Predict which solution in each pair below will have the...

Predict which solution in each pair below will have the lower pH. a. $2.56 \times 10^{-2} \mathrm{M} \mathrm{HCl}$ or $4.09 \times 10^{-2} \mathrm{MHBr}$ b. $1.00 \times 10^{-5} M$ acctic acid $\left(K_{\mathrm{a}}=1.76 \times 10^{-5}\right)$ or $1.00 \times 10^{-5} M$ formic acid $\left(K_{a}=1.77 \times 10^{-4}\right)$ c. $22 \mathrm{mM} \mathrm{CH}_{3} \mathrm{NH}_{2}\left(\mathrm{p} K_{\mathrm{b}}=3.36\right)$ or $22 \mathrm{mM}\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}\left(K_{\mathrm{b}}=5.9 \times 10^{-4}\right)$ d. $158 \mathrm{mM} \mathrm{NH}_{3}\left(\mathrm{p} K_{\mathrm{b}}=4.75\right)$ or $158 \mathrm{m} M$ acetic acid $\left(p K_{a}=4.75\right)$ e. $0.00395 M \mathrm{HNO}_{3}$ or $0.00145 M \mathrm{HClO}_{4}$ f. $2.05 \times 10^{-1} M$ propionic acid $\left(K_{2}=1.4 \times 10^{-5}\right)$ or $2.05 \times 10^{-1} M$ fluoroacetic acid $\left(K_{2}=2.6 \times 10^{-3}\right)$ g. 375 m $M$ pyridine $\left(p K_{b}=8.77\right)$ or $375 \mathrm{mM}$ aniline $\left(\mathrm{p} K_{\mathrm{b}}=9.40\right)$ h. $0.555 M \mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\left(K_{2}=3 \times 10^{-3}\right)$ or $0.355 M \mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\left(K_{2}=1 \times 10^{-4}\right)$

Predict which solution in each pair below will have the lower pH.
a. $2.56 \times 10^{-2} \mathrm{M} \mathrm{HCl}$ or $4.09 \times 10^{-2} \mathrm{MHBr}$
b. $1.00 \times 10^{-5} M$ acctic acid $\left(K_{\mathrm{a}}=1.76 \times 10^{-5}\right)$ or $1.00 \times 10^{-5} M$ formic acid $\left(K_{a}=1.77 \times 10^{-4}\right)$
c. $22 \mathrm{mM} \mathrm{CH}_{3} \mathrm{NH}_{2}\left(\mathrm{p} K_{\mathrm{b}}=3.36\right)$ or
$22 \mathrm{mM}\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}\left(K_{\mathrm{b}}=5.9 \times 10^{-4}\right)$
d. $158 \mathrm{mM} \mathrm{NH}_{3}\left(\mathrm{p} K_{\mathrm{b}}=4.75\right)$ or $158 \mathrm{m} M$ acetic acid
$\left(p K_{a}=4.75\right)$
e. $0.00395 M \mathrm{HNO}_{3}$ or $0.00145 M \mathrm{HClO}_{4}$
f. $2.05 \times 10^{-1} M$ propionic acid $\left(K_{2}=1.4 \times 10^{-5}\right)$ or $2.05 \times 10^{-1} M$ fluoroacetic acid $\left(K_{2}=2.6 \times 10^{-3}\right)$
g. 375 m $M$ pyridine $\left(p K_{b}=8.77\right)$ or $375 \mathrm{mM}$ aniline $\left(\mathrm{p} K_{\mathrm{b}}=9.40\right)$
h. $0.555 M \mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\left(K_{2}=3 \times 10^{-3}\right)$ or $0.355 M \mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\left(K_{2}=1 \times 10^{-4}\right)$

Key Concepts

pH Scale

The pH scale is a logarithmic measure of the hydrogen ion concentration in a solution, where lower pH values indicate higher acidity and higher pH values indicate more basic solutions. It serves as a quantitative tool in determining and comparing the acidity or basicity of different solutions.

Acid Strength

Acid strength refers to the extent to which an acid dissociates in water to release hydrogen ions. Strong acids completely dissociate in aqueous solution, yielding a high concentration of hydrogen ions, while weak acids only partially dissociate, leading to lower concentrations of hydrogen ions.

Acid Dissociation Constant (Ka) and pKa

The acid dissociation constant (Ka) quantifies the strength of an acid by measuring the equilibrium concentration of its dissociated ions relative to its undissociated form. A larger Ka (or equivalently, a lower pKa) indicates a stronger acid that more readily donates protons, which generally results in a lower pH when the acid is in solution.

Base Dissociation Constant (Kb) and pKb

For bases, the base dissociation constant (Kb) measures the extent of reaction with water to produce hydroxide ions. Lower pKb values (or higher Kb values) indicate stronger bases that more effectively accept protons, influencing the pH of the solution by making it more alkaline.

Effect of Concentration on pH

The concentration of acid or base in a solution directly affects its pH. Even a strong acid at a lower concentration might have a pH comparable to that of a weak acid at a higher concentration. Thus, both the inherent strength (as indicated by Ka or Kb) and the actual molar amount present are critical in predicting the overall pH.

Metal Ion Hydrolysis

Certain metal ions, particularly those with high positive charges like transition metal complexes, can undergo hydrolysis in water, producing hydrogen ions and thereby lowering the pH of the solution. This process is important in understanding the acidity of solutions containing such metal complexes.

Transcript

00:01 Problem we are given eight pairs of compounds with varying concentrations and occasionally some other information and we're told to determine which compound out of each pair will give a lower ph.

00:12 So starting with our first problem we've got two acids so we know we're gonna have a low ph for both but we've got two different concentrations and two different acids.

00:23 Now hcl is a weaker acid than hbr because br minus is a more stable anion so that means overall we're going to have a stronger acid for our hydrobromic acid.

00:36 But not only is it a stronger acid, but we have a higher concentration of it.

00:40 So we have a higher concentration of a stronger acid.

00:44 This one's going to have a lower ph.

00:47 So the answer to our first one would be the 4 .09 times 10 to the negative second molar hydrobromic acid, stronger acid and higher concentration.

00:56 For problem two, we've got 1 times 10 to the negative fifth molar, acetic acid and 1 times 10 to the negative 5th molar formic acid.

01:04 So we have the same concentration of two different acids.

01:08 So really we just need to figure out which one's a stronger acid.

01:11 And from our k .a value, we can see that formic acid is a stronger acid.

01:15 It has a higher ka value, meaning it's stronger.

01:18 So since we have the same concentration and this is the stronger acid, we know that this is going to give us a lower ph.

01:27 So the answer to our second one is the 1 times 10 to the negative 5th formic acid because of its higher k -a value.

01:34 Now for our third one, we're given 22 millimoles of ch3nh2 and ch3 -2nh2.

01:43 So same thing with our previous example.

01:45 We're looking to see which one is just a stronger acid.

01:49 So for this one, we're given a pkb and a kb.

01:53 So for this problem, the first thing that we have to do is actually get them into the same form.

01:58 So let's get them both in the form of kb.

02:02 So if we do 10 to the negative 3 .36, we get our kb value, and our kb value is going to be 4 .37 times 10 to the negative 4th.

02:15 So now we've got two values we can compare.

02:18 Now we know whichever one is going to be the weaker base is the stronger acid.

02:24 So the one with the lower kb value is going to be the stronger acid.

02:29 So our lower kb value is the one here on the left.

02:34 So our 22 millimolar ch3nh2 is going to give us a lower ph.

02:40 They're the same concentration, but we have a weaker base, meaning we have a stronger acid.

02:47 Lower kb means a greater k -a.

02:51 So in that case, our component on the left is going to give us a lower ph.

02:58 Now for our fourth problem, we've got again two of the same concentrations.

03:02 We've got 158 millimolar nh3 and 158 millimolar acetic acid.

03:08 This is an easy problem.

03:10 We have an acid and we have a base.

03:12 Our acid is going to give us the lower ph.

03:15 Disregarding any of the information we were given, we could have figured that out.

03:19 Now, of course, one we're given a pkb and one we're given a pca.

03:22 So if we weren't told that acetic acid was an acid and we didn't know that nh3 was a base because of that lone pair, we could have figured it out that way.

03:31 Lower pka means a stronger acid...

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