How Many Moles Are In 9.8 G Of Calcium

How Many Moles Are in 9.8 g of Calcium? A Comprehensive Guide

Determining the number of moles in a given mass of a substance is a fundamental concept in chemistry. This article will guide you through the process of calculating the number of moles in 9.8 grams of calcium, explaining the underlying principles and providing a step-by-step solution. We'll also delve into related concepts, exploring the importance of molar mass and Avogadro's number in stoichiometric calculations.

Understanding Moles and Molar Mass

Before we embark on the calculation, let's solidify our understanding of key terms:

What is a Mole? A mole (mol) is a fundamental unit in chemistry that represents Avogadro's number (approximately 6.022 x 10²³) of particles. These particles can be atoms, molecules, ions, or any other specified entity. Essentially, a mole provides a convenient way to count incredibly large numbers of atoms or molecules.

What is Molar Mass? Molar mass is the mass of one mole of a substance. It's expressed in grams per mole (g/mol). The molar mass of an element is numerically equal to its atomic weight (found on the periodic table) but with the unit g/mol. For example, the atomic weight of carbon is approximately 12, so its molar mass is 12 g/mol.

Calculating Moles from Mass: The Formula

The relationship between moles (n), mass (m), and molar mass (M) is given by the following formula:

n = m / M

Where:

• n represents the number of moles
• m represents the mass of the substance in grams
• M represents the molar mass of the substance in g/mol

Step-by-Step Calculation for 9.8 g of Calcium

Now, let's apply this formula to determine the number of moles in 9.8 g of calcium (Ca).

Step 1: Find the molar mass of Calcium

Consult the periodic table. The atomic weight of calcium is approximately 40.08. Therefore, the molar mass of calcium (M) is 40.08 g/mol.

Step 2: Plug the values into the formula

We have:

• m = 9.8 g
• M = 40.08 g/mol

Substitute these values into the formula:

n = 9.8 g / 40.08 g/mol

Step 3: Calculate the number of moles

Performing the calculation:

n ≈ 0.2445 mol

Therefore, there are approximately 0.2445 moles of calcium in 9.8 grams of calcium.

Avogadro's Number and the Number of Atoms

While the above calculation gives us the number of moles, we can extend this to find the actual number of calcium atoms present. Remember, one mole contains Avogadro's number of particles.

Step 4: Calculate the number of atoms

To find the number of calcium atoms, multiply the number of moles by Avogadro's number:

Number of atoms = n x Avogadro's number

Number of atoms = 0.2445 mol x 6.022 x 10²³ atoms/mol

Number of atoms ≈ 1.47 x 10²³ atoms

Thus, there are approximately 1.47 x 10²³ calcium atoms in 9.8 grams of calcium.

Understanding Significant Figures

In scientific calculations, it's crucial to pay attention to significant figures. The given mass (9.8 g) has two significant figures. The molar mass of calcium (40.08 g/mol) has four significant figures. When performing calculations, the result should be rounded to the same number of significant figures as the measurement with the fewest significant figures. In this case, our final answer for moles should be rounded to two significant figures, giving us 0.24 moles. However, we maintained an extra digit in our intermediate steps for greater accuracy.

Applications of Mole Calculations

The ability to convert between mass and moles is essential in various chemical calculations and applications, including:

• Stoichiometry: Calculating the amounts of reactants and products in chemical reactions. Knowing the number of moles allows us to determine the relative amounts of substances involved in a reaction based on the balanced chemical equation.
• Solution Chemistry: Determining the concentration of solutions (e.g., molarity) requires knowing the number of moles of solute dissolved in a given volume of solvent.
• Gas Laws: The ideal gas law (PV = nRT) uses the number of moles to relate pressure, volume, and temperature of a gas.
• Thermochemistry: Many thermodynamic calculations involve the number of moles to determine enthalpy changes and other thermodynamic properties.

Potential Sources of Error

While our calculation is straightforward, several factors could introduce minor errors:

• Impurities in the Calcium Sample: If the 9.8 g sample of calcium contains impurities, the actual number of calcium atoms would be slightly lower than our calculated value.
• Rounding Errors: Rounding during calculations can lead to small discrepancies in the final answer.
• Accuracy of the Periodic Table: The atomic weight of calcium given on the periodic table is an average value based on the isotopic composition. Slight variations in isotopic abundance can lead to minor differences in the molar mass.

Conclusion: Moles are Key to Chemical Calculations

This article comprehensively explained how to calculate the number of moles in 9.8 g of calcium, highlighting the significance of molar mass and Avogadro's number. Mastering this fundamental concept unlocks the ability to perform a vast range of stoichiometric and chemical calculations. Remember that attention to significant figures and an awareness of potential error sources are essential for obtaining accurate and reliable results. This understanding is fundamental to success in chemistry and related scientific fields. The process demonstrated here can be applied to calculate the number of moles for any element or compound, given its mass and molar mass. By understanding these principles, you equip yourself with a critical tool for problem-solving in chemistry.