Ionic compounds can be made from a metallic ion (cation) and a nonmetallic ion (anion). Metallic ions (M) are positive, and nonmetallic ions (N) are negative. Let $x$ stand for the number of metallic ions and $y$ stand for the number of nonmetallic ions. For each equation given below, determine the correct values.

$x(+1 M) + (-2 N) = 0$

What does $x$ have to be? [ ]

(+2 M) + y(-1 N) = 0

What does $y$ have to be? [ ]

$x(+2 M) + y(-3 N) = 0$

What do $x$ and $y$ have to be?

$x =$ [ ] and $y =$ [ ]

Question

06-11-2026
Chemistry

Answered

Ionic compounds can be made from a metallic ion (cation) and a nonmetallic ion (anion). Metallic ions (M) are positive, and nonmetallic ions (N) are negative. Let $x$ stand for the number of metallic ions and $y$ stand for the number of nonmetallic ions. For each equation given below, determine the correct values.

$x(+1 M) + (-2 N) = 0$

What does $x$ have to be? [ ]

(+2 M) + y(-1 N) = 0

What does $y$ have to be? [ ]

$x(+2 M) + y(-3 N) = 0$

What do $x$ and $y$ have to be?

$x =$ [ ] and $y =$ [ ]

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-06T19:28:12-05:00

Solving $x(+1) - 2 = 0$ gives $x = 2$.
Solving $2 - y = 0$ gives $y = 2$.
Solving the system $2x - 3y = 0$ for the smallest integers gives $x = 3$ and $y = 2$.
Final answers: $x = \boxed{2}$, $y = \boxed{2}$, and for the last part $x = \boxed{3}, y = \boxed{2}$.

Explanation

Analyzing the First Equation

Ionic compounds are formed when cations (positively charged metallic ions) and anions (negatively charged nonmetallic ions) bond such that the total net charge is zero. We are given three equations representing different charge balances and need to find the smallest positive integer coefficients for the ions involved.

For the first equation:
\[x(+1) + (-2) = 0\]
We are looking for the value of $x$. By adding $2$ to both sides, we get:
\[x(1) = 2 \implies x = 2\]
Thus, for a metallic ion with a charge of $+1$ and a nonmetallic ion with a charge of $-2$, we need $2$ cations to balance the charge of one anion.

Analyzing the Second Equation

For the second equation:
\[(+2) + y(-1) = 0\]
Here, we have one metallic ion with a charge of $+2$. To balance this, we need:
\[2 - y = 0 \implies y = 2\]
So, for a metallic ion with a charge of $+2$ and a nonmetallic ion with a charge of $-1$, we need two anions to balance one cation.

Analyzing the Third Equation

For the third equation:
\[x(+2) + y(-3) = 0\]
This simplifies to:
\[2x = 3y\]
We need the smallest positive integers $x$ and $y$ that satisfy this equality. This is equivalent to finding the least common multiple of the absolute values of the charges, which are $2$ and $3$. The least common multiple of $2$ and $3$ is $6$.
Setting $2x = 6$ gives $x = 3$.
Setting $3y = 6$ gives $y = 2$.
Thus, we need $3$ metallic ions with a charge of $+2$ and $2$ nonmetallic ions with a charge of $-3$ to achieve a total charge of zero.

Conclusion

In summary, we have determined the values for the ion counts:

For the first equation, $x = 2$.
For the second equation, $y = 2$.
For the third equation, $x = 3$ and $y = 2$.

These values ensure that the total charge of each ionic compound is zero, satisfying the requirement for charge neutrality.

Examples

In chemistry, balancing charges is essential to determining the chemical formulas of compounds. For instance, if you have magnesium ($Mg^{2+}$) and chlorine ($Cl^-$), you know the compound must be neutral. Since $Mg$ has a $+2$ charge and $Cl$ has a $-1$ charge, you need two $Cl^-$ ions to balance one $Mg^{2+}$ ion, resulting in the formula $MgCl_2$. This is exactly like solving the equation $1(+2) + y(-1) = 0$, which yields $y=2$. Understanding this helps in predicting how atoms combine to form substances in everyday products like table salt or medicines.