Math Snap

STEP 1

What is this asking?
Which expression correctly shows how much magnesium carbonate dissolves in a solution?
Watch out!
Don't mix up the K_sp expression with other equilibrium expressions! K_sp is specifically for how much a solid dissolves.

STEP 2

1. Understand K_sp
2. Write the balanced dissolution equation
3. Build the K_sp expression

STEP 3

K_sp, the solubility product constant, tells us how much a solid dissolves into its ions in a saturated solution.
A bigger K_sp means more dissolving!
It's like a popularity contest for dissolved ions!

STEP 4

K_sp is all about equilibrium.
When the solid is dissolving as fast as the ions are coming back together, we've hit equilibrium, and K_sp describes that balance.

STEP 5

We're dealing with magnesium carbonate, MgCO₃$_{(s)}$.
When it dissolves, it breaks into its ions: magnesium, Mg²⁺$_{(aq)}$, and carbonate, CO₃²⁻$_{(aq)}$.

STEP 6

The balanced equation looks like this:
$$\text{MgCO}_3(s) \rightleftharpoons \text{Mg}^{2+}(aq) + \text{CO}_3^{2-}(aq)$$ See? One magnesium carbonate breaks down into one magnesium ion and one carbonate ion.
Perfectly balanced, as all things should be!

STEP 7

The K_sp expression is built by multiplying the concentrations of the dissolved ions, each raised to the power of its coefficient in the balanced equation.

STEP 8

From our balanced equation, both Mg²⁺ and CO₃²⁻ have a coefficient of 1.
So, our K_sp expression is:
$$K_{sp} = [\text{Mg}^{2+}]^1 \cdot [\text{CO}_3^{2-}]^1$$ We don't include the solid MgCO₃$_{(s)}$ in the K_sp expression because its concentration is constant.

STEP 9

Since anything raised to the power of 1 is just itself, we can simplify to:
$$K_{sp} = [\text{Mg}^{2+}] \cdot [\text{CO}_3^{2-}]$$

The correct expression for the K_sp of MgCO₃ is $K_{sp} = [\text{Mg}^{2+}] \cdot [\text{CO}_3^{2-}]$, which is the first option.