Grams Of Water Calculation A Chemistry Problem Solution

In the fascinating world of chemistry, one often encounters the need to convert between moles and grams. This conversion is crucial for accurate measurements and calculations in various experiments and reactions. This article delves into a practical problem involving the calculation of the mass of water, given its molar mass and the number of moles. Specifically, we will address the question: If Yun has 0.025 mol of water ($H_2O$) for a laboratory experiment, and the molar mass of water is 18.02 g/mol, how many grams of water does she have? This seemingly simple problem highlights fundamental concepts in stoichiometry and provides a clear example of how molar mass acts as a conversion factor between moles and grams. Let's embark on this chemical calculation journey and unravel the solution step by step.

Understanding Molar Mass and Moles

Before diving into the calculation, it’s essential to grasp the concepts of molar mass and moles. The molar mass of a substance is the mass of one mole of that substance, expressed in grams per mole (g/mol). It's a fundamental property that connects the macroscopic world (grams) to the microscopic world (number of molecules). One mole, on the other hand, is a unit of measurement representing $6.022 imes 10^{23}$ entities (atoms, molecules, ions, etc.), a number known as Avogadro's constant. Essentially, the mole concept provides a convenient way to count and measure incredibly tiny particles like atoms and molecules.

In the context of our problem, the molar mass of water ($H_2O$) is given as 18.02 g/mol. This means that one mole of water molecules weighs 18.02 grams. This value is derived from the atomic masses of hydrogen (H) and oxygen (O) as found on the periodic table. Water comprises two hydrogen atoms (each approximately 1.01 g/mol) and one oxygen atom (approximately 16.00 g/mol). Adding these atomic masses together (2 * 1.01 + 16.00) gives us the molar mass of water, which is approximately 18.02 g/mol.

The number of moles, in this case, 0.025 mol of $H_2O$, tells us how many 'sets' of $6.022 imes 10^{23}$ water molecules Yun has. However, in a laboratory setting, it's more practical to measure substances in grams, which leads us to the conversion process using molar mass.

Understanding the relationship between molar mass and moles is crucial for various chemical calculations, such as determining the amount of reactants needed for a reaction, predicting the yield of a product, and converting between different units of measurement. By mastering these fundamental concepts, one can confidently tackle a wide range of stoichiometric problems and gain a deeper understanding of the quantitative nature of chemistry.

The Formula for Conversion

The core of this problem lies in the conversion between moles and grams, a fundamental skill in chemistry. The formula that governs this conversion is elegantly simple yet profoundly powerful:

Mass (in grams) = Number of moles × Molar mass

This equation serves as the bridge between the microscopic world of moles and the macroscopic world of grams, allowing chemists to accurately measure and manipulate chemical substances in the laboratory. The formula underscores the direct proportionality between the mass of a substance and the number of moles present, with the molar mass acting as the constant of proportionality.

To further elucidate the formula, let's break it down into its components. The mass (in grams) represents the quantity we are trying to find – the weight of the substance in question. This is the practical, measurable quantity that we can determine using a balance in the lab. The number of moles, as discussed earlier, is a unit that quantifies the amount of a substance, specifically the number of entities (atoms, molecules, etc.) present. It's a convenient way to handle the vast numbers of particles involved in chemical reactions. The molar mass, as the name suggests, is the mass of one mole of the substance, serving as a conversion factor between moles and grams. It is a characteristic property of each substance, determined by the atomic masses of its constituent elements.

In the context of our problem, we are given the number of moles of water (0.025 mol) and the molar mass of water (18.02 g/mol). Our goal is to find the mass of water in grams. By applying the formula, we can directly calculate the mass by multiplying the number of moles by the molar mass. This straightforward application of the formula exemplifies its versatility and importance in chemical calculations. Mastering this conversion formula is a cornerstone of understanding stoichiometry and quantitative chemistry, enabling accurate and reliable experimental results.

Applying the Formula to the Problem

Now that we've established the formula Mass (in grams) = Number of moles × Molar mass, let's apply it to the specific problem at hand. We are given that Yun has 0.025 mol of water ($H_2O$) and the molar mass of water is 18.02 g/mol. Our objective is to determine the mass of water Yun has in grams.

To solve this, we simply substitute the given values into the formula:

Mass (in grams) = 0.025 mol × 18.02 g/mol

Performing the multiplication, we get:

Mass (in grams) = 0.4505 g

Rounding the result to two significant figures (since 0.025 mol has two significant figures), we obtain:

Mass (in grams) ≈ 0.45 g

Therefore, Yun has approximately 0.45 grams of water. This result showcases the direct application of the conversion formula and highlights the importance of paying attention to significant figures in scientific calculations. The process involves a straightforward multiplication, but the underlying concept is crucial for understanding the relationship between moles and grams. This example illustrates how molar mass acts as a bridge, allowing us to convert the amount of a substance expressed in moles to its corresponding mass in grams. By mastering this calculation, one can confidently handle a wide array of stoichiometry problems and gain a deeper understanding of quantitative relationships in chemistry.

Analyzing the Answer Choices

Having calculated the mass of water to be approximately 0.45 g, it's crucial to compare our result with the provided answer choices to ensure we select the correct one. The given options are:

A. 0.025 g B. 0.45 g C. 0.90 g D. 18 g

By carefully examining these options, we can clearly see that our calculated answer, 0.45 g, matches option B. This confirms the accuracy of our calculation and the proper application of the formula Mass = Moles × Molar mass. Let's briefly analyze why the other options are incorrect:

• Option A (0.025 g): This value is numerically equal to the number of moles of water, but it doesn't account for the molar mass. It's a common mistake to simply use the number of moles as the mass, neglecting the crucial conversion factor.
• Option C (0.90 g): This value is twice our calculated answer. There's no logical step in the calculation that would lead to doubling the result. It might arise from a misunderstanding of the formula or an arithmetic error.
• Option D (18 g): This value is close to the molar mass of water (18.02 g/mol). While the molar mass is essential for the calculation, it's not the final answer. This option might result from confusing molar mass with the mass of the given amount of substance.

Therefore, by systematically calculating the mass and comparing it with the answer choices, we can confidently select option B as the correct answer. This process of verification is crucial in problem-solving, ensuring that we not only arrive at a numerical result but also understand its meaning and context within the problem.

Conclusion

In summary, we've successfully calculated the mass of water Yun has for her experiment, given the number of moles (0.025 mol) and the molar mass of water (18.02 g/mol). By applying the fundamental formula Mass = Moles × Molar mass, we determined the mass to be approximately 0.45 g. This problem underscores the crucial role of molar mass as a conversion factor between moles and grams, a cornerstone concept in stoichiometry and quantitative chemistry.

We walked through the essential concepts of molar mass and moles, highlighting their significance in chemical calculations. Understanding that molar mass is the mass of one mole of a substance and that one mole contains $6.022 imes 10^{23}$ entities (Avogadro's number) is fundamental for converting between the microscopic and macroscopic worlds of chemistry. The formula Mass = Moles × Molar mass provides a direct and reliable method for this conversion, allowing us to accurately determine the mass of a substance given its number of moles, or vice versa.

Furthermore, we analyzed the provided answer choices, emphasizing the importance of verifying our result and understanding why incorrect options are flawed. This step-by-step approach ensures not only a correct answer but also a deeper comprehension of the underlying chemical principles. The problem-solving process involved identifying the given information, selecting the appropriate formula, substituting the values, performing the calculation, and verifying the result.

Ultimately, this exercise demonstrates the practical application of stoichiometric principles in a laboratory setting. The ability to convert between moles and grams is essential for accurate measurements, reaction calculations, and a comprehensive understanding of chemical quantities. By mastering these fundamental concepts and problem-solving techniques, one can confidently tackle a wide range of chemical challenges and excel in the field of chemistry.