Chapter 6: Problem 35
How many aluminum atoms are in \(3.78 \mathrm{~g}\) of aluminum?
Short Answer
Expert verified
There are approximately 8.43 \(\times\) 10^22 aluminum atoms in 3.78 g of aluminum.
Step by step solution
01
Find the Molar Mass of Aluminum
Use the periodic table to find the molar mass of aluminum (Al). The molar mass of Al is approximately 26.98 g/mol.
02
Calculate the Number of Moles of Aluminum
Use the mass of aluminum given (3.78 g) and divide it by the molar mass (26.98 g/mol) to find the number of moles. The formula is: Number of moles = Mass of Al (g) / Molar mass of Al (g/mol).
03
Use Avogadro's Number to Find the Number of Atoms
Avogadro's number (6.022 \(\times\) 10^23 atoms/mol) is the number of atoms in one mole of a substance. Multiply the number of moles calculated in the previous step by Avogadro's number to find the number of atoms. The formula is: Number of atoms = Number of moles \(\times\) Avogadro's number.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Molar Mass
When working with chemical substances, it's crucial to know how much of a given element or compound we're dealing with. This is where the concept of molar mass comes in. Molar mass is a measure of the mass of one mole of a substance, which is defined as the mass in grams that is numerically equal to the atomic or molecular weight of the substance.
For instance, to calculate how many atoms are present in a given substance, like in the exercise with aluminum (Al), we first need the molar mass of Al. This value is derived from the periodic table, where each element's atomic weight reflects its average mass per atom, accounting for naturally occurring isotopes. The molar mass of aluminum, which is approximately 26.98 grams per mole (g/mol), means that one mole of aluminum atoms weighs about 26.98 grams.
By understanding the molar mass, students can bridge the gap between the microscopic atomic scale and the macroscopic scale that we can measure. This is the first step in the process of calculating the number of aluminum atoms in a sample.
For instance, to calculate how many atoms are present in a given substance, like in the exercise with aluminum (Al), we first need the molar mass of Al. This value is derived from the periodic table, where each element's atomic weight reflects its average mass per atom, accounting for naturally occurring isotopes. The molar mass of aluminum, which is approximately 26.98 grams per mole (g/mol), means that one mole of aluminum atoms weighs about 26.98 grams.
By understanding the molar mass, students can bridge the gap between the microscopic atomic scale and the macroscopic scale that we can measure. This is the first step in the process of calculating the number of aluminum atoms in a sample.
Avogadro's Number
A central figure in understanding chemical quantities is Avogadro's Number, which is 6.022 \(\times\) 10^23. This incredibly large number represents the amount of particles, usually atoms or molecules, in one mole of any substance. The significance of Avogadro's Number lies in its ability to connect the molar mass of a substance to the actual number of entities it contains.
For example, when knowing the molar mass of aluminum, using Avogadro's Number allows us to understand that one mole of aluminum will contain exactly 6.022 \(\times\) 10^23 aluminum atoms. This fixed number enables chemists to perform precise calculations on the atomic scale, ensuring accurate chemical reactions and experiments. So in the context of our exercise, Avogadro's Number is used to convert moles of aluminum into a clearly defined number of aluminum atoms.
For example, when knowing the molar mass of aluminum, using Avogadro's Number allows us to understand that one mole of aluminum will contain exactly 6.022 \(\times\) 10^23 aluminum atoms. This fixed number enables chemists to perform precise calculations on the atomic scale, ensuring accurate chemical reactions and experiments. So in the context of our exercise, Avogadro's Number is used to convert moles of aluminum into a clearly defined number of aluminum atoms.
Moles to Atoms Conversion
To transition from the scale of moles to individual atoms, we use a two-step process. First, we determine the number of moles from the given mass of a substance. Then, we convert those moles into atoms using Avogadro's Number. This conversion is crucial in many chemical calculations and is fundamental in learning how to interconvert between different chemical units of measure.
In our practice problem, after finding out the molar mass of aluminum, we calculated the moles of aluminum by dividing the given mass (3.78 g) by the molar mass of aluminum (26.98 g/mol). With the number of moles at hand, we then multiplied this value by Avogadro's Number to get the total number of aluminum atoms. This process exemplifies the moles to atoms conversion, enabling students to apprehend the quantitative aspect of chemical substances at the atomic level.
In our practice problem, after finding out the molar mass of aluminum, we calculated the moles of aluminum by dividing the given mass (3.78 g) by the molar mass of aluminum (26.98 g/mol). With the number of moles at hand, we then multiplied this value by Avogadro's Number to get the total number of aluminum atoms. This process exemplifies the moles to atoms conversion, enabling students to apprehend the quantitative aspect of chemical substances at the atomic level.
Chemical Quantities
Chemical quantities encompass different measures of chemical substances. These include moles, mass, volume for gases, and the number of atoms or molecules. These measures are interrelated through laws and constants like Avogadro's Number and molar mass. Being able to calculate and interconvert these quantities is essential for understanding and performing chemistry in both theoretical and practical aspects.
In the given problem, we combined the concepts of molar mass and Avogadro's Number to transform a physical mass of aluminum into a countable number of atoms. This transformation underlies much of what students learn in stoichiometry, which is the study of the quantitative relationships between the reactants and products in chemical reactions. Real-world applications range from creating new materials to understanding biological processes, making the comprehension of chemical quantities invaluable for students.
In the given problem, we combined the concepts of molar mass and Avogadro's Number to transform a physical mass of aluminum into a countable number of atoms. This transformation underlies much of what students learn in stoichiometry, which is the study of the quantitative relationships between the reactants and products in chemical reactions. Real-world applications range from creating new materials to understanding biological processes, making the comprehension of chemical quantities invaluable for students.
