Question

dimensional analysis two steps:
use both avogadros number and a molar mass to solve:
$\frac{1 mol}{6.02e23 things}$ and $\frac{1 mol}{molar mass (g)}$

1. 3.77 g $h_2o$ to molecules of $h_2o$
2. $4.2 \times 10^{24}$ atoms of ag to g ag
3. $1.56 \times 10^{24}$ molecules of $mgcl_2$ to grams $mgcl_2$
4. $4.96 \times 10^{24}$ atoms au to g au
5. 3.25g $caco_3$ to molecules $caco_3$
6. $8.56 \times 10^3$ molecules nacl to g nacl

Explanation:

Step1: Calculate molar mass of $\text{H}_2\text{O}$

Molar mass of $\text{H}_2\text{O} = 2\times1.008 + 16.00 = 18.016\ \text{g/mol}$

Step2: Convert grams to moles

$\text{Moles of H}_2\text{O} = \frac{3.77\ \text{g}}{18.016\ \text{g/mol}} \approx 0.2093\ \text{mol}$

Step3: Convert moles to molecules

$\text{Molecules of H}_2\text{O} = 0.2093\ \text{mol} \times 6.02\times10^{23}\ \text{molecules/mol} \approx 1.26\times10^{23}$

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Step1: Convert Ag atoms to moles

$\text{Moles of Ag} = \frac{4.2\times10^{24}\ \text{atoms}}{6.02\times10^{23}\ \text{atoms/mol}} \approx 6.977\ \text{mol}$

Step2: Molar mass of Ag = 107.87 g/mol

$\text{Mass of Ag} = 6.977\ \text{mol} \times 107.87\ \text{g/mol} \approx 752\ \text{g}$

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Step1: Calculate molar mass of $\text{MgCl}_2$

Molar mass of $\text{MgCl}_2 = 24.305 + 2\times35.45 = 95.205\ \text{g/mol}$

Step2: Convert molecules to moles

$\text{Moles of MgCl}_2 = \frac{1.56\times10^{24}\ \text{molecules}}{6.02\times10^{23}\ \text{molecules/mol}} \approx 2.591\ \text{mol}$

Step3: Convert moles to grams

$\text{Mass of MgCl}_2 = 2.591\ \text{mol} \times 95.205\ \text{g/mol} \approx 247\ \text{g}$

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Step1: Convert Au atoms to moles

$\text{Moles of Au} = \frac{4.96\times10^{24}\ \text{atoms}}{6.02\times10^{23}\ \text{atoms/mol}} \approx 8.239\ \text{mol}$

Step2: Molar mass of Au = 196.97 g/mol

$\text{Mass of Au} = 8.239\ \text{mol} \times 196.97\ \text{g/mol} \approx 1623\ \text{g}$

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Step1: Calculate molar mass of $\text{CaCO}_3$

Molar mass of $\text{CaCO}_3 = 40.08 + 12.01 + 3\times16.00 = 100.09\ \text{g/mol}$

Step2: Convert grams to moles

$\text{Moles of CaCO}_3 = \frac{3.25\ \text{g}}{100.09\ \text{g/mol}} \approx 0.03247\ \text{mol}$

Step3: Convert moles to molecules

$\text{Molecules of CaCO}_3 = 0.03247\ \text{mol} \times 6.02\times10^{23}\ \text{molecules/mol} \approx 1.95\times10^{22}$

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Step1: Calculate molar mass of $\text{NaCl}$

Molar mass of $\text{NaCl} = 22.99 + 35.45 = 58.44\ \text{g/mol}$

Step2: Convert molecules to moles

$\text{Moles of NaCl} = \frac{8.56\times10^{3}\ \text{molecules}}{6.02\times10^{23}\ \text{molecules/mol}} \approx 1.422\times10^{-20}\ \text{mol}$

Step3: Convert moles to grams

$\text{Mass of NaCl} = 1.422\times10^{-20}\ \text{mol} \times 58.44\ \text{g/mol} \approx 8.31\times10^{-19}\ \text{g}$

Answer:

1. $\boldsymbol{1.26\times10^{23}}$ molecules of $\text{H}_2\text{O}$
2. $\boldsymbol{752\ \text{g}}$ of $\text{Ag}$
3. $\boldsymbol{247\ \text{g}}$ of $\text{MgCl}_2$
4. $\boldsymbol{1623\ \text{g}}$ of $\text{Au}$
5. $\boldsymbol{1.95\times10^{22}}$ molecules of $\text{CaCO}_3$
6. $\boldsymbol{8.31\times10^{-19}\ \text{g}}$ of $\text{NaCl}$