To determine the mass of [tex]\(6.02 \times 10^{23}\)[/tex] atoms of calcium, we start by understanding some fundamental concepts and relationships in chemistry.
1. Atomic Mass and Its Relevance:
- The atomic mass of calcium, which is a measure of the mass of one mole of calcium atoms, is given as 40.08 atomic mass units (amu).
- One mole of any substance contains exactly [tex]\(6.02 \times 10^{23}\)[/tex] (Avogadro's number) of its constituent particles (atoms, molecules, etc.).
2. Avogadro's Number:
- Avogadro's number [tex]\( (N_A) \)[/tex] is [tex]\( 6.02 \times 10^{23} \)[/tex] and signifies the number of atoms in one mole of an element.
3. Calculation Methodology:
- According to the definition, one mole of calcium has an atomic mass of 40.08 grams.
- Since one mole of calcium contains [tex]\( 6.02 \times 10^{23} \)[/tex] calcium atoms, it directly corresponds that [tex]\( 6.02 \times 10^{23} \)[/tex] calcium atoms would have the mass equivalent to the atomic mass of calcium.
4. Mass Determination:
- Therefore, the mass of [tex]\( 6.02 \times 10^{23} \)[/tex] calcium atoms is:
[tex]\[
\frac{40.08 \, \text{grams}}{6.02 \times 10^{23} \, \text{atoms}} \times 6.02 \times 10^{23} \, \text{atoms}
\][/tex]
5. Simplification:
- Notice that the [tex]\(6.02 \times 10^{23}\)[/tex] atoms in the numerator and the denominator cancel each other out:
[tex]\[
40.08 \, \text{grams}
\][/tex]
Thus, the mass of [tex]\(6.02 \times 10^{23}\)[/tex] atoms of calcium is [tex]\(40.08\)[/tex] grams.
