Question

how many moles of atoms are contained in each of the following?
6.65 x 10²⁴ k atoms
mol
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26.0 g of au.
mol

Explanation:

Step1: Use the formula \(n=\frac{N}{N_A}\) for \(K\) atoms

Here, \(N = 6.65\times10^{24}\) (number of \(K\) atoms) and \(N_A=6.022\times 10^{23}\space mol^{-1}\) (Avogadro's number). So, \(n=\frac{6.65\times 10^{24}}{6.022\times 10^{23}}\).

Step2: Calculate the value for \(K\) atoms

\(n=\frac{6.65\times 10^{24}}{6.022\times 10^{23}}=\frac{6.65}{6.022}\times10\approx 11.0\space mol\)

Step3: Use the formula \(n = \frac{m}{M}\) for \(Au\)

The molar mass of \(Au\) (\(M\)) is \(196.97\space g/mol\) and \(m = 26.0\space g\). So, \(n=\frac{26.0}{196.97}\)

Step4: Calculate the value for \(Au\)

\(n=\frac{26.0}{196.97}\approx0.132\space mol\)

Answer:

For \(6.65\times 10^{24}\space K\) atoms: \(11.0\space mol\)
For \(26.0\space g\) of \(Au\): \(0.132\space mol\)