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Math  /  Data & Statistics

QuestionMISSED THIS? Watch KCV 16.5; Read Section 16.5. You can click on the Review link to access the section in your eText. \begin{tabular}{|c|l|l|} \hline Name & \multicolumn{1}{|c|}{ Formula } & \multicolumn{1}{c|}{Ka1K_{\mathrm{a}_{1}}} \\ \hline Acetic & HC2H3O2\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} & 1.8×10−51.8 \times 10^{-5} \\ \hline Benzoic & HC7H5O2\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2} & 6.5×10−56.5 \times 10^{-5} \\ \hline Chloric & HClO3\mathrm{HClO}_{3} & >1>1 \\ \hline Chlorous & HClO2\mathrm{HClO}_{2} & 1.1×10−21.1 \times 10^{-2} \\ \hline Hydrochloric & HCl & >1>1 \\ \hline Hydrocyanic & HCN & 4.9×10−104.9 \times 10^{-10} \\ \hline Hydrobromic & HBr & >1>1 \\ \hline Hydrofluoric & HF & 6.8×10−46.8 \times 10^{-4} \\ \hline Hydroiodic & HI & >1>1 \\ \hline Hypochlorous & HClO10\mathrm{HClO}_{10} & 2.9×10−82.9 \times 10^{-8} \\ \hline Nitric & HNO3\mathrm{HNO}_{3} & >1>1 \\ \hline Nitrous & HNO2\mathrm{HNO}_{2} & 4.6×10−44.6 \times 10^{-4} \\ \hline Perchloric & HClO4\mathrm{HClO}_{4} & >1>1 \\ \hline Phenol & HC6H5O\mathrm{HC}_{6} \mathrm{H}_{5} \mathrm{O} & 1.3×10−101.3 \times 10^{-10} \\ \hline \end{tabular}
Part A
Rank the solutions in order of decreasing [H3O+]\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]. Rank solutions from largest to smallest hydronium irin concentration. To rank items as equivalent, overlap them. View Available Hint(s) \begin{tabular}{|l|l|l|l|l|} \hline \multicolumn{5}{|c|}{ Largest concentration } \\ & & & Smallest concentration \\ & & & \\ \hline \end{tabular}
The correct ranking cannot be determined. Submit Previous Answers

Studdy Solution

STEP 1

What is this asking? We need to arrange four **0.100.10 M** acid solutions—**HClO2\text{HClO}_2, HBr\text{HBr}, HC6H5O\text{HC}_6\text{H}_5\text{O}, and HClO\text{HClO}**—from highest to lowest hydronium ion concentration. Watch out! Don't just look at the exponents of the KaK_a values!
The concentration of the acid matters too!

STEP 2

1. Understand Acid Strength
2. Find the Hydronium Concentration
3. Rank the Solutions

STEP 3

A **larger** KaK_a value means a **stronger** acid, which means it dissociates more and produces **more** hydronium ions [H3O+][\text{H}_3\text{O}^+].
A **smaller** KaK_a means a **weaker** acid, meaning it doesn't like to give up its protons and produces **less** hydronium ions.

STEP 4

For **strong acids** like HBr\text{HBr}, the KaK_a is much greater than 11.
This means they fully dissociate.
So, for a **0.100.10 M** HBr\text{HBr} solution, the [H3O+][\text{H}_3\text{O}^+] is also **0.100.10 M**.

STEP 5

For **weak acids**, we can approximate [H3O+][\text{H}_3\text{O}^+] using the formula: [H3O+]=Ka⋅C [\text{H}_3\text{O}^+] = \sqrt{K_a \cdot C} where CC is the **initial concentration** of the acid.

STEP 6

For HClO2\text{HClO}_2, Ka=1.1×10−2K_a = 1.1 \times 10^{-2} and C=0.10C = 0.10 M. [H3O+]=(1.1×10−2)⋅(0.10)=1.1×10−3≈3.3×10−2 M [\text{H}_3\text{O}^+] = \sqrt{(1.1 \times 10^{-2}) \cdot (0.10)} = \sqrt{1.1 \times 10^{-3}} \approx 3.3 \times 10^{-2} \text{ M}

STEP 7

For HC6H5O\text{HC}_6\text{H}_5\text{O}, Ka=1.3×10−10K_a = 1.3 \times 10^{-10} and C=0.10C = 0.10 M. [H3O+]=(1.3×10−10)⋅(0.10)=1.3×10−11≈3.6×10−6 M [\text{H}_3\text{O}^+] = \sqrt{(1.3 \times 10^{-10}) \cdot (0.10)} = \sqrt{1.3 \times 10^{-11}} \approx 3.6 \times 10^{-6} \text{ M}

STEP 8

For HClO\text{HClO}, Ka=2.9×10−8K_a = 2.9 \times 10^{-8} and C=0.10C = 0.10 M. [H3O+]=(2.9×10−8)⋅(0.10)=2.9×10−9≈5.4×10−5 M [\text{H}_3\text{O}^+] = \sqrt{(2.9 \times 10^{-8}) \cdot (0.10)} = \sqrt{2.9 \times 10^{-9}} \approx 5.4 \times 10^{-5} \text{ M}

STEP 9

From our calculations, we have: * HBr:1.0×10−1 M\text{HBr}: 1.0 \times 10^{-1} \text{ M} * HClO2:3.3×10−2 M\text{HClO}_2: 3.3 \times 10^{-2} \text{ M} * HClO:5.4×10−5 M\text{HClO}: 5.4 \times 10^{-5} \text{ M} * HC6H5O:3.6×10−6 M\text{HC}_6\text{H}_5\text{O}: 3.6 \times 10^{-6} \text{ M}

STEP 10

Therefore, the order from **largest** to **smallest** [H3O+][\text{H}_3\text{O}^+] is: HBr\text{HBr}, HClO2\text{HClO}_2, HClO\text{HClO}, HC6H5O\text{HC}_6\text{H}_5\text{O}.

STEP 11

The solutions ranked in order of **decreasing** [H3O+][\text{H}_3\text{O}^+] are: **HBr\text{HBr}, HClO2\text{HClO}_2, HClO\text{HClO}, HC6H5O\text{HC}_6\text{H}_5\text{O}**.

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