Problem 147 - Chemistry The Molecular Science

Question

Dolomite, found in soil, is \(\mathrm{CaMg}\left(\mathrm{CO}_{3}\right)_{2}\). If a \(20.0-\mathrm{g}\) sample of soil is titrated with \(65.25 \mathrm{~mL}\) of \(0.2500-\mathrm{M} \mathrm{HCl}\) calculate the mass percent of dolomite in the soil sample.

Step-by-Step Solution

Answer

The mass percent of dolomite in the soil sample is 3.76%.

Step 1: Write the Balanced Chemical Equation

Dolomite reacts with HCl according to the following balanced chemical equation:\[\text{CaMg(CO}_3)_2 + 4\text{HCl} \rightarrow \text{CaCl}_2 + \text{MgCl}_2 + 2\text{CO}_2 + 2\text{H}_2\text{O} \]

Step 2: Calculate Moles of HCl Used

First, we calculate the moles of HCl used in the titration. Using the concentration and volume of HCl: \[\text{Moles of HCl} = 0.2500\, \text{M}\times 65.25\,\text{mL}\times\frac{1\,\text{L}}{1000\, \text{mL}} = 0.0163125\,\text{mol}\]

Step 3: Determine Moles of Dolomite

From the balanced equation, 1 mole of dolomite reacts with 4 moles of HCl. Therefore, moles of dolomite are:\[\text{Moles of dolomite} = \frac{0.0163125}{4} = 0.0040781\,\text{mol}\]

Step 4: Calculate Mass of Dolomite

Find the molar mass of dolomite: \[\text{Molar mass of CaMg(CO}_3)_2 = 40.08 + 24.31 + 2\times(12.01 + 3\times16.00) = 184.39\, \text{g/mol}\]Then calculate the mass:\[\text{Mass of dolomite} = 0.0040781 \,\text{mol} \times 184.39\,\text{g/mol} = 0.7519\, \text{g}\]

Step 5: Calculate Mass Percent of Dolomite in Soil

Use the mass of dolomite and the total mass of the soil sample to find the mass percent:\[\text{Mass percent} = \left(\frac{0.7519\, \text{g}}{20.0\, \text{g}}\right)\times 100 = 3.759\,\%\]

Key Concepts

Dolomite

Dolomite is a mineral that holds significant importance in both geology and chemistry. It is a compound made up of calcium magnesium carbonate, with the chemical formula \( \text{CaMg(CO}_3)_2 \). This mineral is commonly found in sedimentary rocks. It provides essential nutrients and contributes to soil fertility.

In the context of titration, dolomite is noteworthy due to its ability to react with acids, such as hydrochloric acid (HCl). This reaction helps determine its presence and concentration through laboratory analysis. Understanding the role of dolomite in soil chemistry aids in environmental studies and agriculture.

• Composed of calcium, magnesium, and carbonate ions
• Takes part in acid-base reactions
• Used to determine composition in soil analysis

Its interactions in titration serve as a practical example of chemical reactions in mineral analysis.

Mass Percent

Mass percent is a way of expressing the concentration of a component in a mixture. It tells us what fraction of the total mass is made up by the specific component. Calculating the mass percent involves using the formula: \[ \text{Mass percent} = \left(\frac{\text{mass of component}}{\text{total mass of mixture}}\right) \times 100 \] In the context of the exercise, we need to find the mass percent of dolomite in a soil sample.

To do this, we determine the mass of dolomite reacting in the titration and divide it by the total mass of the soil sample, then multiply by 100 to convert to a percentage.

• Useful for comparing compositions
• Requires accurate mass measurements
• Expressed as a percentage

This calculation provides a clearer understanding of the composition in various applications, such as identifying nutrient levels in soil.

Molar Mass Calculation

Calculating molar mass is essential in chemistry, especially when dealing with reactions. Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find dolomite's molar mass, sum up the atomic masses of its constituent elements in its chemical formula \( \text{CaMg(CO}_3)_2 \).

The calculation is as follows:

• Calcium (Ca): \( 40.08 \, \text{g/mol} \)
• Magnesium (Mg): \( 24.31 \, \text{g/mol} \)
• Carbon (C) in \( 2 \text{CO}_3 \): \( 2 \times 12.01 \, \text{g/mol} \)
• Oxygen (O) in \( 6 \times 16.00 \, \text{g/mol} \)

The total molar mass calculated is \( 184.39 \, \text{g/mol} \).
This value is crucial for converting between moles and grams, enabling precise stoichiometric calculations in chemical equations.

Balanced Chemical Equation

A balanced chemical equation is fundamental for understanding chemical reactions. It ensures that the same number of atoms of each element is present on both sides of the equation, reflecting the law of conservation of mass.

The balanced equation provided in the exercise is:\[\text{CaMg(CO}_3)_2 + 4\text{HCl} \rightarrow \text{CaCl}_2 + \text{MgCl}_2 + 2\text{CO}_2 + 2\text{H}_2\text{O} \] This equation illustrates the reactants and products of dolomite reacting with hydrochloric acid.

Key aspects of a balanced equation include:

• Equality in the number of each atom on both sides
• Coordination of complex multi-element compounds
• Clear identification of phases (solid, liquid, gas)

This balanced equation is vital for determining stoichiometry and understanding the proportions in which reactants combine and products form.