- Evaluate the sum of positive and negative charges to determine if ionic compounds maintain neutrality.
- Solve the five arithmetic expressions: \((+1) + (-1) = 0\), \((+2) + (-2) = 0\), \(2(+1) + (-2) = 0\), \((+3) + 3(-1) = 0\), and \(3(+2) + 2(-3) = 0\).
- Recognize that each expression equals 0, verifying the principle of charge neutrality.
- Final results: \(\boxed{0, 0, 0, 0, 0}\).
Explanation
- Analysis of Chemical Charge Neutrality
In chemistry, ionic compounds are formed when cations (positive ions) and anions (negative ions) combine in such a way that the total charge of the compound is zero. This principle is known as charge neutrality. Mathematically, this corresponds to the property that the sum of the positive charges and negative charges must equal zero. We are asked to evaluate five expressions representing these charges to confirm they result in a neutral total of zero.
- Calculating Basic Pairwise Neutrality
The first two expressions are straightforward additions of additive inverses:
- \((+1) + (-1) = 1 - 1 = 0\)
- \((+2) + (-2) = 2 - 2 = 0\)
These represent simple 1:1 combinations of ions, such as Sodium (Na⁺) and Chlorine (Cl⁻), or Magnesium (Mg²⁺) and Oxygen (O²⁻), where the positive and negative charges balance out perfectly.
- Handling Stoichiometric Coefficients
Next, we examine cases where stoichiometry is required to balance the charges:
- \(2(+1) + (-2) = 2(1) - 2 = 2 - 2 = 0\)
- \((+3) + 3(-1) = 3 + 3(-1) = 3 - 3 = 0\)
In these scenarios, we multiply the charge by the number of ions present. For instance, in the third expression, two ions with a +1 charge require one ion with a -2 charge to maintain neutrality. In the fourth expression, one ion with a +3 charge requires three ions with a -1 charge.
- Final Calculation and Conclusion
Finally, we evaluate the last expression involving multiple ion types and quantities:
- \(3(+2) + 2(-3) = 3(2) + 2(-3) = 6 - 6 = 0\)
Here, three ions with a +2 charge contribute a total of +6, and two ions with a -3 charge contribute a total of -6. Combining these results in 0, demonstrating that the charge is balanced. The evaluated results are:
- \((+1) + (-1) = 0\)
- \((+2) + (-2) = 0\)
- \(2(+1) + (-2) = 0\)
- \((+3) + 3(-1) = 0\)
- \(3(+2) + 2(-3) = 0\)
Examples
Imagine you are balancing a chemical scale to create a stable ionic compound. If you have ions with a +3 charge (like Aluminum, Al³⁺), you need exactly enough negative ions (like Chlorine, Cl⁻, with a -1 charge) to ensure the total charge is 0. To achieve this, you need 3 Chlorine ions for every Aluminum ion because \(1(+3) + 3(-1) = 0\). This mathematical balancing acts as a fundamental rule for chemists when they write chemical formulas like \(\text{AlCl}_3\).