To determine the correctly balanced chemical equation for the reaction between [tex]\( Ca(OH)_2 \)[/tex] (calcium hydroxide) and [tex]\( HNO_3 \)[/tex] (nitric acid):
Let's analyze the options provided.
1. Option 1:
[tex]\[
Ca(OH)_2 + HNO_2 \rightarrow Ca^{2+} + NO_3^{-}
\][/tex]
This equation does not balance correctly. The reactants and products do not match in terms of atom count and charge balance.
2. Option 2:
[tex]\[
Ca(OH)_2 + 2 HNO_2 \rightarrow 2 H_2O + 2 NO_3
\][/tex]
This might seem correct at first glance, but let's verify this (Note: Actual balanced equation involves 2 [tex]\(HNO_3\)[/tex] rather than [tex]\(HNO_2\)[/tex]).
3. Option 3:
[tex]\[
CarOH + 2 HNO_2 \rightarrow H_2O + CaNO
\][/tex]
This equation also doesn’t follow proper chemical formulas and balanced forms.
4. Option 4:
[tex]\[
Ca(OH)_2 + 2 HNO_3 \rightarrow 2 H_2O + Ca(NO_2)_2
\][/tex]
Here, the chemical formulas make logical sense and the elemental count balances correctly:
[tex]\[
Ca(OH)_2 + 2 HNO_3 \rightarrow 2 H_2O + Ca(NO_3)_2
\][/tex]
This equates correctly where:
1 [tex]\(Ca\)[/tex] on both sides,
2 [tex]\(OH\)[/tex] from reactant yielding 2 [tex]\(H_2O\)[/tex] product,
2 [tex]\(HNO_3\)[/tex] yielding 2 [tex]\(NO_3\)[/tex] groups.
Hence, the balanced equation for the given reaction involving calcium hydroxide and nitric acid is:
[tex]\[
Ca(OH)_2 + 2 HNO_3 \rightarrow 2 H_2O + Ca(NO_3)_2
\][/tex]
From the above detailed analysis, Option 4 is indeed the correct answer.
