Calculation of Calcium Carbonate Mass from Atoms of Calcium
Understanding the relationship between the number of atoms and the mass of a chemical compound is a fundamental concept in chemistry. This article provides a detailed guide on how to calculate the mass of a sample of calcium carbonate (CaCO3) based on the number of calcium atoms present. Letrsquo;s dive into the step-by-step process, including necessary conversion factors and calculations.
Step-by-Step Conversion
Given: The sample contains 3.25 times 10^{23} atoms of calcium (Ca).
Objective: To find the mass of the calcium carbonate sample in grams (g).
Conversion Path:
Atoms of Ca → Moles of Ca → Moles of CaCO3 → Grams of CaCO3Conversion Factors
We will use the following conversion factors:
1 mol Ca 6.022 times 10^{23} atoms of Ca (Avogadrorsquo;s number) 1 mol CaCO3 1 mol Ca 1 mol CaCO3 100.09 gCalculation
Step 1: Convert atoms of Ca to moles of Ca.
The number of moles of Ca is calculated as:
moles of Ca (3.25 times 10^{23} atoms of Ca) / (6.022 times 10^{23} atoms of Ca per mol) 0.54 moles of Ca
Step 2: Convert moles of Ca to moles of CaCO3.
Since 1 mole of CaCO3 contains 1 mole of Ca, the number of moles of CaCO3 is also 0.54 moles.
Step 3: Convert moles of CaCO3 to grams of CaCO3.
The molar mass of CaCO3 is:
Molar mass of CaCO3 40.08 g/mol (for Ca) 12.01 g/mol (for C) 3 times 16.00 g/mol (for 3 O) 100.09 g/mol
The mass of the sample is then calculated as:
mass of CaCO3 0.54 mol times 100.09 g/mol 54.05 g
Summary
The mass of the calcium carbonate sample containing 3.25 times 10^{23} atoms of calcium is 54.05 g.
Conclusion
Understanding the relationships between atoms, moles, and grams is crucial in chemistry. By following the steps outlined above, we can accurately calculate the mass of any sample based on the given number of atoms. This method can be applied to various compounds, enhancing our ability to comprehend and manipulate chemical substances effectively.
Frequently Asked Questions
Q: What is Avogadrorsquo;s number?
A: Avogadrorsquo;s number, denoted as NA, is the number of constituent particles (usually atoms or molecules) in one mole of a substance. It is approximately 6.022 times 10^{23}.
Q: How do we find the molar mass of a compound?
A: The molar mass of a compound is found by adding the atomic masses of all the atoms in the formula. For example, the molar mass of CaCO3 is calculated as:
40.08 g/mol (for Ca) 12.01 g/mol (for C) 3 times 16.00 g/mol (for 3 O) 100.09 g/mol
Q: Why is it important to use significant figures in calculations?
A: Significant figures are used to express the precision of measurements. In the calculation we performed, the number of significant figures should reflect the precision of the input data. In this case, the final answer should be reported as 54.1 g when rounded to three significant figures.