Calculate the [h3o+] of the following polyprotic acid solution: 0.135 M H2CO3

k1 and k2 are far enough apart in H2CO3 that k2 can be ignored; therefore, treat this as a monoprotic acid with just k1.

H2CO3 ===> H^+ + HCO3^-

k1 = (H^+)(HCO3^-)/(H2CO3)
Set up an ICE chart, substitute into k1 and solve for H^+.

Ah, H2CO3, the comedian of polyprotic acids! Now, let's see if we can get that punchline for you. In this case, H2CO3 dissociates twice, giving us HCO3- and then CO3^2-. But since we're looking for [H3O+], we'll focus on that first dissociation equation:

H2CO3 ⇌ H+ + HCO3-

Now, since this is a weak acid, we can use the Ka expression:

Ka = [H+][HCO3-] / [H2CO3]

Since we start with 0.135 M H2CO3 and we assume it fully dissociates (in this comedy club called chemistry), we can drop the [H2CO3] from the equation. Now, let's call [H+] as x:

Ka = x * (0.135 - x) / 0.135

Now, solving for x, we get:

x^2 - 0.135x + (0.135 * Ka) = 0

Now, if we replace Ka with the Ka value for H2CO3, we can solve the quadratic equation and get a numerical value for [H+], which will be the same as [H3O+]. But remember, this is just one of the comedic acts of H2CO3, so be sure to look out for the next one, as H2CO3 loves to be unpredictable!

To calculate the concentration of hydronium ions ([H3O+]) in a polyprotic acid solution, such as H2CO3, you need to consider the acid dissociation constants (Ka) at each dissociation step.

H2CO3 can undergo two dissociation steps:
H2CO3 ⇌ H+ + HCO3- (Ka1)
HCO3- ⇌ H+ + CO3^2- (Ka2)

Since the question does not specify the temperatures, we will use the values for Ka from 25 degrees Celsius.

Step 1: Calculate the concentration of H+ ions after the first dissociation step.
Given:
Ka1 for H2CO3 = 4.2 x 10^-7
Initial concentration of H2CO3 = 0.135 M

Let's represent the concentration of H+ after the first dissociation step as x. Since x is small compared to the initial concentration of H2CO3 (0.135 M), we can neglect x in comparison to 0.135 M.

Using the equilibrium expression for Ka1:
Ka1 = [H+][HCO3-] / [H2CO3]

Since the concentration of H+ and HCO3- is x, we can rewrite the equation as:
4.2 x 10^-7 = x² / 0.135

Rearranging the equation, we find:
x² = 4.2 x 10^-7 * 0.135
x² = 5.67 x 10^-8
x ≈ 7.53 x 10^-4 M

Therefore, the concentration of H+ ions after the first dissociation step is approximately 7.53 x 10^-4 M.

Step 2: Calculate the concentration of H+ ions after the second dissociation step.
Given:
Ka2 for HCO3- = 4.8 x 10^-11

Again, let's represent the concentration of H+ after the second dissociation step as x. Since x is small compared to the initial concentration of HCO3- ions (7.53 x 10^-4 M), we can neglect x in comparison to 7.53 x 10^-4 M.

Using the equilibrium expression for Ka2:
Ka2 = [H+][CO3^2-] / [HCO3-]

Since the concentration of H+ and CO3^2- is x, we can rewrite the equation as:
4.8 x 10^-11 = x² / (7.53 x 10^-4)

Rearranging the equation, we find:
x² = 4.8 x 10^-11 * 7.53 x 10^-4
x² = 3.6096 x 10^-14
x ≈ 1.9 x 10^-7 M

Therefore, the concentration of H+ ions after the second dissociation step is approximately 1.9 x 10^-7 M.

Hence, the [H3O+] concentration in the 0.135 M H2CO3 solution is primarily determined by the first dissociation step and is approximately 7.53 x 10^-4 M.

To calculate the concentration of [H3O+] in a polyprotic acid solution, you need to consider the dissociation of the acid and the equilibrium constants involved.

For the polyprotic acid H2CO3 (carbonic acid), it dissociates in two stages:

H2CO3 ⇌ H+ + HCO3-

HCO3- ⇌ H+ + CO32-

Since the concentration of the carbonic acid is given as 0.135 M, we need to determine the concentrations of the dissociated H+ ions at each step.

Step 1:
The initial concentration of H2CO3 is 0.135 M, but assuming no dissociation has occurred, the concentration of H+ ions is initially zero.

Step 2:
At equilibrium, for every 1 mole of carbonic acid that dissociates, 1 mole of H+ ions is produced. Therefore, the concentration of H+ ions will be equal to the concentration of H2CO3 that has dissociated.

Now, we need to calculate the concentrations of H+ ions at each step:

Step 1:
[H+] = [H2CO3] (initially zero) = 0 M

Step 2:
[H+] = [H2CO3] (dissociated) = 0.135 M

Therefore, the concentration of [H3O+] in the polyprotic acid solution of 0.135 M H2CO3 is 0.135 M after the dissociation reaction has reached equilibrium.