Question

Gold has a molar mass of $\mathbf{197}\mathbf{}\mathit{g}\mathbf{/}\mathit{m}\mathit{o}\mathit{l}$,

(a) How many moles of gold are in a sample ofpure gold?

(b) How many atoms are in the sample?

Short answer

(a) 0.0127 mol of gold is in a sample of pure gold.

(b) There are $7.64\times {10}^{21}$atoms in the sample.

Step-by-step solution

Determining the concept

Use Equation 19-2 and equation 19-3 to find the number of moles and the number of atoms in the sample.

The formulae are as follows:

$N=n{N}_A$

$n=\frac{M_{sam}}{M}$

Here,$N_A$is Avogadro’s number, N is the total number of atoms, $M_{sam}$is sample mass, $M$is molar mass of gold and $n$is the number of moles of gold.

(a) Determining the number of moles of gold in a sample of 2.5 g pure gold 

According to Equation19-3,is sample mass andis molar mass of gold. From that, find the number of moles of gold.

$n=\frac{M_{sam}}{M}$

$n=\frac{2.5}{197}$

$n=0.0127\text{mol}$

Therefore, 0.0127 mol of gold is in a sample of $2.5g$pure gold.

(b) Determining the number of atoms in the sample

According to equation 19.2, the number of atoms is

$N=n{N}_A$

Here,is Avogadro’s number andis the number of moles of gold. By substituting$n$value, the total number of atoms is found from the equation to be

$N=0.0127\times 6.02\times {10}^{23}$

$N=7.64\times {10}^{21}$

Therefore, there are $7.64\times {10}^{21}$atoms in the sample.