Q4.117CP - Chemistry: Molecular Nature Of Matter And Change

Question

To find the mass percent of dolomite CaMg(CO₃)₂ in a soil sample, a geochemist titrates 13.86g of soil with 33.56mL of 0.2516M HCl. What is the mass percent of dolomite in the soil?

Step-by-Step Solution

Answer

You need to calculate the mass percent of dolomite in the soil.

Step 1: Balanced chemical equation

Reaction of dolomite and HCl forms calcium, magnesium, chlorine ions; water and carbon dioxide. The balanced equation can be written as

 

 $\mathrm{CaMg}{\left({\mathrm{CO}}_3\right)}_2\left(\mathrm{s}\right)+4\mathrm{HCl}\left(\mathrm{aq}\right)\to {\mathrm{Ca}}^{2+}\left(\mathrm{aq}\right)+{\mathrm{Mg}}^{2+}\left(\mathrm{aq}\right)+4{\mathrm{Cl}}^{-}\left(\mathrm{aq}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)+2{\mathrm{CO}}_2\left(\mathrm{g}\right)$

Step 2: Calculation of moles of HCl

According to the question,

 

Volume of HCl = 33.56mL = 0.03356L

 

Molarity of HCl = 0.2516M

 

Again you know,

 

 $\mathrm{moles}=\mathrm{molarity}\times \mathrm{volume}$

 

Now, moles of HCl

 $\begin{array}{l}=(0.2516\times 0.03356)\left(\mathrm{mol}\right)\\ =0.00844\left(\mathrm{mol}\right)\end{array}$

 

 

Hence, moles of HCl are 0.00844mol.

Step 3: Calculation of moles of CaMg(CO 3 ) 2

According to the balanced equation

 

$\mathrm{CaMg}{\left({\mathrm{CO}}_3\right)}_2\left(\mathrm{s}\right)+4\mathrm{HCl}\left(\mathrm{aq}\right)\to {\mathrm{Ca}}^{2+}\left(\mathrm{aq}\right)+{\mathrm{Mg}}^{2+}\left(\mathrm{aq}\right)+4{\mathrm{Cl}}^{-}\left(\mathrm{aq}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)+2{\mathrm{CO}}_2\left(\mathrm{g}\right)$

 

1 mole of CaMg(CO₃)₂ reacts with 4 moles HCl

 

Now, moles of CaMg(CO₃)₂

 

 $\begin{array}{l}=0.00844\times \frac{1}{4}\left(\mathrm{mol}\right)\\ =0.00211\left(\mathrm{mol}\right)\end{array}$

 

Hence, moles of CaMg(CO₃)₂ are 0.00211mol.

Step 4: Calculation of mass of CaMg(CO 3 ) 2

Moles of CaMg(CO₃)₂ = 0.00211moles

 

Molecular mass of CaMg(CO₃)₂ = 184.305g/mol

 

Again you know,

 

 $\mathrm{mass}=\mathrm{moles}\times \mathrm{mass}\left(\mathrm{molar}\right)$

 

Mass of CaMg(CO₃)₂

 _{$\begin{array}{l}=0.00211\times 184.305\left(\mathrm{g}\right)\\ =0.3889\left(\mathrm{g}\right)\end{array}$}

 

 

Hence, mass of CaMg(CO₃)₂ is 0.3889g.

Step 5: Calculation of mass percent of CaMg(CO 3 ) 2

Again you know, 

 

Mass percent of CaMg(CO₃)₂

 $\begin{array}{l}=\frac{\mathrm{mass}\left[\mathrm{CaMg}{\left({\mathrm{CO}}_3\right)}_2\right]}{\mathrm{mass}\left(\mathrm{sample}\right)}\times 100\mathrm{\%}\\ =\frac{0.3889}{13.86}\times 100\mathrm{\%}\\ =2.806\mathrm{\%}\end{array}$

 

 

Hence, mass percent of CaMg(CO₃)₂ is 2.806%.

Step 6: Conclusion

Hence, the mass percent of dolomite in the soil is 2.806%.