- Balance charges for neutral compounds using the equation \(n \cdot q^{+} = m \cdot |q^{-}|\).
- For \(Na^{+}: Br^{-}\), solve \(1 \cdot 1 = m \cdot 1\) to get \(m = 1\).
- For \(Al^{3+}: Cl^{-}\), solve \(1 \cdot 3 = m \cdot 1\) to get \(m = 3\).
- For \(Mg^{2+}: O^{2-}\), solve \(1 \cdot 2 = m \cdot 2\) to get \(m = 1\).
- For \(Al^{3+}: O^{2-}\), solve \(2 \cdot 3 = m \cdot 2\) to get \(m = 3\).
- Final ratios: \(1:1, 1:3, 1:1, 2:3\). \(\boxed{1:1, 1:3, 1:1, 2:3}\)
Explanation
- Understanding Neutral Compound Formation
To form a neutral ionic compound, the total positive charge from the cations must balance the total negative charge from the anions. This means that if we have a cation with charge \(q^{+}\) and an anion with charge \(q^{-}\), the number of cations \(n\) and the number of anions \(m\) must satisfy the equation \(n \cdot q^{+} + m \cdot q^{-} = 0\), or equivalently, \(n \cdot |q^{+}| = m \cdot |q^{-}|\). We want to find the missing integer \(m\) for each given ratio \(n:m\).
- Calculating the Stoichiometric Ratios
For each pair, we substitute the known values into the neutrality equation:
- For \(Na^{+}:Br^{-}\) with ratio \(1:m\):
The charges are \(q^{+} = +1\) and \(q^{-} = -1\).
\(1 \cdot (+1) + m \cdot (-1) = 0 \implies 1 - m = 0 \implies m = 1\).
The ratio is \(1:1\).
- For \(Al^{3+}:Cl^{-}\) with ratio \(1:m\):
The charges are \(q^{+} = +3\) and \(q^{-} = -1\).
\(1 \cdot (+3) + m \cdot (-1) = 0 \implies 3 - m = 0 \implies m = 3\).
The ratio is \(1:3\).
- For \(Mg^{2+}:O^{2-}\) with ratio \(1:m\):
The charges are \(q^{+} = +2\) and \(q^{-} = -2\).
\(1 \cdot (+2) + m \cdot (-2) = 0 \implies 2 - 2m = 0 \implies m = 1\).
The ratio is \(1:1\).
- For \(Al^{3+}:O^{2-}\) with ratio \(2:m\):
The charges are \(q^{+} = +3\) and \(q^{-} = -2\).
\(2 \cdot (+3) + m \cdot (-2) = 0 \implies 6 - 2m = 0 \implies 2m = 6 \implies m = 3\).
The ratio is \(2:3\).
- Final Results and Conclusion
The completed ratios for neutral ionic compounds are as follows:
- \(Na^{+}: Br^{-} = 1: 1\)
- \(Al^{3+}: Cl^{-} = 1: 3\)
- \(Mg^{2+}: O^{2-} = 1: 1\)
- \(Al^{3+}: O^{2-} = 2: 3\)
These ratios represent the simplest integer combination that results in a net charge of zero.
Examples
Understanding ionic ratios is essential in chemistry for predicting how different substances interact. For instance, when designing medicines, chemists need to know how ions combine to form stable, neutral salts that can be safely absorbed by the body. Mastering this skill allows students to predict chemical formulas simply by looking at the charges of the constituent elements, a foundational step in understanding chemical reactions and material science.