Question

atoms of elements
use the molar mass of the element to convert from g to mol.

1. 3.90 g radium to mol radium
2. $4.88 \times 10^{5}$ g mercury to mol mercury
3. $2.91 \times 10^{-3}$ g arsenic to mol arsenic

multi-step conversions: use both avogadros number and a molar mass to solve:

1. $7.3 \times 10^{15}$ atoms neon to grams neon
2. $5.24 \times 10^{-2}$ grams uranium to atoms of uranium
3. $9.21 \times 10^{25}$ atoms of zirconium to g zirconium

Explanation:

Step1: Get radium molar mass, convert g to mol

Molar mass of radium (Ra) = $226\ \text{g/mol}$.
$\text{mol Ra} = \frac{3.90\ \text{g}}{226\ \text{g/mol}} = 0.0173\ \text{mol}$

Step2: Get mercury molar mass, convert g to mol

Molar mass of mercury (Hg) = $200.59\ \text{g/mol}$.
$\text{mol Hg} = \frac{4.88 \times 10^5\ \text{g}}{200.59\ \text{g/mol}} \approx 2433\ \text{mol}$

Step3: Get arsenic molar mass, convert g to mol

Molar mass of arsenic (As) = $74.92\ \text{g/mol}$.
$\text{mol As} = \frac{2.91 \times 10^{-3}\ \text{g}}{74.92\ \text{g/mol}} \approx 3.88 \times 10^{-5}\ \text{mol}$

Step4: Convert Ne atoms to mol, then to g

Molar mass of neon (Ne) = $20.18\ \text{g/mol}$, Avogadro's number $N_A = 6.022 \times 10^{23}\ \text{atoms/mol}$.
$\text{mol Ne} = \frac{7.3 \times 10^{15}\ \text{atoms}}{6.022 \times 10^{23}\ \text{atoms/mol}} \approx 1.212 \times 10^{-8}\ \text{mol}$
$\text{g Ne} = 1.212 \times 10^{-8}\ \text{mol} \times 20.18\ \text{g/mol} \approx 2.44 \times 10^{-7}\ \text{g}$

Step5: Convert U grams to mol, then to atoms

Molar mass of uranium (U) = $238.03\ \text{g/mol}$.
$\text{mol U} = \frac{5.24 \times 10^{-2}\ \text{g}}{238.03\ \text{g/mol}} \approx 2.201 \times 10^{-4}\ \text{mol}$
$\text{atoms U} = 2.201 \times 10^{-4}\ \text{mol} \times 6.022 \times 10^{23}\ \text{atoms/mol} \approx 1.325 \times 10^{20}\ \text{atoms}$

Step6: Convert Zr atoms to mol, then to g

Molar mass of zirconium (Zr) = $91.22\ \text{g/mol}$.
$\text{mol Zr} = \frac{9.21 \times 10^{25}\ \text{atoms}}{6.022 \times 10^{23}\ \text{atoms/mol}} \approx 152.94\ \text{mol}$
$\text{g Zr} = 152.94\ \text{mol} \times 91.22\ \text{g/mol} \approx 1.395 \times 10^4\ \text{g}$

Answer:

1. $0.0173\ \text{mol radium}$
2. $2433\ \text{mol mercury}$
3. $3.88 \times 10^{-5}\ \text{mol arsenic}$
4. $2.44 \times 10^{-7}\ \text{grams neon}$
5. $1.33 \times 10^{20}\ \text{atoms of uranium}$
6. $1.40 \times 10^4\ \text{g zirconium}$