To determine how many moles are present in a sample containing [tex]\( 4.99 \times 10^{27} \)[/tex] molecules, we need to use Avogadro's number. Avogadro's number is [tex]\( 6.02214076 \times 10^{23} \)[/tex] molecules per mole. The relationship is given by:
[tex]\[ \text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}} \][/tex]
Given that the number of molecules is [tex]\( 4.99 \times 10^{27} \)[/tex], we can plug this into the formula:
[tex]\[ \text{Number of moles} = \frac{4.99 \times 10^{27}}{6.02214076 \times 10^{23}} \][/tex]
Now, performing the division:
[tex]\[ \text{Number of moles} = \frac{4.99 \times 10^{27}}{6.02214076 \times 10^{23}} \approx 8286.089945197495 \][/tex]
So, the number of moles in a gas with [tex]\( 4.99 \times 10^{27} \)[/tex] molecules is approximately [tex]\( 8286.089945197495 \)[/tex] moles.
