Problem

Propionic acid, $\mathrm{C}_{2} \mathrm{H}_{5} \m…

01:17

Problem 69 Easy Difficulty

Calculate the concentration of all solute species in each of the following solutions of acids or bases. Assume that the ionization of water can be neglected, and show the change in the initial concentrations can be neglected. Ionization constants can be found in Appendix $\mathrm{H}$ and Appendix $1 .$
$$
\begin{array}{l}{\text { (a) } 0.0092 \text { M HClO, a weak acid }} \\ {\text { (b) } 0.0784 M \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}, \text { a weak base }} \\ {\text { (c) } 0.0810 \mathrm{M} \mathrm{HCN} \text { , a weak acid }} \\ {\text { (d) } 0.11 \mathrm{M}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{N} \text { , a weak base }} \\ {\text { (e) } 0.120 \mathrm{M} \mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+} \text { a weak acid, } K_{\mathrm{a}}=1.6 \times 10^{-7}}\end{array}
$$

Answer

A. $c\left(H^{+}\right)=c\left(C l O^{-}\right)=1.63 \cdot 10^{-5} M$
$c(H C l O)=0.0092 M$
B. $c\left(O H^{-}\right)=c\left(C_{6} H_{5} N H_{3}^{+}\right)=5.8 \cdot 10^{-6} M$
$c\left(C_{6} H_{5} N H_{2}\right)=0.0784 M$
C. $c\left(H^{+}\right)=c\left(C N^{-}\right)=6.3 \cdot 10^{-6} M$
$c(H C N)=0.0810 M$
D. $\begin{aligned} c\left(O H^{-}\right)=& c\left(\left(C H_{3}\right)_{3} N H^{+}\right)=2.6 \cdot 10^{-3} M \\ & c\left(\left(C H_{3}\right)_{3} N\right)=0.11 M \end{aligned}$
E. $\begin{aligned} c\left(H^{+}\right)=& c\left(\left[F e\left(H_{2} O\right)_{5} O H\right]^{+}\right)=1.4 \cdot 10^{-4} M \\ & c\left(\left[F e\left(H_{2} O\right)_{6}\right]^{2+}\right)=0.120 M \end{aligned}$

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Video Transcript

Let's calculate the concentration of all saw it species in each of the following acids air bases and we'll have to apply the 5% rule to see if the assumptions we make are valid for a we have a weak acid. A 0.92 Moeller hcl Oh, we're told that is a weak acid. We can look up. It's K a value which is 35 times 10 to the negative eight at the the concentration of all species. First by starting to rate, Brown said. Lower equilibrium for a weak acid initial polarity pleader race table. No assumption here We're gonna assume that 0.9 to minus X is approximately equal. The 0.92 and a K expression Que is 3.5. It was 10 of the negative. Eat Yeah, solving for X. I get 1.8 times 10 to the negative five. Let's verify your assumption. Okay, so assumption here 5% of 0092 is equal to 4.6 times 10 to the negative four. So X, which is 1.8 times 10 to the negative five, is less than 46 times 10 to the negative four. Therefore, since it is less according to the 5% wrote, the assumption is valid. And now we can report the concentration of all species the concentration of H 30 plus sequel of the concentration of ceelo minus one. Whereas table this was X which is equal to 1.8 times 10 to the negative five Mueller on the concentration of HCL Oh is equal the 0.92 molars. Our assumption is valid for be We have zero 78 four Moeller C six h five and h two and we're told that it is a weak base for the week base. Well, look up the K B value, which is equal to 4.6 times 10 to the minus 10. Let's calculate the concentration of all species. That's right. The equation for the week base initial polarity is 0.784 Peter a stable here K b expression way. No, the baby values We're gonna assume here E didn't write the assumption here, but we will squeeze it in here. We're gonna assume that 0.784 minus X is approximately equal 2.784 will include that in our expression here, the K B, we found out, was 4.6 times 10 to the negative 10 from the appendix people that x x and our assumption here is 0.784 solving for X. Here we find that X is equal the 6.0 times 10 to the negative six. Let's were this above here. Uh, let's look at our assumption here. 5% of 0.784 is equal to 39 times 10 to the negative three. Therefore, X, which is 6.0 times 10 to the negative six, is less than 39 times 10 to the negative three. Therefore, the assumption is valid concentration of C six, h five and H three plus Z equal to the concentration of O H minus and their ice table. That's they're both equal. The X of these were both equal to 6.0 times 10 to the negative six Mohler and the majority of the C six h five and H two is equal to 2.0 784 Moeller. There would be the concentration of all species proceed, we have weak acid. 0.0 810 Moeller h c n We can look up the value for H C N, which is equal to 40 times 10 to the negative 10. It's Richard Brown said Lowry. Equation for h c n initial polarity. That's your 810 minus x x and x. We're going to assume here the 0.810 minus X is approximately 0810 que c h 30 plus C and minus over eight c N Katie value 4.0 times 10 to the minus 10. Take the x x Clinton 0810 X is equal to 5.7 times 10 to the negative. Six. Let's look at our assumption for the assumption to be valid will apply the 5% rule of 5% of 50.810 and that would be equal to 4.1 times 10 to the negative three. Therefore, X, which is 5.7 times 10 to the negative six, is less than 4.1 times 10 to the negative three, and therefore the assumption is valid, and the mill arat e of the H 30 plus sequel of the military of the CN minus, which is equal to X. These air equal to you 5.7 times 10 to the negative. Six. Smaller The morality of the H. C N equal the 0.810 Moeller for D. We have a weak base. 0.11 Moeller C. H. 33 and we can look up the K B value for this week base and find that the baby value is equal to 7.4 times 10 to the negative. Five. Start by writing a bronze that Lowery equilibrium here over Get ch 33 and each plus and which minus I C e 0.11 Peter writes table one minus x x and X, and we could make our assumption here. Assume that 10.11 minus X is approximately 0.11 K B is equal to C H 33 n h plus Oh H minus over C h that again ch 33 and and our Kate value was 74 times 10 to the negative five Sequel to you x x 0.11 solving for X here with the assumption. We find that it's equal to 2.9 times 10 to the negative three. And let's verify your assumption. With the 5% rule, 5% of 0.11 would be equal to 5.5 times 10 to the negative three. So X, which is 2.9 times 10 to the negative three, is less than 5.5 comes 10 to the negative three. Therefore, the assumption is valid, and the concentration of CH 33 n H plus is equal to the concentration of O H minus, which is equal to X. According to Reis Table. These are both equal to 2.9 times 10 to the negative three Mueller on the concentration of ch 33 and is equal 2.11 Moeller for eat. We have a weak acid 0.1 to 0 Mueller F E. H. 206 to plus and were given its K in the question. It's equal to 1.6 times 10 to the negative seven. It's greater once, said Lowry. Equation here for a weak acid h 30 plus at f E. H. 20 five o. H. And this would be a, um plus one a que? Yes, that would be correct. Initial change Equilibrium. This is 0.1 to 0 00 minus x plus X plus x went 1 to 0 minus x x and x que expression here would be h 30 plus over f e h 205 oh h plus over f e h 20 six two plus on the K A. Here is 16 times 10 to the negative seven sequel. The X x on, um, make our assumption here. We're gonna assume that 0.1 to 0 minus X is approximately 00.1 to 0. So 0.1 to 0 in the denominator. Here, solving for X here will get X equal toe 1.4 times 10 to the negative four, and we'll verify your assumption. Here. 5% of 0.1 to 0 is equal to 6.0 times 10 to the negative three. So X, which is 1.4 times 10 to the negative four, is less than the 5% 6.0 times 10 to the negative three. Therefore, the assumption is valid and the malaria t of the H 30 plus is equal to the majority of the F D H 205 oh h plus just these air body called X 14 times 10 to the negative four Moeller and the morality of the F E H 206 to plus through the this would be equal to 0.1 to 0 Mueller.

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