Question

Write an equation to represent the reaction of gypsum, \(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O},\) with ammonium carbonate to produce ammonium sulfate (a fertilizer), calcium carbonate, and water.

Short answer

The balanced equation is \( \mathrm{CaSO_4 . 2H_2O} + 2 \mathrm{(NH_4)_2CO_3} → 2 \mathrm{(NH_4)_2SO_4} + \mathrm{CaCO_3} + 2\mathrm{H_2O} \)

Step-by-step solution

Identify the Reactants and Products

The reactants in the equation are given as gypsum (\( \mathrm{CaSO_4.2H_2O} \)) and ammonium carbonate (\( \mathrm{(NH_4)_2CO_3} \)). The products of the equation are given as ammonium sulfate (\( \mathrm{(NH_4)_2SO_4} \)), calcium carbonate (\( \mathrm{CaCO_3} \)), and water (\( \mathrm{H_2O} \)).

Write the Unbalanced Equation

Begin by writing an unbalanced chemical equation using the formulae of the reactants and products: \( \mathrm{CaSO_4.2H_2O} + \mathrm{(NH_4)_2CO_3} → \mathrm{(NH_4)_2SO_4} + \mathrm{CaCO_3} + \mathrm{H_2O} \)

Balance the Equation

One way to balance the equation is starting with the substances that appear once on each side - in this case, calcium and sulfate ions Ca and SO4. Verify that they are balanced. Next you can move to ammonium and carbonate ions. Both the left and right side of the equation should have two ammonium ions. You can balance this by placing a 2 in front of ammonium carbonate and ammonium sulfate. Lastly, balance the number of water molecules on both sides. The equation becomes: \( \mathrm{CaSO_4 . 2H_2O} + 2 \mathrm{(NH_4)_2CO_3} → 2 \mathrm{(NH_4)_2SO_4} + \mathrm{CaCO_3} + 2\mathrm{H_2O} \)

Key concepts

Balanced Chemical Equation

A balanced chemical equation represents a chemical reaction accurately. It shows the number of atoms for each element involved in the reactants and products. To balance a chemical equation, each kind of atom must have the same number of atoms on both sides of the equation. This ensures that mass is conserved, following the Law of Conservation of Mass. In our exercise, we tackled balancing the reaction of gypsum with ammonium carbonate.

• First, identify the elements and count the number of atoms on each side.
• Next, adjust coefficients to equalize the number of each type of atom on both sides of the reaction.

Here, the equation \[ \mathrm{CaSO_4 . 2H_2O} + 2 \mathrm{(NH_4)_2CO_3} \rightarrow 2 \mathrm{(NH_4)_2SO_4} + \mathrm{CaCO_3} + 2\mathrm{H_2O} \] shows that all atoms are balanced. Always double-check each atom, element by element, to ensure precision.

Reactants and Products

Reactants are the substances initially involved in a chemical reaction. They are transformed during the reaction to form different substances known as products. Understanding the distinction and transition from reactants to products is vital. In the given exercise, the reactants were gypsum (\(\mathrm{CaSO_4.2H_2O}\)) and ammonium carbonate (\(\mathrm{(NH_4)_2CO_3}\)), while the products were ammonium sulfate (\(\mathrm{(NH_4)_2SO_4}\)), calcium carbonate (\(\mathrm{CaCO_3}\)), and water (\(\mathrm{H_2O}\)).

• Recognizing reactants helps in writing the initial unbalanced equation.
• Listing the products allows tracking of what each reactant transforms into.

Reactants undergo breaking and forming of bonds, resulting in new products. Each reaction has its unique stoichiometry, reflecting the conversion from reactants to products.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It's rooted in the balanced chemical equation, which provides the ratio of the substances involved. Stoichiometry allows chemists to predict the quantities of products formed from given quantities of reactants. The coefficients in a balanced equation represent molar ratios of the reactants and products in the reaction.

• In our exercise, the balanced equation is necessary to understand how many moles of ammonium carbonate react with gypsum to yield ammonium sulfate and water.
• It shows that for every mole of \(\mathrm{CaSO_4.2H_2O}\), two moles of \(\mathrm{(NH_4)_2CO_3}\) are needed to produce two moles of \(\mathrm{(NH_4)_2SO_4}\), one mole of \(\mathrm{CaCO_3}\), and two moles of \(\mathrm{H_2O}\).

Understanding stoichiometry is crucial for accurately calculating reactant proportions and predicting the yield of a reaction. It is a foundational concept in both laboratory work and industrial processes.