How Many Atoms Of Ca Are Present In 80.156 Grams Of Ca?A. $1.2044 \times 10^{24}$B. $2.4088 \times 10^{24}$C. $4.8270 \times 10^{25}$D. $1.9346 \times 10^{27}$
Understanding the Problem
In this problem, we are asked to find the number of atoms of calcium (Ca) present in 80.156 grams of Ca. To solve this, we need to use the concept of atomic mass and Avogadro's number.
Atomic Mass and Avogadro's Number
The atomic mass of calcium is 40.078 g/mol. Avogadro's number is a constant that represents the number of particles (atoms or molecules) in one mole of a substance. It is equal to 6.022 x 10^23 particles/mol.
Calculating the Number of Moles
To find the number of moles of calcium in 80.156 grams, we can use the formula:
Number of moles = mass of substance / atomic mass
Plugging in the values, we get:
Number of moles = 80.156 g / 40.078 g/mol = 2.00 mol
Calculating the Number of Atoms
Now that we have the number of moles, we can use Avogadro's number to find the number of atoms:
Number of atoms = number of moles x Avogadro's number
Plugging in the values, we get:
Number of atoms = 2.00 mol x 6.022 x 10^23 atoms/mol = 1.2044 x 10^24 atoms
Conclusion
Therefore, the number of atoms of calcium present in 80.156 grams of Ca is 1.2044 x 10^24 atoms.
Answer
The correct answer is A. .
Additional Information
To verify the answer, we can also use the formula:
Number of atoms = (mass of substance x Avogadro's number) / atomic mass
Plugging in the values, we get:
Number of atoms = (80.156 g x 6.022 x 10^23 atoms/g) / 40.078 g/mol = 1.2044 x 10^24 atoms
This confirms that the correct answer is A. .
Calculating the Number of Atoms in Different Masses of Calcium
To calculate the number of atoms in different masses of calcium, we can use the same formula:
Number of atoms = (mass of substance x Avogadro's number) / atomic mass
Here are some examples:
- 10.016 grams of Ca: Number of atoms = (10.016 g x 6.022 x 10^23 atoms/g) / 40.078 g/mol = 1.2044 x 10^23 atoms
- 50.078 grams of Ca: Number of atoms = (50.078 g x 6.022 x 10^23 atoms/g) / 40.078 g/mol = 6.022 x 10^23 atoms
- 100.156 grams of Ca: Number of atoms = (100.156 g x 6.022 x 10^23 atoms/g) / 40.078 g/mol = 1.2044 x 10^24 atoms
Conclusion
In conclusion, the number of atoms of calcium present in a given mass of Ca can be calculated using the formula:
Number of atoms = (mass of substance x Avogadro's number) / atomic mass
Q: What is the atomic mass of calcium?
A: The atomic mass of calcium is 40.078 g/mol.
Q: What is Avogadro's number?
A: Avogadro's number is a constant that represents the number of particles (atoms or molecules) in one mole of a substance. It is equal to 6.022 x 10^23 particles/mol.
Q: How do I calculate the number of moles of calcium in a given mass?
A: To calculate the number of moles of calcium in a given mass, you can use the formula:
Number of moles = mass of substance / atomic mass
For example, if you have 80.156 grams of Ca, the number of moles would be:
Number of moles = 80.156 g / 40.078 g/mol = 2.00 mol
Q: How do I calculate the number of atoms of calcium in a given mass?
A: To calculate the number of atoms of calcium in a given mass, you can use the formula:
Number of atoms = number of moles x Avogadro's number
For example, if you have 2.00 moles of Ca, the number of atoms would be:
Number of atoms = 2.00 mol x 6.022 x 10^23 atoms/mol = 1.2044 x 10^24 atoms
Q: What is the relationship between the mass of a substance and the number of atoms?
A: The mass of a substance is directly proportional to the number of atoms. This means that if you have a larger mass of a substance, you will have more atoms.
Q: Can I use the formula to calculate the number of atoms in different masses of calcium?
A: Yes, you can use the formula to calculate the number of atoms in different masses of calcium. Simply plug in the values for the mass of the substance and the atomic mass, and you will get the number of atoms.
Q: What are some examples of calculating the number of atoms in different masses of calcium?
A: Here are some examples:
- 10.016 grams of Ca: Number of atoms = (10.016 g x 6.022 x 10^23 atoms/g) / 40.078 g/mol = 1.2044 x 10^23 atoms
- 50.078 grams of Ca: Number of atoms = (50.078 g x 6.022 x 10^23 atoms/g) / 40.078 g/mol = 6.022 x 10^23 atoms
- 100.156 grams of Ca: Number of atoms = (100.156 g x 6.022 x 10^23 atoms/g) / 40.078 g/mol = 1.2044 x 10^24 atoms
Q: What are some common mistakes to avoid when calculating the number of atoms in a given mass of calcium?
A: Some common mistakes to avoid include:
- Not using the correct atomic mass of calcium
- Not using the correct value for Avogadro's number
- Not converting the mass of the substance to grams
- Not using the correct formula to calculate the number of atoms
Q: How can I verify the answer to a calculation of the number of atoms in a given mass of calcium?
A: To verify the answer, you can use a different method to calculate the number of atoms, such as using the formula:
Number of atoms = (mass of substance x Avogadro's number) / atomic mass
This will give you the same answer as the original calculation, confirming that the answer is correct.