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Zorluk: ZorPercentage Composition and Percentage Purity Calculations

A 5.00 g5.00\text{ g} sample of impure limestone (CaCO3\text{CaCO}_3) is strongly heated until decomposition is complete. If the loss in mass due to the escape of carbon dioxide (CO2\text{CO}_2) gas is 1.76 g1.76\text{ g}, what is the percentage purity of the limestone sample? [Relative atomic masses: Ca=40,C=12,O=16][\text{Relative atomic masses: } \text{Ca} = 40, \text{C} = 12, \text{O} = 16]

Cevap: 80 %

Cevap

The percentage purity of the limestone sample is 80%.
Thermal decomposition of calcium carbonate yields calcium oxide and carbon dioxide. The mass loss of 1.76 g corresponds to the evolved CO2. From the molar masses (CaCO3 = 100 g/mol, CO2 = 44 g/mol), 44 g of CO2 is released by 100 g of pure CaCO3. Thus, 1.76 g of CO2 is released by 4.00 g of pure CaCO3. Dividing the pure mass (4.00 g) by the original sample mass (5.00 g) and multiplying by 100 yields a percentage purity of 80%.

Adım Adım Çözüm

1
Write the balanced equation for the decomposition reaction.
\text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g)
The decrease in mass is entirely due to the evolved carbon dioxide gas.
2
Calculate the relative formula mass of calcium carbonate and carbon dioxide.
\text{Molar mass of } \text{CaCO}_3 = 100\text{ g/mol}, \quad \text{Molar mass of } \text{CO}_2 = 44\text{ g/mol}
Required to relate the mass of evolved gas to the mass of reacting calcium carbonate.
3
Calculate the mass of pure calcium carbonate in the sample.
\text{Mass of pure } \text{CaCO}_3 = \left(\frac{100}{44}\right) \times 1.76\text{ g} = 4.00\text{ g}
Direct stoichiometric ratio derived from 1 mol CaCO3 producing 1 mol CO2.
4
Calculate percentage purity.
\text{Percentage purity} = \left(\frac{4.00\text{ g}}{5.00\text{ g}}\right) \times 100 = 80\%
Ratio of pure reactant mass to total sample mass expressed as a percentage.

Anahtar Kavram

Calculating percentage purity using stoichiometry and gravimetric decomposition data.
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Percentage Composition and Percentage Purity Calculations

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