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Calculate the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of aqueous solutions with the following concentration at 298 \(\mathrm{K} .\) \begin{equation} \begin{array}{l}{\text { a. }\left[\mathrm{OH}^{-}\right]=0.000033 M} \\\ {\text { b. }\left[\mathrm{H}^{+}\right]=0.0095 M}\end{array} \end{equation}

Short Answer

Expert verified
a. pH 鈮 9.52, pOH 鈮 4.48; b. pH 鈮 2.02, pOH 鈮 11.98.

Step by step solution

01

Calculating pOH from given [OH鈦籡

To find the pOH, use the formula: \( \mathrm{pOH} = -\log_{10}( [\mathrm{OH}^-] ) \). For \([\mathrm{OH}^-] = 0.000033 \, M\), calculate:\[pOH = -\log_{10}(0.000033) \approx 4.48\]
02

Calculating pH from pOH

Use the relation between pH and pOH for water at 298 K: \( \mathrm{pH} + \mathrm{pOH} = 14 \). Solve for pH:\[\mathrm{pH} = 14 - \mathrm{pOH} = 14 - 4.48 \approx 9.52 \]
03

Calculating pH from given [H鈦篯

To find the pH, use the formula: \( \mathrm{pH} = -\log_{10}( [\mathrm{H}^+] ) \). For \([\mathrm{H}^+] = 0.0095 \, M\), calculate:\[pH = -\log_{10}(0.0095) \approx 2.02\]
04

Calculating pOH from pH

Use the relation between pH and pOH for water at 298 K: \( \mathrm{pH} + \mathrm{pOH} = 14 \). Solve for pOH:\[\mathrm{pOH} = 14 - \mathrm{pH} = 14 - 2.02 \approx 11.98 \]

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Key Concepts

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

Ionic Concentration
When dealing with solutions, understanding ionic concentration is crucial. This refers to the amount of ions that are present within a given volume of solution. For instance, if we have \([\text{OH}^-]\) with a concentration of 0.000033 M, this tells us there are 0.000033 moles of hydroxide ions per liter of solution. These concentrations are fundamental in determining other properties of the solution, such as pH and pOH.
Ionic concentration plays a central role in chemistry and biology since it affects reactions and processes. In aqueous solutions, ions are formed when compounds dissociate in water, influencing the acidity or basicity of the solution. Therefore, knowing the ionic concentration allows us to calculate and predict other chemical properties. This sets the stage for pH and pOH calculations, which are deeply rooted in these concentrations.
Logarithmic Calculations
Logarithmic calculations are essential in determining the pH and pOH of solutions. The pH scale, which measures how acidic or basic a solution is, is logarithmic. This means each step on the pH scale represents a tenfold change in concentration.
To calculate pH from the concentration of hydrogen ions in the solution, the formula is \[ \text{pH} = -\log_{10}([\text{H}^+]) \] This calculation utilizes the base-10 logarithm, translating the concentration of ions into a more manageable number for human interpretation. Similarly, pOH is calculated from the concentration of hydroxide ions using \[ \text{pOH} = -\log_{10}([\text{OH}^-]) \]
These logarithmic calculations convert tiny numbers (like 0.0095 M) into clear, understandable figures (such as a pH of 2.02). This method provides an intuitive understanding of a solution's acidity or basicity, which can be crucial in scientific and industrial contexts.
Aqueous Solutions
Aqueous solutions are those where water acts as the solvent. Water's polarity allows it to dissolve a wide range of substances, making it an excellent medium for chemical reactions, especially acid-base reactions. In these solutions, substances like acids and bases dissociate into their respective ions.
For example, hydrochloric acid ( HCl ) dissociates into H鈦 and Cl鈦 ions in water, making it an acidic solution. Conversely, a base such as sodium hydroxide ( NaOH ) separates into OH鈦 and Na鈦 ions, increasing the solution鈥檚 basicity.
The unique properties of water, like its high dielectric constant, facilitate the easy dissociation into ions necessary for conducting electricity and driving chemical reactions. Thus, aqueous solutions provide an accessible environment for studying ionic concentration, pH, and other chemical phenomena.
Acid-Base Chemistry
Acid-base chemistry revolves around the balance of hydrogen ions (H鈦) and hydroxide ions (OH鈦) in a solution. An acid increases the concentration of H鈦 ions, while a base increases that of OH鈦 ions.
The pH value is a measure of the concentration of H鈦 ions, while pOH relates to OH鈦. Their relationship is expressed by the equation \(\text{pH} + \text{pOH} = 14\) at 298 K, which is known as the water dissociation constant at room temperature.This equilibrium relationship helps in determining the acidity or basicity of a solution when given either the concentration of H鈦 or OH鈦. The pH scale ranges from 0 to 14, with 7 being neutral鈥攊ndicating equal concentrations of H鈦 and OH鈦. Values below 7 indicate acidity, while those above 7 indicate alkalinity.
  • Acids contribute to lowering the pH by increasing H鈦 concentration.
  • Bases contribute to raising the pH by increasing OH鈦 concentration.
This basic understanding of acid-base chemistry is pivotal for industries like pharmaceuticals, agriculture, and environmental science, where controlling the acidity or basicity can influence product effectiveness and safety.

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