How many moles of magnesium, chlorine, and oxygen are in 7.90 mol of #"Mg"("ClO"_4)_2#?

Question

Peyton Adams · Accepted Answer

There are 7.90 mol of #"Mg"#, 15.8 mol of #"Cl"#, and 63.2 mol of #"O"#.

We could simplify the calculation by multiplying the total number of atoms inside parenthesis by the subscript 2. Then the formula becomes #"MgCl"_2"O"_8#. We see that one formula unit of #"Mg"("ClO"_4)_2# contains 1 #"Mg"# atom, 2 #"Cl"# atoms, and 8 #"O"# atoms. Then 1 mol of #"Mg"("ClO"_4)_2# contains 1 mol of #"Mg"# atoms, 2 mol of #"Cl"# atoms, and 8 mol of #"O"# atoms. #"Moles of Mg atoms" = 7.90 color(red)(cancel(color(black)("mol Mg"("ClO"_4)_2))) × "1 mol Mg atoms"/(1 color(red)(cancel(color(black)("mol Mg"("ClO"_4)_2)))) = "7.90 mol Mg atoms"# #"Moles of Cl atoms" = 7.90 color(red)(cancel(color(black)("mol Mg"("ClO"_4)_2))) × "2 mol Cl atoms"/(1 color(red)(cancel(color(black)("mol Mg"("ClO"_4)_2)))) = "15.8 mol Cl atoms"# #"Moles of O atoms" = 7.90 color(red)(cancel(color(black)("mol Mg"("ClO"_4)_2))) × "8 mol O atoms"/(1 color(red)(cancel(color(black)("mol Mg"("ClO"_4)_2)))) = "63.2 mol O atoms"#

Peyton Adams · Answer

undefined To find the number of moles of magnesium (Mg), chlorine (Cl), and oxygen (O) in 7.90 mol of Mg(ClO4)2, we need to analyze the chemical formula.

For Mg(ClO4)2:
- There is 1 magnesium atom (Mg).
- There are 2 chlorine atoms (Cl).
- There are 8 oxygen atoms (O) because each perchlorate ion (ClO4-) contains 4 oxygen atoms.

Using the given amount of 7.90 mol of Mg(ClO4)2:

Moles of Mg = 7.90 mol × 1 mol Mg/mol Mg(ClO4)2 = 7.90 mol
Moles of Cl = 7.90 mol × 2 mol Cl/mol Mg(ClO4)2 = 15.80 mol
Moles of O = 7.90 mol × 8 mol O/mol Mg(ClO4)2 = 63.20 mol

So, there are 7.90 moles of magnesium, 15.80 moles of chlorine, and 63.20 moles of oxygen in 7.90 mol of Mg(ClO4)2.