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The solubility of silver acetate in water at \(20{ }^{\circ} \mathrm{C}\) is \(10.5 \mathrm{~g} / \mathrm{L}\) of solution. Calculate \(\mathrm{K}_{\mathrm{sp}}\) for silver acetate.

Short Answer

Expert verified
The solubility product constant (K_sp) for silver acetate at 20掳C is 0.00396.

Step by step solution

01

Calculate the number of moles of silver acetate dissolving in water

First, we'll convert the solubility of silver acetate given in g/L into moles/L (M). The molar mass of silver acetate (AgC鈧侶鈧僌鈧) is: Molar mass of AgC鈧侶鈧僌鈧 = 107.87 g/mol (Ag) + 12.01 g/mol (C) 脳 2 + 1.01 g/mol (H) 脳 3 + 16.00 g/mol (O) 脳 2 = 166.92 g/mol Now, we'll convert the solubility of silver acetate (10.5 g/L) into moles/L (M): \( \textrm{Molarity (M)} = \frac{10.5 \textrm{ g/L}}{166.92 \textrm{ g/mol}} = 0.0629 \textrm{ M} \) The concentration of silver acetate in water is 0.0629 M.
02

Write the balanced chemical equation for the dissolution of silver acetate

The dissolution of silver acetate in water can be represented by the following balanced chemical equation: \[ AgC_{2}H_{3}O_{2}(s) \rightleftharpoons Ag^{+}(aq) + C_{2}H_{3}O_{2}^{-}(aq) \]
03

Find the concentrations of Ag鈦 and C鈧侶鈧僌鈧傗伝 ions in the water

For every 1 mol of silver acetate dissolved, it gets separated into 1 mol of Ag鈦 ions and 1 mol of C鈧侶鈧僌鈧傗伝 ions. Therefore, the concentrations of Ag鈦 and C鈧侶鈧僌鈧傗伝 ions are equal to the concentration of silver acetate: Concentration of Ag鈦 ions: [Ag鈦篯 = 0.0629 M Concentration of C鈧侶鈧僌鈧傗伝 ions: [C鈧侶鈧僌鈧傗伝] = 0.0629 M
04

Calculate the K_sp for silver acetate

The solubility product constant (K_sp) for silver acetate can be calculated using the following equation: \[ K_{sp} = [Ag^{+}][C_{2}H_{3}O_{2}^{-}] \] Plugging in the concentrations of Ag鈦 and C鈧侶鈧僌鈧傗伝 ions, we get: K_sp = (0.0629)(0.0629) K_sp = 0.00396 So, the solubility product constant (K_sp) for silver acetate at 20掳C is 0.00396.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molarity
Molarity is a measure of concentration. It tells us how many moles of a substance are in one liter of solution. Think of it as a way to count how many particles of a substance are in a solution, using moles rather than individual atoms or molecules, which would be too many to count.

To calculate molarity, we use the formula:
  • Molarity (M) = \(\frac{\text{moles of solute}}{\text{liters of solution}}\)
Let's see it in action. In our exercise, the problem gives us the solubility of silver acetate in grams per liter. We first need to convert grams to moles since molarity is in moles per liter.

Once we find the number of moles (by dividing the mass by the molar mass), we divide it by the volume of the solution in liters to find the molarity. In this case, for silver acetate, this conversion revealed a molarity of 0.0629 M.
Silver Acetate
Silver acetate is a chemical compound composed of silver ( Ag ) and the acetate ion (C鈧侶鈧僌鈧傗伝 ).

Silver acetate's formula is AgC鈧侶鈧僌鈧 . This compound is known for its relatively low solubility in water, which makes it an interesting study for solubility product concepts.

In practical terms, when silver acetate is added to water, not all of it will dissolve. Instead, a certain amount will stay as a solid, while the rest will break apart into silver ions ( Ag鈦 ) and acetate ions ( C鈧侶鈧僌鈧傗伝 ).
  • Silver ion ( Ag鈦) : this is the positively charged ion after losing its acetate counterpart.
  • Acetate ion ( C鈧侶鈧僌鈧傗伝 ): the remaining part that carries a negative charge.
This equilibrium between undissolved silver acetate and its dissolved ions is crucial for understanding its solubility and calculating its solubility product constant ( K_{sp} ).
Dissolution Reaction
A dissolution reaction describes how a solid dissolves in a solvent, breaking into its constituent ions, ions, or molecules in the process. For many students, the concept becomes easier to grasp with a visual example.

Take silver acetate: When it dissolves in water, it dissociates, or splits apart, into silver ( Ag鈦) ions and acetate ( C鈧侶鈧僌鈧傗伝 ) ions. Here's what happens visually:
  • The silver acetate molecules in the solid state come into contact with water.
  • Water, a polar solvent, surrounds and separates the ions of silver acetate.
  • This ongoing process results in the equilibrium in the solution, balancing between compounds in solution and undissolved solid.
This is captured by the balanced chemical equation, and ultimately leads us to compute the Ksp to quantify this equilibrium.
Balanced Chemical Equation
A balanced chemical equation is essential in chemistry. It shows how reactants transform into products during a chemical reaction while conserving mass and charge. Without a balanced equation, it would be like attempting to bake without a recipe, where ingredients don鈥檛 match up.

In our case of silver acetate dissolution:\[ AgC_{2}H_{3}O_{2}(s) \rightleftharpoons Ag^{+}(aq) + C_{2}H_{3}O_{2}^{-}(aq) \]

This equation tells us:
  • On the left, we have undissolved solid silver acetate.
  • On the right, we see it dissociating into its ions, silver and acetate, in aqueous form.
It鈥檚 balanced because it shows the same number of atoms and charge on both sides. Such equations are pivotal when calculating solubility products, like \(K_{sp}\), because they express exactly how much product forms relative to how much starting material dissolves.

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