Calculate the concentrations of all species in a 0.300 M ##Na_2SO_3## (sodium sulfite) solution? The ionization constants for sulfurous acid are ##K_(a1) = 1.4* 10^(–2)## and ##K_(a2) = 6.3 * 10^(–8)##. ##[Na^+]## ##[SO_3^-2]## ##[HSO_3^-]## ##[OH^-]## ##[H^+]##

!! LONG ANSWER !!
Sodium sulfate will dissociate completely in aqueous solution to give sodium cations, ##Na^(+)##, and sulfite anions, ##SO_3^(2-)##.
##Na_2SO_(3(s)) -> color(red)(2)Na_((aq))^(+) + SO_(3(aq))^(2-)##
Notice that 1 mole of sodium sulfite will produce ##color(red)(2)## moles of sodium cations and 1 mole of sulfite anions. This means that you get
##[Na^(+)] = 2 * [Na_2SO_3] = 2 * 0.300 = “0.600 M”##
##[SO_3^(2-)] = [Na_2SO_3] = “0.300 M”##
The sulfite anion will act as a base and react with water to form the bisulfate ion, or ##HSO_3″”^(-)##. The base dissociation constant, ##K_b##, for the sulfite ion, will be equal to
##K_b = K_W/K_(a2) = 10^(-14)/(6.3 * 10^(-8)) = 1.59 * 10^(-7)##
Use an ICE table for the equilibrium reaction that will be established to determine the of the bisulfate and hydroxide ions
##” “SO_(3(aq))^(2-) + H_2O_((l)) rightleftharpoons HSO_(3(aq))^(-) + OH_((aq))^(-)##I……0.300……………………………0…………………0C……(-x)………………………………(+x)……………..(+x)E…0.300-x…………………………..x………………….x
The base dissociation constant will be equal to
##K_b = ([HSO_3^(-)] * [OH^(-)])/([SO_3^(2-)]) = (x * x)/(0.300 – x) = x^2/(0.300 – x)##
Because the value of ##K_b## is so small, you can approximate (0.300 – x) with 0.300. This means that
##K_b = x^2/0.300 = 1.59 * 10^(-7) => x = 2.18 * 10^(-4)##
As a result, you’ll get
##[OH^(-)] = 2.18 * 10^(-4)”M”##
##[HSO_3″”^(-)] = 2.18 * 10^(-4)”M”##
##[SO_3^(2-)] = 0.300 – 2.18 * 10^(-4) ~= “0.300 M”##
Now for the tricky part. The bisulfate ion can also act as a base and react with water to form sulfurous acid, ##H_2SO_3##. The problem with sulfurous acid is that it doesn’t exist in aqueous solution in that form, but rather as sulfur dioxid, ##SO_2##, and water.
##underbrace(SO_2 + H_2O)_(“color(blue)(H_2SO_3)) + H_2O_((l)) rightleftharpoons HSO_(3(aq))^(-) + H_3O_((aq))^(+)##
The base dissociation constant for the bisulfate ion will be
##K_b = K_W/K_(a1) = 10^(-14)/(1.4 * 10^(-2)) = 7.14 * 10^(-13)##
When the bisulfate ion reacts with water, it’ll form
##” “HSO_(3(aq))^(-) + cancel(H_2O_((l))) rightleftharpoons SO_(2(aq)) + cancel(H_2O_((l))) + OH_((aq))^(-)##I….##2.18 * 10^(-4)##………………………..0……………………………..##2.18 * 10^(-4)##C………(-x)………………………………..(+x)………………………………….(+x)E…##2.18 * 10^(-4)”-x”##…………………..x…………………………….##2.18 * 10^(-4)”+x”##
##K_b = ([SO_2] * [OH^(-)])/([HSO_3″”^(-)]) = ((2.18 * 10^(-4) + x) * x)/(2.18 * 10^(-4)-x)##
Once again, the very, very small value of ##K_b## will allow you to approximate ##(2.18 * 10^(-4)”-x”)## and ##(2.18 * 10^(-4)”+x”)## with ##2.18 * 10^(-4)##. This will get you
##K_b = (cancel(2.18 * 10^(-4)) * x)/(cancel(2.18 * 10^(-4))) = x = 7.14 * 10^(-13)##
As a result, the of all the species listed will be
##[Na^(+)] = color(green)(“0.600 M”)##
##[SO_3^(2-)] = color(green)(“0.300 M”)##
##[HSO_3″”^(-)] = 2.18 * 10^(-4)-7.14 * 10^(-13) ~= color(green)(2.18 * 10^(-4)”M”)##
##[OH^(-)] = 2.18 * 10^(-4) + 7.14 * 10^(-13) ~= color(green)(2.18 * 10^(-4)”M”)##
##[H^(+)] = 10^(-14)/([OH^(-)]) = 10^(-14)/(2.18 * 10^(-4)) = color(green)(4.59 * 10^(-11)”M”)##

Calculate the price
Make an order in advance and get the best price
Pages (550 words)
$0.00
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Upload your instructions
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with Homework Mules
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
Testimonials
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Finance
Thank you very much!! I should definitely pass my class now. I appreciate you!!
Customer 452591, June 18th, 2022
Business Studies
Great paper thanks!
Customer 452543, January 23rd, 2023
Political science
I like the way it is organized, summarizes the main point, and compare the two articles. Thank you!
Customer 452701, February 12th, 2023
Psychology
I requested a revision and it was returned in less than 24 hours. Great job!
Customer 452467, November 15th, 2020
Accounting
Thank you for your help. I made a few minor adjustments to the paper but overall it was good.
Customer 452591, November 11th, 2021
Technology
Thank you for your work
Customer 452551, October 22nd, 2021
Psychology
Thank you. I will forward critique once I receive it.
Customer 452467, July 25th, 2020
Political science
Thank you!
Customer 452701, February 12th, 2023
Education
Thank you so much, Reaserch writer. you are so helpfull. I appreciate all the hard works. See you.
Customer 452701, February 12th, 2023
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend
OUR GIFT TO YOU
15% OFF your first order
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat
Show more
<