Question

finding moles from atoms: how many moles are in 1.5x10²⁴ atoms of neon (ne)?

Explanation:

Step1: Recall Avogadro's number

Avogadro's number \( N_A=6.022\times 10^{23}\text{ atoms/mol}\). The formula to convert atoms to moles is \( n=\frac{N}{N_A}\), where \( N\) is the number of atoms and \( n\) is the number of moles.

Step2: Substitute the values

Given \( N = 1.5\times 10^{24}\text{ atoms}\) and \( N_A=6.022\times 10^{23}\text{ atoms/mol}\). Then \( n=\frac{1.5\times 10^{24}}{6.022\times 10^{23}}\).

$$ n=\frac{1.5}{6.022}\times\frac{10^{24}}{10^{23}} $$

Using the rule of exponents \( a^m\div a^n=a^{m - n}\), so \(\frac{10^{24}}{10^{23}}=10^{24-23}=10\). And \(\frac{1.5}{6.022}\approx0.249\). Then \( n\approx0.249\times10 = 2.49\approx2.5\)

Answer:

\( 2.5\) moles