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A solution is made by adding \(0.300 \mathrm{g} \mathrm{Ca}(\mathrm{OH})_{2}(s), 50.0 \mathrm{mL}\) of \(1.40 \mathrm{MNN}_{3},\) and enough water to make a final volume of 75.0 \(\mathrm{mL}\) . Assuming that all of the solid dissolves, what is the pH of the final solution?

Short Answer

Expert verified
The pH of the final solution when 0.300 g of Ca(OH)鈧, 50.0 mL of 1.40 M NH鈧, and enough water to make the final volume 75.0 mL is approximately 13.034.

Step by step solution

01

Calculate the initial moles of Ca(OH)鈧 and NH鈧 in the solution

To do this, we will use the given information: - mass of Ca(OH)鈧 = 0.300 g - volume of NH鈧 solution = 50.0 mL - concentration of NH鈧 = 1.40 M First, we need to convert the mass of Ca(OH)鈧 to moles. We will use the molar mass of Ca(OH)鈧 which is about 74.1 g/mol. Moles of Ca(OH)鈧 = mass / molar mass Moles of Ca(OH)鈧 = \(0.300 \mathrm{g} / 74.1 \mathrm{g/mol}\) Moles of Ca(OH)鈧 鈮 0.00405 mol Next, we will calculate the moles of NH鈧 by multiplying its concentration by the volume of the solution: Moles of NH鈧 = concentration 脳 volume (in L) Moles of NH鈧 = 1.40 M 脳 0.050 L Moles of NH鈧 = 0.0700 mol
02

Calculate concentrations in final solution

Now that we have the initial moles of both Ca(OH)鈧 and NH鈧, we will find their concentrations in the final solution. The total volume of the final solution is 75.0 mL: Concentration of Ca(OH)鈧 = moles / volume Concentration of Ca(OH)鈧 = \(0.00405 \mathrm{mol} / 0.075 \mathrm{L}\) Concentration of Ca(OH)鈧 鈮 0.0540 M Concentration of NH鈧 = moles / volume Concentration of NH鈧 = \(0.0700 \mathrm{mol} / 0.075 \mathrm{L}\) Concentration of NH鈧 鈮 0.933 M
03

Calculate concentration of OH鈦 ions

Ca(OH)鈧 dissociates in water to form 2 moles of OH鈦 ions for every 1 mole of Ca(OH)鈧. Therefore, the concentration of OH鈦 ions in the solution will be: Concentration of OH鈦 = 2 脳 concentration of Ca(OH)鈧 Concentration of OH鈦 = 2 脳 0.0540 M Concentration of OH鈦 鈮 0.108 M
04

Calculate the pOH of the solution

Now calculate the pOH of the solution using the concentration of OH鈦 ions: pOH = - log鈧佲個([OH鈦籡) pOH = - log鈧佲個(0.108) pOH 鈮 0.966
05

Calculate the pH of the solution

To find the pH, we will use the relationship between pH and pOH: pH + pOH = 14 pH = 14 - pOH pH = 14 - 0.966 pH 鈮 13.034 The pH of the final solution is approximately 13.034.

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Key Concepts

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

Chemical Solution
A chemical solution is formed when a solute is dissolved in a solvent, resulting in a homogeneous mixture. In the context of the exercise, we are tasked with finding the pH of a solution comprised of multiple components, namely calcium hydroxide ( Ca(OH)_2 ) and ammonia ( NH_3 ) .

A solution's properties significantly change based on the substances mixed and their respective concentrations and volumes. Calcium hydroxide, when dissolved in water, dissociates into calcium ions ( Ca^{2+} ) and hydroxide ions ( OH^{-} ) , affecting the basicity of the solution. Meanwhile, ammonia contributes its alkalinity, thus impacting the overall pH of the solution negatively. Understanding this ability of solutes to affect a solution's characteristics is a crucial part of chemistry.

To grasp how chemical solutions are created and interact, remember:
  • Both solute's known properties and the solvent's ability play critical roles in chemical behaviors of the entire solution.
  • Complete dissolution assumes the solute entirely interacts and integrates with the solvent, impacting resultant solution properties like pH.
Molar Concentration
Molar concentration, also known as molarity, is a measure of the number of moles of a solute dissolved in one liter of solution. It's vital in determining how different solutes will interact with each other and the overall solution. In this problem, computing molar concentrations allows us to predict how the solution reacts, particularly concerning its pH.

Here鈥檚 how you can find the molar concentration:
  • Calculate the number of moles of each substance in the solution. This typically involves dividing the mass of the solute by its molar mass.
  • Divide the moles of solute by the final solution volume in liters to get molarity.
In our example, the concentration calculations for calcium hydroxide and ammonia revealed values critical to determining the solution's pH.

Remember, higher molarity can sharply steer the balance of a solution towards acidity or basicity, hence modifying the solution鈥檚 pH substantively.
Acid-Base Equilibrium
Acid-base equilibrium principles guide us in understanding how acids and bases interact in a chemical solution. This equilibrium pertains to the delicate balance between acids donating protons and bases accepting protons within a solution. The significance of equilibrium is observed in finding related measures such as pH and pOH.

In this exercise, both calcium hydroxide and ammonia are bases, contributing to the overall basic nature of the solution. Calcium hydroxide dissociates to yield hydroxide ions, making the solution more basic and leading to the calculation of pOH.
  • Basic solutions typically have higher concentrations of OH^{-} ions.
  • The relationship (pH + pOH = 14) is utilized to interrelate these two measures 鈥 knowing one allows the other to be calculated.
Ultimately, understanding acid-base equilibrium permits us to evaluate how various components of a solution will determine its behavior, particularly its pH.

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Most popular questions from this chapter

Determine whether each of the following is true or false: (a) All strong bases are salts of the hydroxide ion. (b) The addition of a strong base to water produces a solution of \(\mathrm{pH}>\)7.0 .(c) Because \(\mathrm{Mg}(\mathrm{OH})_{2}\) is not very soluble, it cannot be a strong base.

If a neutral solution of water, with \(\mathrm{pH}=7.00\) , is cooled to \(10^{\circ} \mathrm{C},\) the ph rises to \(7.27 .\) Which of the following three statements is correct for the cooled water: (i) \(\left[\mathrm{H}^{+}\right]>\left[\mathrm{OH}^{-}\right],\) (ii) \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{OH}^{-}\right],\) or (iii) \(\left[\mathrm{H}^{+}\right]<\left[\mathrm{OH}^{-}\right] ?\)

Ephedrine, a central nervous system stimulant, is used in nasal sprays as a decongestant. This compound is a weak organic base: $$\mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ON}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ONH}^{+}(a q)+\mathrm{OH}^{-}(a q)$$ A 0.035\(M\) solution of ephedrine has a pH of 11.33 . (a) What are the equilibrium concentrations of \(\mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ON}, \mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ONH}^{+},\) and \(\mathrm{OH}^{-} ?\) (b) Calculate \(K_{b}\) for ephedrine.

Indicate whether each of the following statements is true or false. For each statement that is false, correct the statement to make it true. (a) Acid strength in a series of \(\mathrm{H}-\) A molecules increases with increasing size of \(\mathrm{A} .\) (b) For acids of the same general structure but differing electronegativities of the central atoms, acid strength decreases with increasing electronegativity of the central atom.(c) The strongest acid known is HF because fluorine is the most electronegative element.

The odor of fish is due primarily to amines, especially methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right) .\) Fish is often served with a wedge of lemon, which contains citric acid. The amine and the acid react forming a product with no odor, thereby making the less-than-fresh fish more appetizing. Using data from Appendix \(\mathrm{D},\) calculate the equilibrium constant for the reaction of citric acid with methylamine, if only the first proton of the citric acid \(\left(K_{a 1}\right)\) is important in the neutralization reaction.

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