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Chapter 2: Problem 4

That is the \(\mathrm{pH}\) of a solution that has an \(\mathrm{H}^{+}\)concentration of a. \(1.75 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\); b. \(6.50 \times 10^{-10} \mathrm{~mol} / \mathrm{L}\); c. \(1.0 \times 10^{-4} \mathrm{~mol} / \mathrm{L}\); d. \(1.50 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\) ?

Short Answer

Expert verified
a. pH 鈮� 4.76; b. pH 鈮� 9.19; c. pH = 4.00; d. pH 鈮� 4.82.

Step by step solution

01

Understanding pH Calculation

The pH of a solution is calculated using the formula \( \mathrm{pH} = -\log_{10}[\mathrm{H}^{+}] \), where \([\mathrm{H}^{+}]\) is the concentration of hydrogen ions in moles per liter. This formula indicates that pH is the negative logarithm (base 10) of the \([\mathrm{H}^{+}]\) concentration.
02

Calculate pH for Case A

Using the given concentration for case (a): \(1.75 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\), we apply the formula: \( \mathrm{pH} = -\log_{10}(1.75 \times 10^{-5}) \). Calculating, we find \( \mathrm{pH} \approx 4.76 \).
03

Calculate pH for Case B

For case (b) with \([\mathrm{H}^{+}] = 6.50 \times 10^{-10} \mathrm{~mol} / \mathrm{L}\), the calculation is \( \mathrm{pH} = -\log_{10}(6.50 \times 10^{-10}) \). This results in \( \mathrm{pH} \approx 9.19 \).
04

Calculate pH for Case C

For case (c), we use \([\mathrm{H}^{+}] = 1.0 \times 10^{-4} \mathrm{~mol} / \mathrm{L}\). The pH is calculated as \( \mathrm{pH} = -\log_{10}(1.0 \times 10^{-4}) \), which simplifies to \( \mathrm{pH} = 4.00 \).
05

Calculate pH for Case D

In case (d), with \([\mathrm{H}^{+}] = 1.50 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\), apply the formula: \( \mathrm{pH} = -\log_{10}(1.50 \times 10^{-5}) \). The pH value is \( \mathrm{pH} \approx 4.82 \).

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Key Concepts

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

Understanding Hydrogen Ion Concentration
The concentration of hydrogen ions (B[ {H}^{+} ] ) in a solution is a fundamental aspect when it comes to calculating the pH. This concentration indicates how many moles of hydrogen ions are present in one liter of solution.
  • A higher {H}^{+} concentration means a more acidic solution.
  • Conversely, a lower {H}^{+} concentration indicates a more basic (alkaline) solution.
Measuring this is pivotal in acid-base chemistry because the nature and strength of the solution鈥攚hether acidic, neutral, or basic鈥攃an be understood through it. Remember, the concentration is usually given in scientific notation for precision and ease, such as {6.50 imes 10^{-10} ext{ mol/L} }.
It is important to handle these small numbers carefully during calculations as they greatly affect the pH value.
Logarithmic Scale and pH Calculation
The pH scale is a logarithmic scale used to measure the acidity or basicity of a solution. Unlike a linear scale, a logarithmic scale captures more detail by expanding small ranges at lower values. The formula for calculating pH, [ ext{pH} = - ext{log}_{10}[ ext{H}^{+}] ], demonstrates this principle.
  • A change of one unit on the pH scale reflects a tenfold change in {H}^{+} concentration. Hence, even a small shift in pH can imply a significant change in acidity.
  • The negative sign in the formula indicates that increasing {H}^{+} concentration lowers the pH, marking enhanced acidity.

Understanding the logarithmic nature of the pH scale helps us interpret solutions more accurately. A subtle change in pH might mean a substantial shift in the nature of the solution's acidity or basicity. Thus, when you see a pH of 4.76, like in case A, remember, this reflects much more than just a numerical change.
Insights into Acid-Base Chemistry
Acid-base chemistry explores the reactions and properties of acids and bases, providing critical insights into the pH behavior in solutions. When talking about acids and bases, we usually refer to their ability to donate or accept hydrogen ions, respectively.
  • An acidic solution ( ext{pH} < 7 ) contains a higher concentration of {H}^{+} ions than a neutral solution.
  • The neutral value of pH is 7, which typically indicates the presence of pure water.
  • On the other hand, a basic solution ( ext{pH} > 7 ) is characterized by a lower concentration of {H}^{+} ions.

In practical scenarios, knowing the pH helps in numerous applications such as medicine, agriculture, and environmental science. Accurately calculating pH from {H}^{+} concentration allows chemists and scientists to make well-informed decisions regarding the suitability of a solution for a particular purpose.

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Most popular questions from this chapter

Duration of Hydrogen Bonds PCR is a laboratory process in which specific DNA sequences are copied and amplified manyfold. The two DNA strands, which are held together in part by hydrogen bonds between them, are heated in a buffered solution to separate the two strands, then cooled to allow them to reassociate. What do you predict about the average duration of \(\mathrm{H}\) bonds at the high temperature in comparison to the low temperature?

Effect of Holding One's Breath on Blood pH The pH of the extracellular fluid is buffered by the bicarbonate/carbonic acid system. Holding your breath can increase the concentration of \(\mathrm{CO}_{2}(\mathrm{aq})\) in the blood. What effect might this have on the pH of the extracellular fluid? Explain the effect on \(\mathrm{pH}\) by writing the relevant equilibrium equation(s) for this buffer system.

Calculation of \(\mathrm{pH}\) from Concentration of Strong Acid Calculate the \(\mathrm{pH}\) of a solution prepared by diluting \(3.0 \mathrm{~mL}\) of \(2.5 \mathrm{M} \mathrm{HCl}\) to a final volume of \(100 \mathrm{~mL}\) with \(\mathrm{H}_{2} \mathrm{O}\).

Choice of Weak Acid for a Buffer Determine whether each weak acid would best buffer at \(\mathrm{pH} 3.0\), at \(\mathrm{pH} 5.0\), or at \(\mathrm{pH} 9.0\) : a. formic acid \(\left(p K_{\mathrm{x}}=3.8\right)\); b. acetic acid \(\left(p K_{a}=4.76\right)\); c. ammonium \(\left(\mathrm{p} K_{\mathrm{n}}-9.25\right) ;\) d. boric acid \(\left(\mathrm{p} K_{\mathrm{a}}=9.24\right)\); e. chloroscetic acid \(\left(\mathrm{p} K_{\mathrm{z}}=2.87\right)\); f. hycdrazoic acid \(\left(p K_{a}=4.6\right)\). Briefly justify your answer.

Solubility of Ethanol in Water Ethane \(\left(\mathrm{CH}_{3} \mathrm{CH}_{3}\right)\) and ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)\) differ in their molecular makeup by only one atom, yet ethanol is much more soluble in water than ethane. Describe the features of ethanol that make it more water soluble than ethane.
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