Problem 118 - General Chemistry

Question

An antacid tablet has calcium carbonate as the active ingredient; other ingredients include a starch binder. You dissolve the tablet in hydrochloric acid and filter off insoluble material. You add potassium oxalate to the filtrate (containing calcium ion) to precipitate calcium oxalate. If a tablet weighing \(0.680 \mathrm{~g}\) gave \(0.629 \mathrm{~g}\) of calcium oxalate, what is the mass percentage of active ingredient in the tablet?

Step-by-Step Solution

Answer

The mass percentage of calcium carbonate in the tablet is approximately 72.21%.

Step 1: Write the relevant chemical equations

When calcium carbonate (CaCO₃) reacts with hydrochloric acid (HCl), calcium chloride (CaCl₂), water, and carbon dioxide are formed: \[ \text{CaCO}_3 + 2 \text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2 \] When calcium ions (Ca²⁺) react with potassium oxalate (K₂C₂O₄), calcium oxalate (CaC₂O₄) precipitates: \[ \text{Ca}^{2+} + \text{C}_2\text{O}_4^{2-} \rightarrow \text{CaC}_2\text{O}_4 \]

Step 2: Calculate moles of calcium oxalate

Use the molar mass of calcium oxalate \(\text{CaC}_2\text{O}_4\) to find the moles. The molar mass of \(\text{CaC}_2\text{O}_4\) is approximately 128.10 g/mol. For 0.629 g of calcium oxalate, the moles are given by: \[ \frac{0.629 \text{ g}}{128.10 \text{ g/mol}} \approx 0.00491 \text{ mol} \]

Step 3: Determine moles of calcium carbonate

Each mole of calcium oxalate precipitated corresponds to one mole of calcium carbonate dissolved. Therefore, the moles of calcium carbonate also equal 0.00491 mol.

Step 4: Calculate mass of calcium carbonate

Find the mass of calcium carbonate using its molar mass (100.09 g/mol): \[ 0.00491 \text{ mol} \times 100.09 \text{ g/mol} = 0.491 \text{ g} \]

Step 5: Calculate the mass percentage of calcium carbonate

Mass percentage is calculated as: \[ \frac{\text{Mass of CaCO}_3}{\text{Total mass of tablet}} \times 100 = \frac{0.491 \text{ g}}{0.680 \text{ g}} \times 100 \approx 72.21\% \]

Key Concepts

Calcium Carbonate

Calcium carbonate, chemically known as \( \text{CaCO}_3 \), is a common substance found in rocks as minerals like limestone and marble. It's the active ingredient in many antacid tablets. Antacids work by neutralizing stomach acid to relieve symptoms like heartburn and indigestion. Calcium carbonate has a simple chemical formula which makes calculations straightforward in chemical analysis. This compound reacts with acids, like hydrochloric acid (HCl), to form calcium chloride, water, and carbon dioxide, releasing a gas that provides the 'fizz' in effervescing antacids.
When using calcium carbonate for chemical analysis, it is crucial to understand how it interacts with other chemicals and how its mass can be measured accurately. Usually, calcium carbonate is measured by precipitating it in another form, like calcium oxalate, allowing for quantification based on the weight of the precipitate formed.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform into different substances called products. They involve the breaking and forming of bonds between atoms. In the exercise, there are two chemical reactions to consider:

• The reaction between calcium carbonate (\( \text{CaCO}_3 \)) and hydrochloric acid (\( \text{HCl} \)), which yields calcium chloride (\( \text{CaCl}_2 \)), water, and carbon dioxide. It's an example of an acid-carbonate reaction that produces a salt, water, and gas.
• The reaction between calcium ions (\( \text{Ca}^{2+} \)) and potassium oxalate (\( \text{K}_2\text{C}_2\text{O}_4 \)), which forms calcium oxalate (\( \text{CaC}_2\text{O}_4 \)) as a precipitate. This is a precipitation reaction, where a solid forms out of a solution.

Understanding these reactions is essential for predicting the products and determining the quantities of substances involved. The reactions highlight important concepts such as stoichiometry and the conservation of mass.

Molar Mass

Molar mass is a fundamental concept in chemistry, referring to the mass of one mole of a given substance. It's usually expressed in grams per mole (g/mol). For calcium carbonate \( \text{CaCO}_3 \), the molar mass is approximately 100.09 g/mol, while for calcium oxalate \( \text{CaC}_2\text{O}_4 \), it's about 128.10 g/mol.
The process of calculating molar mass involves summing the atomic masses of all atoms in a molecule. For example:

• Calcium (Ca): 40.08 g/mol
• Carbon (C): 12.01 g/mol
• Oxygen (O): each approximately 16.00 g/mol

Adding these values gives the molar mass of \( \text{CaCO}_3 \) as \( 40.08 + 12.01 + (3 \times 16.00) \) g/mol, which totals approximately 100.09 g/mol.
Understanding molar masses allows precise calculations during chemical analysis, such as determining how many moles of a substance are present in a measured mass, which is crucial to solving many chemistry problems.

Precipitation Reaction

Precipitation reactions are an important type of chemical reaction. They occur when two soluble salts react in a solution to form one or more insoluble products, called precipitates. Precipitates are solids that settle out of the solution, usually because the product's solubility in the solution conditions is minimal.
In the exercise, a precipitation reaction is utilized to isolate calcium from a solution containing calcium ions. When potassium oxalate (\( \text{K}_2\text{C}_2\text{O}_4 \)) is added to this solution, calcium oxalate (\( \text{CaC}_2\text{O}_4 \)) forms as a precipitate. This reaction is particularly useful in chemical analysis for determining the amount of calcium because the precipitate can be filtered, dried, and weighed.
Key aspects of a precipitation reaction include:

• The formation of a solid from a liquid solution.
• Ability to separate and quantify components of mixtures.
• General requirement for the reaction to occur under certain conditions, such as pH and temperature, to ensure maximum yield of the precipitate.

These reactions are widely used in laboratory settings for qualitative and quantitative analysis purposes.