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Chapter 4: Problem 102

Which has the larger concentration of hydronium ions, \(0.015 \mathrm{M} \mathrm{HCl}\) or aqueous \(\mathrm{HCl}\) with a \(\mathrm{pH}\) of \(1.20 ?\)

Short Answer

Expert verified
HCl with a pH of 1.20 has a higher [H鈦篯.

Step by step solution

01

Understand the Problem

We need to compare the concentration of hydronium ions ([H鈦篯) for two different solutions of HCl: a 0.015 M solution and another solution with a pH of 1.20.
02

Determine [H鈦篯 from pH

The concentration of hydronium ions can be calculated using the pH of a solution. The formula is \([H^{+}] = 10^{- ext{pH}}\). Let鈥檚 calculate for HCl with a pH of 1.20.\[[H^{+}] = 10^{-1.20} = 0.0631 ext{ M}\]
03

Compare Concentrations

Now, compare the [H鈦篯 concentrations from the two scenarios: - 0.015 M - 0.0631 M The concentration 0.0631 M from the pH 1.20 solution is greater than the 0.015 M solution.

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Key Concepts

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

Understanding Hydronium Ions
Hydronium ions, commonly represented as \(\text{H}_3\text{O}^+\), play a crucial role in acid solutions.When an acid dissolves in water, it donates a proton (\(\text{H}^+\)) to a water molecule to form a hydronium ion. This chemical species is a reflection of the acidic nature of a solution and is frequently used to discuss the acidity levels in aqueous solutions.
  • Hydronium ions result from the protonation of a water molecule.
  • The concentration of hydronium ions in a solution indicates its acidity. Higher concentrations mean a more acidic solution.
  • In dilute solutions, the concentration of hydronium ions is often used interchangeably with the concentration of hydrogen ions (\(\text{H}^+\)).
Understanding the concentration of hydronium ions is essential for pH calculations, as it directly impacts the pH value of a solution.This concentration informs us about the acidic strength and potential chemical reactivity of the solution.
The Process of pH Calculation
Calculating the pH of a solution is a fundamental concept in chemistry.It provides insights into the acidity or basicity (alkalinity) of a solution.The pH scale is logarithmic, ranging from 0 to 14, and is derived from the concentration of hydronium ions.
To calculate pH, we use the formula: \[pH = -\log_{10}[\text{H}_3\text{O}^+]\]This formula highlights the inverse relationship between hydronium ion concentration and pH.
  • Low pH values (0-6.9) indicate a high concentration of hydronium ions, suggesting the solution is acidic.
  • Neutral solutions have a pH of approximately 7, where hydronium and hydroxide ions are in equilibrium.
  • High pH values (7.1-14) indicate a low concentration of hydronium ions, meaning the solution is basic.
It's important to understand that even small changes in pH reflect significant changes in hydronium ion concentrations due to the logarithmic nature of the scale.
Exploring Acid Solutions
Acid solutions are characterized by their ability to donate protons (hydrogen ions) and their low pH values.An acid like hydrochloric acid (HCl) dissociates in water to increase hydronium ion concentration.
  • The strength of an acid depends on its degree of ionization in water.
  • Strong acids completely ionize, leading to higher concentrations of hydronium ions.
  • Weak acids partially ionize, resulting in lower concentrations of hydronium ions compared to strong acids of the same concentration.
When comparing acid solutions, one should note both the concentration of the acid (\(\text{M}\), meaning molarity) and its degree of ionization, both of which affect the hydronium ion concentration.For example, an acid solution of 0.015 M HCl is less acidic than one with a pH of 1.20, indicating fewer hydronium ions in the former, as shown in the original exercise solution.

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Most popular questions from this chapter

The following questions may use concepts from this and previous chapters. Two beakers sit on a balance; the total mass is \(167.170 \mathrm{g} .\) One beaker contains a solution of \(\mathrm{KI}\) the other contains a solution of \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} .\) When the solution in one beaker is poured completely into the other, the following reaction occurs: $$ 2 \mathrm{KI}(\mathrm{aq})+\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) \rightarrow 2 \mathrm{KNO}_{3}(\mathrm{aq})+\mathrm{PbI}_{2}(\mathrm{s}) $$ (IMAGE CANNOT COPY) What is the total mass of the beakers and solutions after reaction? Explain completely.

A You need to know the volume of water in a small swimming pool, but, owing to the pool's irregular shape, it is not a simple matter to determine its dimensions and calculate the volume. To solve the problem, you stir in a solution of a dye \((1.0 \mathrm{g}\) of methylene blue, \(\mathrm{C}_{16} \mathrm{H}_{18} \mathrm{ClN}_{3} \mathrm{S},\) in \(50.0 \mathrm{mL}\) of water). After the dye has mixed with the water in the pool, you take a sample of the water. Using a spectrophotometer, you determine that the concentration of the dye in the pool is \(4.1 \times 10^{-8} \mathrm{M} .\) What is the volume of water in the pool?

The deep blue compound \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4}\) is made by the reaction of copper(II) sulfate and ammonia. $$ \mathrm{CuSO}_{4}(\mathrm{aq})+4 \mathrm{NH}_{3}(\mathrm{aq}) \rightarrow \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4}(\mathrm{aq}) $$ (a) If you use \(10.0 \mathrm{g}\) of \(\mathrm{CuSO}_{4}\) and excess \(\mathrm{NH}_{3}\), what is the theoretical yield of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4} ?\) (b) If you isolate \(12.6 \mathrm{g}\) of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4},\) what is the percent yield of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4} ?\)

To analyze an iron-containing compound, you convert all the iron to \(\mathrm{Fe}^{2+}\) in aqueous solution and then titrate the solution with standardized \(\mathrm{KMnO}_{4} .\) The balanced, net ionic equation is \(\mathrm{MnO}_{4}^{-}(\mathrm{aq})+5 \mathrm{Fe}^{2+}(\mathrm{aq})+8 \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq}) \rightarrow\) $$ \mathrm{Mn}^{2+}(\mathrm{aq})+5 \mathrm{Fe}^{3+}(\mathrm{aq})+12 \mathrm{H}_{2} \mathrm{O}(\ell) $$ A \(0.598-\mathrm{g}\) sample of the iron-containing compound requires \(22.25 \mathrm{mL}\) of \(0.0123 \mathrm{M} \mathrm{KMnO}_{4}\) for titration to the equivalence point. What is the mass percent of iron in the sample?

Black smokers are found in the depths of the oceans (page 110 ). Thinking that the conditions in these smokers might be conducive to the formation of organic compounds, two chemists in Germany found the following reaction could occur in similar conditions. $$ 2 \mathrm{CH}_{3} \mathrm{SH}+\mathrm{CO} \rightarrow \mathrm{CH}_{3} \mathrm{COSCH}_{3}+\mathrm{H}_{2} \mathrm{S} $$ If you begin with \(10.0 \mathrm{g}\) of \(\mathrm{CH}_{3} \mathrm{SH}\) and excess \(\mathrm{CO}\) (a) What is the theoretical yield of \(\mathrm{CH}_{3} \mathrm{COSCH}_{3} ?\) (b) If \(8.65 \mathrm{g}\) of \(\mathrm{CH}_{3} \mathrm{COSCH}_{3}\) is isolated, what is its percent yield?
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