Calculating The Mass Of 1.84 Mol NaCl

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Determining the mass of a given amount of a chemical substance is a fundamental concept in chemistry, especially in stoichiometry. This article will guide you through the process of calculating the mass of 1.84 moles of sodium chloride (NaCl), providing a detailed explanation and adhering to the rules of significant figures. Understanding these calculations is crucial for various applications in chemistry, from preparing solutions to performing quantitative analysis.

Understanding Moles and Molar Mass

Before diving into the calculation, it's essential to understand the concepts of moles and molar mass. The mole is the SI unit for the amount of a substance. One mole contains Avogadro's number (approximately 6.022 x 10^23) of elementary entities (atoms, molecules, ions, etc.). Molar mass, on the other hand, is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). Molar mass is numerically equivalent to the atomic or molecular weight of the substance in atomic mass units (amu).

For sodium chloride (NaCl), the molar mass is calculated by adding the atomic masses of sodium (Na) and chlorine (Cl). The atomic mass of Na is approximately 22.99 g/mol, and the atomic mass of Cl is approximately 35.45 g/mol. Therefore, the molar mass of NaCl is:

Molar Mass of NaCl=22.99 g/mol+35.45 g/mol=58.44 g/molMolar\ Mass\ of\ NaCl = 22.99\ g/mol + 35.45\ g/mol = 58.44\ g/mol

This value, 58.44 g/mol, indicates that one mole of NaCl weighs 58.44 grams. Knowing this, we can calculate the mass of any given number of moles of NaCl.

Calculating the Mass of 1.84 mol NaCl

The problem asks us to find the mass of 1.84 moles of NaCl. To do this, we use the relationship between moles, mass, and molar mass:

Mass=Moles×Molar MassMass = Moles × Molar\ Mass

Given that we have 1.84 moles of NaCl and the molar mass of NaCl is 58.44 g/mol, we can plug these values into the formula:

Mass of NaCl=1.84 mol×58.44 g/molMass\ of\ NaCl = 1.84\ mol × 58.44\ g/mol

Performing this calculation:

Mass of NaCl=107.5376 gMass\ of\ NaCl = 107.5376\ g

Now, we need to consider significant figures to provide the answer in the correct format.

Significant Figures: Ensuring Accuracy in Calculations

Significant figures are the digits in a number that contribute to its precision. They include all non-zero digits, zeros between non-zero digits, and trailing zeros in a number containing a decimal point. In calculations, the result should be rounded to the same number of significant figures as the measurement with the fewest significant figures.

In our calculation, we have two values: 1.84 mol and 58.44 g/mol. The number 1.84 has three significant figures, and the number 58.44 has four significant figures. Therefore, our final answer should be rounded to three significant figures.

The calculated mass is 107.5376 g. To round this to three significant figures, we look at the first four digits: 107. The next digit is 5, which means we round up the last significant digit. Thus, 107.5376 g rounded to three significant figures is 108 g.

Detailed Explanation of Significant Figures Rules

Understanding the rules of significant figures is essential for accurately representing the precision of measurements and calculations in scientific contexts. Here’s a detailed explanation of these rules:

  1. Non-zero digits are always significant: Any digit from 1 to 9 is considered significant. For example, the number 234 has three significant figures, and the number 1.2345 has five significant figures.
  2. Zeros between non-zero digits are significant: Zeros that appear between non-zero digits are always counted as significant. For instance, the number 405 has three significant figures, and 10.02 has four significant figures.
  3. Leading zeros are not significant: Zeros that precede all non-zero digits are not significant because they only serve as placeholders. For example, 0.0025 has two significant figures (2 and 5), and 0.00001 has only one significant figure (1).
  4. Trailing zeros in a number containing a decimal point are significant: Zeros that appear after the last non-zero digit in a number with a decimal point are significant. For example, 1.20 has three significant figures, and 10.00 has four significant figures. These trailing zeros indicate that the measurement was made to the nearest tenth or hundredth, respectively.
  5. Trailing zeros in a number without a decimal point are ambiguous: Zeros that appear after the last non-zero digit in a number without a decimal point are ambiguous and may or may not be significant. For example, the number 100 could have one, two, or three significant figures depending on whether the zeros were measured or are simply placeholders. To avoid ambiguity, it is best to use scientific notation. If 100 has one significant figure, it would be written as 1 × 10^2; if it has two significant figures, it would be 1.0 × 10^2; and if it has three significant figures, it would be 1.00 × 10^2.
  6. Exact numbers have an infinite number of significant figures: Exact numbers are those that are defined or counted rather than measured. These include conversion factors (e.g., 1 meter = 100 centimeters) and counted quantities (e.g., 24 students in a class). Because these numbers are exact, they do not limit the number of significant figures in a calculation.

Rules for Significant Figures in Calculations

When performing calculations, it is crucial to maintain the correct number of significant figures to ensure the accuracy of the final result. Different rules apply to different operations:

  1. Multiplication and Division: In multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures used in the calculation. For example, if you multiply 2.5 (two significant figures) by 3.125 (four significant figures), the result should be rounded to two significant figures.
  2. Addition and Subtraction: In addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places used in the calculation. For example, if you add 12.34 (two decimal places) and 2.5 (one decimal place), the result should be rounded to one decimal place.
  3. Rounding: When rounding, if the digit immediately following the last significant digit is 5 or greater, round up the last significant digit. If the digit is less than 5, leave the last significant digit as it is. For example, rounding 2.35 to two significant figures gives 2.4, while rounding 2.34 to two significant figures gives 2.3.

By following these rules, scientists and students can ensure that their calculations accurately reflect the precision of their measurements and avoid overstating the certainty of their results. Mastering significant figures is an essential skill for anyone working in quantitative fields, ensuring the integrity and reliability of scientific data.

Conclusion: The Final Answer

Therefore, the mass of 1.84 mol NaCl, considering the correct number of significant figures, is:

1.84 mol NaCl=108 g NaCl1. 84\ mol\ NaCl = 108\ g\ NaCl

This calculation demonstrates the importance of understanding molar mass and significant figures in chemistry. By applying these concepts, we can accurately determine the mass of chemical substances, which is crucial for various chemical processes and experiments.

This detailed guide provides not only the answer but also a comprehensive understanding of the underlying principles, ensuring that you can apply this knowledge to similar problems in the future. Remember, accuracy and precision are key in chemistry, and mastering these calculations is a significant step towards achieving that goal.