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Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory
Chapter 6, Problem 78c

Element X reacts with element Y to give a product containing X3+ ions and Y2- ions. (c) What is the formula of the product?

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<insert step 1> Identify the charges of the ions involved in the compound. Element X forms X^{3+} ions, and element Y forms Y^{2-} ions.
<insert step 2> Determine the ratio of X^{3+} ions to Y^{2-} ions needed to balance the overall charge of the compound. The goal is to have a neutral compound.
<insert step 3> Use the least common multiple (LCM) of the charges to find the smallest whole number ratio of X and Y that results in a neutral compound. The LCM of 3 and 2 is 6.
<insert step 4> Calculate the number of X^{3+} ions needed to reach a total positive charge of +6. This requires 2 X^{3+} ions (2 * 3 = +6).
<insert step 5> Calculate the number of Y^{2-} ions needed to reach a total negative charge of -6. This requires 3 Y^{2-} ions (3 * -2 = -6).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ionic Charges

Ionic charges are the electrical charges that ions carry, determined by the loss or gain of electrons. In this case, element X forms X<sup>3+</sup> ions, indicating it has lost three electrons, while element Y forms Y<sup>2-</sup> ions, meaning it has gained two electrons. Understanding these charges is crucial for determining how ions combine to form neutral compounds.
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Chemical Formula

A chemical formula represents the composition of a compound, indicating the types and ratios of atoms present. To derive the formula from the ionic charges, we must balance the total positive and negative charges. This ensures that the resulting compound is electrically neutral, which is a fundamental principle in chemistry.
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Criss-Cross Method

The criss-cross method is a technique used to determine the formula of an ionic compound by using the absolute values of the ionic charges. In this method, the charge of one ion becomes the subscript of the other ion. For example, with X<sup>3+</sup> and Y<sup>2-</sup>, we would take the 2 from Y and make it the subscript of X, and the 3 from X as the subscript of Y, leading to the formula XY<sub>3</sub>.
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