Chapter 14: Problem 157
Calculate the mass of \(\mathrm{HONH}_{2}\) required to dissolve in enough water to make 250.0 \(\mathrm{mL}\) of solution having a pH of 10.00\(\left(K_{\mathrm{b}}\right.\) \(=1.1 \times 10^{-8} )\)
Short Answer
Expert verified
The mass of HONH鈧 required to make a 250.0 mL solution with a pH of 10.00 is approximately 0.0009 g (rounded to four decimal places).
Step by step solution
01
Calculate pOH from given pH
The relationship between pH and pOH is:
pH + pOH = 14
We are given pH = 10, so:
pOH = 14 - 10 = 4
02
Calculate the concentration of OH鈦 ions
We can determine the concentration of OH鈦 ions from the pOH using the following formula:
\[ OH^鈦 = 10^{-pOH} \]
\[ OH^鈦 = 10^{-4} = 1 \times 10^{-4} \, M\]
03
Calculate the concentration of HONH鈧 using the Kb expression
Let's represent the dissociation of HONH鈧 as:
HONH鈧 (aq) + H鈧侽 (l) 鈬 HONH鈦 (aq) + OH鈦 (aq)
The Kb expression can be written as:
\[ K_b = \frac{[HONH鈦籡[OH-]}{[HONH_2]} \]
We know the Kb value and the concentration of OH鈦. Assuming x mol/L is the concentration of HONH鈧 in equilibrium, we have:
\[ 1.1 \times 10^{-8} = \frac{x(1 \times 10^{-4})}{x - 1 \times 10^{-4}} \]
Now we can solve for x, which represents the equilibrium concentration of HONH鈧. The concentration of HONH鈧 is very small compared to the initial concentration; hence x - 1 脳 10^(-4) 鈮 x
\[ 1.1 \times 10^{-8} = \frac{x \times 1 \times 10^{-4}}{x} \]
\[ x = 1.1 \times 10^{-4} \, M\]
04
Determine the mass of HONH鈧
Now that we have the concentration of HONH鈧, we can calculate the mass required. We know that the volume of the solution is 250.0 mL.
First, let's convert the volume into liters:
Volume = 250.0 mL 脳 (1 L / 1000 mL) = 0.250 L
Next, we can calculate the moles of HONH鈧 using the concentration:
Moles of HONH鈧 = concentration 脳 volume
Moles of HONH鈧 = (1.1 脳 10鈦烩伌 M) 脳 (0.250 L) = 2.75 脳 10鈦烩伒 mol
Finally, we can determine the mass by multiplying the moles by the molecular weight of HONH鈧 (Molar mass of HONH鈧 = 1(H) + 15(N) + 16(O) + 1(H) + 1(N) + 2(H) = 33 g/mol):
Mass of HONH鈧 = moles 脳 molecular weight
Mass of HONH鈧 = (2.75 脳 10鈦烩伒 mol) 脳 (33 g/mol) 鈮 0.0009075 g
Therefore, the mass of HONH鈧 required to make a 250.0 mL solution with a pH of 10.00 is approximately 0.0009 g (rounded to four decimal places).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
pH and pOH Calculation
Understanding the relationship between pH and pOH is crucial when dealing with acid-base chemistry. pH measures the acidity of a solution, while pOH indicates its basicity. These two are connected through a simple equation:
- pH + pOH = 14
- pOH = 14 - 10 = 4
Why is pOH Important?
The pOH provides insight into the concentration of hydroxide ions often denoted as OH鈦. A low pOH indicates a high concentration of OH鈦 ions, characterizing the solution's basic nature. Understanding both pH and pOH helps predict and control chemical reactions, especially in equilibrium scenarios.Base Dissociation Constant (Kb)
The Base Dissociation Constant, represented as Kb, is vital for understanding the strength of a base. It indicates how well a base dissociates in water, forming hydroxide ions. In this scenario, we deal with the base dissociation of hydroxylamine, HONH鈧.
- HONH鈧 (aq) + H鈧侽 (l) 鈬 HONH鈦 (aq) + OH鈦 (aq)
- \( K_b = \frac{[HONH鈦籡[OH鈦籡}{[HONH鈧俔} \)
Using Kb in Calculations
The Kb helps calculate unknown concentrations if the concentrations of other species are known. Here, it helped determine the concentration of HONH鈧 necessary to achieve a desired concentration of OH鈦 ions in solution. A small Kb value indicates a weak base, which only partially dissociates in water.Molarity and Concentration
Molarity is an expression of concentration, calculated as moles of solute per liter of solution (mol/L). In equilibrium problems, molarity helps describe how concentrated a solution is. For instance, in our exercise:
- The concentration of OH鈦 ions was calculated as 1 脳 10鈦烩伌 M using the pOH.
Calculating Molarity and Concentration
Molarity allows easy conversion between volume and moles, crucial when preparing solutions of a specific concentration. To find the concentration of HONH鈧, we assumed that at equilibrium, the concentration slightly above the dissociated OH鈦 can give us- the concentration of HONH鈧 needed to reach the equilibrium concentration.
Stoichiometry Calculation
Stoichiometry involves quantifying relationships between reactants and products in a chemical reaction. In equilibrium calculations like this one, stoichiometry is used to calculate the mass of a compound required to produce a particular molarity.
- Once the concentration of HONH鈧 was found, it was used to calculate the moles of HONH鈧 needed for our solution volume.
- Moles of HONH鈧 = concentration 脳 volume
- From the moles, determining the mass required using the molar mass of HONH鈧