To balance the chemical equation [tex]\( Mg + YHCl \rightarrow MgCl_2 + H_2 \)[/tex], you need to ensure that the number of atoms of each element is the same on both sides of the equation. Let's go through the elements one by one:
1. Magnesium (Mg):
- On the left side: 1 [tex]\( Mg \)[/tex].
- On the right side: 1 [tex]\( Mg \)[/tex].
- The number of magnesium atoms is already balanced.
2. Chlorine (Cl):
- On the left side: [tex]\( Y \)[/tex] [tex]\( Cl \)[/tex] atoms (since [tex]\( YHCl \)[/tex] implies [tex]\( Y \)[/tex] [tex]\( Cl \)[/tex] atoms).
- On the right side: 2 [tex]\( Cl \)[/tex] atoms (in [tex]\( MgCl_2 \)[/tex]).
- To balance the chlorine atoms, set [tex]\( Y \)[/tex] to 2.
3. Hydrogen (H):
- On the left side: [tex]\( Y \)[/tex] [tex]\( H \)[/tex] atoms (since [tex]\( YHCl \)[/tex] implies [tex]\( Y \)[/tex] [tex]\( H \)[/tex] atoms).
- On the right side: 2 [tex]\( H \)[/tex] atoms (in [tex]\( H_2 \)[/tex]).
- Confirming [tex]\( Y = 2 \)[/tex] balances the hydrogen atoms as well.
Thus, to balance the equation, we need [tex]\( Y \)[/tex] to be 2:
[tex]\[ Mg + 2HCl \rightarrow MgCl_2 + H_2 \][/tex]
Therefore, the number that should be in place of [tex]\( Y \)[/tex] to balance the equation is:
[tex]\[ \boxed{2} \][/tex]
