Chapter 17: Problem 29
The solubility of silver bromate, \(\mathrm{AgBrO}_{3}\), in water is \(0.0072 \mathrm{~g} / \mathrm{L}\). Calculate \(K_{s p .}\)
Short Answer
Expert verified
The solubility product constant, \( K_{sp} \), is \( 9.30 \times 10^{-10} \).
Step by step solution
01
Determine Molar Mass of Silver Bromate
To convert the solubility from grams per liter to molarity, first find the molar mass of silver bromate, AgBrO鈧. The molar mass is calculated as the sum of the atomic masses: Ag = 107.87 g/mol, Br = 79.904 g/mol, O = 16.00 g/mol (3 oxygens). So, the molar mass of AgBrO鈧 is 107.87 + 79.904 + (3 脳 16.00) = 235.764 g/mol.
02
Convert Solubility to Molarity
The solubility of AgBrO鈧 is given as 0.0072 g/L. To convert this to molarity (moles per liter), divide the solubility by the molar mass of AgBrO鈧. Molarity = (0.0072 g/L) / (235.764 g/mol) = 3.05 脳 10鈦烩伒 mol/L.
03
Write the Dissociation Equation
When AgBrO鈧 dissolves in water, it dissociates as follows:
AgBrO鈧(s) 鈬 Ag鈦(aq) + BrO鈧冣伝(aq).
This dissociation indicates that 1 mole of AgBrO鈧 produces 1 mole of Ag鈦 and 1 mole of BrO鈧冣伝.
04
Express the Concentrations
From the dissociation equation, the concentration of Ag鈦 ions and BrO鈧冣伝 ions in the solution will both equal the solubility of AgBrO鈧, which is 3.05 脳 10鈦烩伒 mol/L.
05
Calculate the Solubility Product Constant, K_{sp}
The solubility product constant, K_{sp}, is calculated using the concentrations of the ions:\[ K_{sp} = [Ag^+][BrO_3^-] = (3.05 脳 10^{-5})^2 = 9.30 脳 10^{-10} \]
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Molar Mass Calculation
The molar mass calculation is often the first step in solving problems related to solubility and reactions. For silver bromate (
AgBrO鈧), determining the molar mass requires summing the atomic masses of each element in the compound.
This molar mass allows you to convert between grams and moles, a crucial factor in calculating molarity.
- Silver ( Ag) has an atomic mass of 107.87 g/mol.
- Bromine ( Br) is 79.904 g/mol.
- Oxygen (O) has a mass of 16.00 g/mol, and there are three oxygens in the formula.
This molar mass allows you to convert between grams and moles, a crucial factor in calculating molarity.
Ionic Dissociation
Understanding ionic dissociation is key to calculating concentrations in solutions. When silver bromate (
AgBrO鈧) dissolves in water, it breaks apart into ions:
This 1:1 stoichiometric ratio informs us that the concentrations of these ions in the solution will be the same as the solubility of AgBrO鈧. Such a balanced equation is vital for finding various chemical properties, like the solubility product constant (K_{sp}).
- AgBrO鈧(s) 鈬 Ag鈦(aq) + BrO鈧冣伝(aq)
This 1:1 stoichiometric ratio informs us that the concentrations of these ions in the solution will be the same as the solubility of AgBrO鈧. Such a balanced equation is vital for finding various chemical properties, like the solubility product constant (K_{sp}).
Molarity Conversion
Molarity (
M) is a way of expressing concentration, representing moles of solute per liter of solution.
To convert from a given solubility in grams per liter to molarity, you'd need the compound's molar mass. For
AgBrO鈧, already calculated as 235.764 g/mol, this conversion follows as:
- Molarity = (0.0072 g/L) / (235.764 g/mol)
- = 3.05 脳 10鈦烩伒 mol/L
Solubility Equilibrium
Solubility equilibrium is the state reached when the dissolution and precipitation of a solute occur at equal rates in a saturated solution. In the case of
AgBrO鈧, this equilibrium can be described using the solubility product constant (
K_{sp}).
The dissociation of AgBrO鈧 provides:
Understanding solubility equilibrium allows us to predict how substances dissolve, formulate chemical reactions, and solve diverse problems in chemistry.
The dissociation of AgBrO鈧 provides:
- [Ag鈦篯 = 3.05 脳 10鈦烩伒 mol/L
- [BrO鈧冣伝] = 3.05 脳 10鈦烩伒 mol/L
Understanding solubility equilibrium allows us to predict how substances dissolve, formulate chemical reactions, and solve diverse problems in chemistry.