Question

1. convert 1.73x10²⁴ atoms of k into moles: (5 points) include all units round to 3 sig figs

Explanation:

Step1: Recall Avogadro's number

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

Step2: Substitute the values

Given \(N = 1.73\times 10^{24}\text{ atoms}\) and \(N_A=6.022\times 10^{23}\text{ atoms/mol}\). Then \(n=\frac{1.73\times 10^{24}\text{ atoms}}{6.022\times 10^{23}\text{ atoms/mol}}\).
Using the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\), we have \(\frac{1.73}{6.022}\times10^{24- 23}\text{ mol}\).
\(\frac{1.73}{6.022}\approx0.287\), and \(10^{24 - 23}=10^1 = 10\). So \(n = 0.287\times10\text{ mol}=2.87\text{ mol}\) (rounded to 3 significant figures).

Answer:

\(2.87\space\text{mol}\)