecule, $XY_4$, using the fundamental relationship between moles, mass, and molar mass. By meticulously determining the molar mass of $XY_4$ and applying the appropriate formula, we arrived at a mass of approximately 158 grams, which corresponds to answer choice B. This exercise underscores the importance of understanding and applying these core concepts in chemistry to solve quantitative problems accurately.
The ability to calculate mass from moles and molar mass is crucial in various chemical applications, including stoichiometry, solution preparation, and chemical analysis. A solid grasp of these principles empowers chemists and students alike to make accurate predictions and interpretations in the fascinating world of chemical reactions and compounds.
Additional Practice Problems
To further solidify your understanding of these concepts, consider tackling the following practice problems:
- What is the mass of 2.5 moles of water ($H_2O$)? (Molar mass of water = 18.015 g/mol)
- How many moles are present in 100 grams of sodium chloride (NaCl)? (Molar mass of NaCl = 58.44 g/mol)
- Calculate the mass of 0.75 moles of methane ($CH_4$). (Molar mass of methane = 16.04 g/mol)
By working through these practice problems, you can reinforce your understanding and build confidence in your ability to apply these concepts to a variety of chemical scenarios. Remember, practice makes perfect, and the more you engage with these calculations, the more proficient you will become.
Further Exploration
For those eager to delve deeper into the realm of moles, molar mass, and stoichiometry, numerous resources are available online and in textbooks. Exploring these resources will provide a more comprehensive understanding of these fundamental concepts and their applications in diverse chemical contexts. Consider investigating topics such as:
- Stoichiometry: The quantitative relationships between reactants and products in chemical reactions.
- Limiting reactants: The reactant that is completely consumed in a chemical reaction, determining the amount of product formed.
- Percent yield: The ratio of the actual yield of a reaction to the theoretical yield, expressed as a percentage.
- Solution stoichiometry: Applying stoichiometric principles to reactions in solutions.
By venturing into these related topics, you can gain a more holistic perspective on the role of moles and molar mass in the broader field of chemistry. The journey of chemical exploration is a continuous one, and the more you learn, the more fascinating the world of molecules and reactions becomes.
