To determine how many moles are contained in [tex]\( 3.131 \times 10^{24} \)[/tex] particles, we can use Avogadro's constant. Avogadro's constant, [tex]\( 6.022 \times 10^{23} \)[/tex], tells us the number of particles in one mole of a substance.
Here’s the step-by-step process to solve this:
1. Identify the given quantity of particles: [tex]\( 3.131 \times 10^{24} \)[/tex] particles.
2. Identify Avogadro's constant: [tex]\( 6.022 \times 10^{23} \)[/tex] particles per mole.
3. Set up the calculation for moles: The number of moles can be calculated by dividing the number of particles by Avogadro's constant.
4. Perform the division: [tex]\[\text{moles} = \frac{3.131 \times 10^{24} \text{ particles}}{6.022 \times 10^{23} \text{ particles/mol}}.\][/tex]
When you perform this calculation:
[tex]\[ \text{moles} = \frac{3.131 \times 10^{24}}{6.022 \times 10^{23}} \approx 5.199269345732315 \text{ moles}.\][/tex]
After simplifying, we find that the number of moles is approximately [tex]\( 5.199 \)[/tex] moles.
Thus, the correct answer is:
A. [tex]\( \quad 5.199 \text{ mol}\)[/tex].
