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## Q. 4.15

Acid rain in the form of aqueous $H_{ 2}SO_{4}$ slowly erodes marble statues, as shown in Figure 4.15. If we add 16.75 mL of 0.0100 M $H_{ 2}SO_{ 4}$ to 25.00 mg of $CaCO_{ 3}$, will all of the $CaCO_{ 3}$ react?

## Verified Solution

Collect and Organize Given the volume and molarity of the $H_{ 2}SO_{ 4}$ solution, we can calculate the mass of $CaCO_{ 3}$ that reacts.

Analyze We need the balanced chemical equation for the reaction to determine the stoichiometry of the reaction between $CaCO_{ 3}$ and $H_{ 2}SO_{ 4}$ . The molecular equation is

$CaCO_{ 3}(s)+H_{ 2}SO_{ 4}(aq) →CaSO_{ 4}(s)+H_{ 2}O (\ell)+CO_{2}(g)$

One mole of $H_{ 2}SO_{ 4} (aq)$ reacts with 1 mole of $CaCO_{ 3} (s)$. The steps involved in calculating the moles of $H_{ 2}SO_{ 4}$ available and the mass (in milligrams) of calcium carbonate that will react with it are

Solve We calculate the mass of calcium carbonate that reacts, starting with the volume of sulfuric acid available and its molarity:

$16.75 \sout{mL H_{ 2}SO_{ 4}}\times \frac{1 \sout{L}}{10^{3} \sout{mL}} \times \frac{1.00\times 10^{-2} \sout{mol H_{ 2}SO_{ 4}}}{1 \sout{L H_{ 2}SO_{ 4}}} \times \frac{1 \sout{mol CaCO_{3}}}{1 \sout{mol H_{2}SO_{4}}} \times \frac{100.09 \sout{g CaCO_{3}}}{1 \sout{mol CaCO_{3}}} \times \frac{1000 mg CaCO_{3}}{1 \sout{g CaCO_{3}}} =16.8 mg CaCO_{3}$

Only 16.8 mg of the 25.00 mg sample will react to form solid calcium sulfate (Table 4.4).

 Table 4.4 Solubility Rules for Common Ionic Compounds in Water All compounds containing the following ions are soluble:  Cations: Group 1 ions (alkali metals) and $NH_{4}^{+}$  Anions: $NO_{3}^{-}$ and $CH_{3}COO^{-}$  (acetate) Compounds containing the following anions are soluble except as noted: $Cl^{-}, Br^{-}$, and $I^{-}$, except those of $Ag^{+}, Cu^{+}, Hg_{2}^{2+}$, and $Pb^{2+}$ $SO_{4}^{2-}$, except those of $Ba^{2+}, Ca^{2+}, Hg_{2}^{2+}, Pb^{2+}$, and $Sr^{2+}$ Insoluble compounds include the following: All hydroxides except those of group 1 cations and $Ca(OH)_{2}, Sr(OH)_{2}$, and $Ba(OH)_{2}$ All sulfides except those of group 1 cations and $NH_{4}^{+}, Cas, SrS$. and $Bas$ All carbonates except those of group 1 cations and $NH_{4}^{+}$ All phosphates except those of group 1 cations and $NH_{4}^{+}$ Most fluorides, though not those of group 1 cations and $NH_{4}^{+}$

Think About It The sulfuric acid is the limiting reactant, since only 67% of the $CaCO_{ 3}$ reacts under the conditions in this exercise.