- Start with the unbalanced skeletal equation: \(Ca(OH)_2 + HNO_3 \rightarrow H_2O + Ca(NO_3)_2\).
- Balance the nitrate ions by adding a coefficient of 2 to \(HNO_3\): \(Ca(OH)_2 + 2HNO_3 \rightarrow H_2O + Ca(NO_3)_2\).
- Balance the hydrogen and oxygen atoms by adding a coefficient of 2 to \(H_2O\): \(Ca(OH)_2 + 2HNO_3 \rightarrow 2H_2O + Ca(NO_3)_2\).
- The final balanced equation is \(\boxed{Ca(OH)_2 + 2HNO_3 \rightarrow 2H_2O + Ca(NO_3)_2}\).
Explanation
- Identifying Reactants and Products
The problem asks for the correctly balanced chemical equation for the neutralization reaction between calcium hydroxide, \(Ca(OH)_2,\) and nitric acid, \(HNO_3\). This is a double displacement reaction, which typically involves the exchange of ions to form water and a salt. Specifically, the calcium ion (\(Ca^{2+}\)) reacts with the nitrate ion (\(NO_3^{-}\)) to form calcium nitrate (\(Ca(NO_3)_2\)), while the hydrogen ions (\(H^+\)) and hydroxide ions (\(OH^-\)) combine to form water (\(H_2O\)). The initial unbalanced chemical equation is:
\[Ca(OH)_2 + HNO_3 \rightarrow H_2O + Ca(NO_3)_2\]
- Balancing the Chemical Equation
To balance the equation, we must ensure that the number of atoms of each element is equal on both sides of the reaction. Starting with the calcium nitrate, we observe that there are two nitrate groups (\(NO_3\)) on the product side. To balance this, we place a coefficient of 2 in front of the \(HNO_3\) on the reactant side:
\[Ca(OH)_2 + 2HNO_3 \rightarrow H_2O + Ca(NO_3)_2\]
Now, let's count the atoms on both sides:
- Reactants: 1 Calcium (Ca), 2 Hydroxide (OH) groups, 2 Hydrogen (H) atoms, and 2 Nitrate (\(NO_3\)) groups.
- Products: 1 Calcium (Ca), 2 Nitrate (\(NO_3\)) groups, 2 Hydrogen (H) atoms, 1 Oxygen (O) atom, and 2 Hydrogen (H) atoms from water.
Total Hydrogen count on the reactant side is \(2 + 2 = 4\). To obtain 4 Hydrogen atoms on the product side, we need 2 water molecules. Thus, the equation becomes:
\[Ca(OH)_2 + 2HNO_3 \rightarrow 2H_2O + Ca(NO_3)_2\]
- Conclusion and Selection of the Balanced Equation
Checking the atom count in the balanced equation \(Ca(OH)_2 + 2HNO_3 \rightarrow 2H_2O + Ca(NO_3)_2\):
- Calcium (Ca): 1 on the left, 1 on the right.
- Oxygen (O): \(2 + (2 \times 3) = 8\) on the left; \((2 \times 1) + (2 \times 3) = 8\) on the right.
- Hydrogen (H): \(2 + 2 = 4\) on the left; \(2 \times 2 = 4\) on the right.
- Nitrogen (N): 2 on the left, 2 on the right.
All atoms are balanced. Comparing this to the given options, we identify the correct choice.
Examples
Chemical equations are vital in everyday life, from cooking to industrial manufacturing. For instance, in agriculture, farmers use neutralization reactions to treat acidic soil by adding substances like lime (\(Ca(OH)_2\)). Understanding how to balance these reactions allows for the precise calculation of materials needed, ensuring that soil pH is optimized for crop health without causing chemical imbalances. This same principle of balancing applies to pharmaceutical development, where exact proportions of chemical components are essential for safety and efficacy.