Question
find the mass in grams of 2.25x10^24 atoms of calcium(Ca
Answers
GPT-4o mini
To find the mass of 2.25 x 10²⁴ atoms of calcium (Ca), we can follow these steps:
1. **Find the number of moles of calcium atoms.**
The number of moles can be calculated using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mol.
\[
\text{Moles of Ca} = \frac{\text{Number of atoms}}{\text{Avogadro's number}} = \frac{2.25 \times 10^{24}}{6.022 \times 10^{23}} \approx 3.74 \text{ moles of Ca}
\]
2. **Determine the molar mass of calcium.**
The molar mass of calcium (Ca) is approximately 40.08 g/mol.
3. **Calculate the mass of calcium in grams.**
Using the number of moles and the molar mass:
\[
\text{Mass of Ca} = \text{Moles of Ca} \times \text{Molar mass of Ca} = 3.74 \, \text{moles} \times 40.08 \, \text{g/mol} \approx 150.7 \, \text{grams}
\]
Therefore, the mass of 2.25 x 10²⁴ atoms of calcium is approximately **150.7 grams**.
1. **Find the number of moles of calcium atoms.**
The number of moles can be calculated using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mol.
\[
\text{Moles of Ca} = \frac{\text{Number of atoms}}{\text{Avogadro's number}} = \frac{2.25 \times 10^{24}}{6.022 \times 10^{23}} \approx 3.74 \text{ moles of Ca}
\]
2. **Determine the molar mass of calcium.**
The molar mass of calcium (Ca) is approximately 40.08 g/mol.
3. **Calculate the mass of calcium in grams.**
Using the number of moles and the molar mass:
\[
\text{Mass of Ca} = \text{Moles of Ca} \times \text{Molar mass of Ca} = 3.74 \, \text{moles} \times 40.08 \, \text{g/mol} \approx 150.7 \, \text{grams}
\]
Therefore, the mass of 2.25 x 10²⁴ atoms of calcium is approximately **150.7 grams**.