Math  /  Algebra

QuestionComplete the Ksp K_{\text {sp }} expression for Ag2CO3\mathrm{Ag}_{2} \mathrm{CO}_{3}. Ksp=8.46×1012=K_{\mathrm{sp}}=8.46 \times 10^{-12}=

Studdy Solution

STEP 1

What is this asking? We need to write the solubility product expression for silver carbonate (Ag2CO3\text{Ag}_2\text{CO}_3). Watch out! Don't forget to use the correct coefficients from the balanced dissolution equation, they're super important!

STEP 2

1. Write the balanced dissolution equation.
2. Write the KspK_\text{sp} expression.

STEP 3

Let's **start** by writing out the **balanced chemical equation** for the dissolution of solid silver carbonate (Ag2CO3\text{Ag}_2\text{CO}_3) in water.
When Ag2CO3\text{Ag}_2\text{CO}_3 dissolves, it breaks apart into its ions: silver ions (Ag+\text{Ag}^{+}) and carbonate ions (CO32\text{CO}_3^{2-}).

STEP 4

The **balanced equation** looks like this: Ag2CO3(s)2Ag+(aq)+CO32(aq) \text{Ag}_2\text{CO}_3(s) \rightleftharpoons 2\text{Ag}^{+}(aq) + \text{CO}_3^{2-}(aq) See how we get **two** silver ions for every **one** carbonate ion?
That **2** is going to be *super* important in our next step!

STEP 5

Now, we can **write the KspK_\text{sp} expression**.
Remember, the KspK_\text{sp} is just the product of the concentrations of the dissolved ions, each raised to the power of its coefficient in the balanced equation.
It tells us how much of the solid can dissolve!

STEP 6

From our balanced equation, we see that the coefficient of Ag+\text{Ag}^{+} is **2**, and the coefficient of CO32\text{CO}_3^{2-} is **1**.
So, our KspK_\text{sp} expression is: Ksp=[Ag+]2[CO32] K_\text{sp} = [\text{Ag}^{+}]^2 [\text{CO}_3^{2-}] We're raising the silver ion concentration to the power of **2** because we have **two** silver ions in the balanced equation!

STEP 7

So, the completed KspK_\text{sp} expression is: Ksp=8.46×1012=[Ag+]2[CO32] K_\text{sp} = 8.46 \times 10^{-12} = [\text{Ag}^{+}]^2 [\text{CO}_3^{2-}]

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