What is the correct formula that would result from the combination of the two ionic species?
[tex]$Mg^{2+} \text { and } PO_4{ }^{3-}$[/tex]
A. [tex]$Mg _3\left( PO _4\right)_2$[/tex]
B. [tex]$Mg _2\left( PO _4\right)_3$[/tex]
C. [tex]$Mg \left( PO _4\right)_3$[/tex]
D. [tex]$MgPO _4$[/tex]
Answer (2)
The compound must be electrically neutral, so the total positive charge must equal the total negative charge.
Let x be the number of M g 2 + ions and y be the number of P O 4 3 − ions, then 2 x = 3 y .
Find the smallest integers x and y that satisfy 2 x = 3 y , which are x = 3 and y = 2 .
The correct formula is M g 3 ( P O 4 ) 2 .
Explanation
Understanding the Problem We are given two ions, M g 2 + and P O 4 3 − , and we need to find the chemical formula of the compound they form. The key principle here is that the compound must be electrically neutral, meaning the total positive charge must equal the total negative charge.
Setting up the Equation Let's denote the number of magnesium ions ( M g 2 + ) as x and the number of phosphate ions ( P O 4 3 − ) as y . The total positive charge is 2 x (since each magnesium ion has a +2 charge) and the total negative charge is 3 y (since each phosphate ion has a -3 charge). To achieve electrical neutrality, we must have: 2 x = 3 y
Finding the Smallest Whole Numbers We need to find the smallest whole numbers x and y that satisfy the equation 2 x = 3 y . This is essentially finding the least common multiple (LCM) of 2 and 3. The LCM of 2 and 3 is 6. So, we want to find x and y such that: 2 x = 6 and 3 y = 6
Solving for x and y Solving for x and y , we get: x = 2 6 = 3 and y = 3 6 = 2 This means we need 3 magnesium ions and 2 phosphate ions to form a neutral compound.
Determining the Chemical Formula Therefore, the chemical formula for the compound formed by M g 2 + and P O 4 3 − is M g 3 ( P O 4 ) 2 .
Examples
In real life, understanding ionic compound formation is crucial in various fields. For example, in agriculture, magnesium phosphate ( M g 3 ( P O 4 ) 2 ) can be used as a fertilizer to provide plants with essential nutrients like magnesium and phosphorus. The correct formulation ensures that the nutrients are available to the plants in the right proportions, promoting healthy growth. Similarly, in medicine, understanding the formation of calcium phosphate compounds is important for bone health and the development of dental materials.
The correct formula resulting from the combination of the ions M g 2 + and P O 4 3 − is M g 3 ( P O 4 ) 2 . This is determined by ensuring that the charges from the ions balance each other, resulting in a neutral compound. Thus, the chosen option is A : M g 3 ( P O 4 ) 2 .
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