Please help me visualize H2O autoionization concepts

[LearninDaMath]

Firstly, I have just read that at 25degC, 1 out of every 10,000,000 H2O molecules breakes into $H^{+}$ and $OH^{-}$.

If this true, then would this be correct:

Assuming no ionization occurs yet..

If 1 liter of H2O = 1000grams, and 1mol H2O = 18.015g, then by Dimensional Analysis:

$[1L*\frac{1000g}{1L}=1000g H2O] => [1000g H2O \frac{1mol}{18.015g}=55.5mol H2O] =>[55.5mol H2O * \frac{6.022E23}{1mol} = 3.3E25 H2O molecules]$

Thus 1 Liter of H2O= 3.3E25 H2O molecules

Then, since 1 out of every 10,000,000 H2O molecules ionizes into $H^{+}$ and $OH^{-}$, then:

$\frac{3.3x10^{25}H2Omolecules}{10^{7}}= 3.3x10^{18} H^{+}ions$

That number, $3.3x10^{18}$ just feels like it's disproportionately too many $H^{+}$

Are these calculations correct? Is it correct to divide 3.3E25/10E7 to find the number of H^{+} ions?

 

[Borek]

What you did looks OK to me, but the information about 1 out of 10⁷ molecules dissociating is not. Somebody got it wrong - concentration of H⁺ (and OH^-) in the neutral water at 25°C is 10^-7 M, that's not equivalent to 1 molecule in 10⁷ being dissociated.

 

[LearninDaMath]

This is where I saw that particular 1 out of 10E7 value:

I stopped watching about a minute into the video when she said 10^7 moles of H2O on one side of the equation and then on the other side of the equation she had 10^{-7) or something to that affect. I couldn't see how those numbers were calculated.

 

[Borek]

Not that difficult to check by yourself. Concentration of H⁺ is 10^-7 M which means in a liter of water 10^-7 moles of water dissociated. That's 10^-7*6.02*10²³=6.02*10¹⁶ molecules. There are 1000/18*6.02*10²³=3.34*10²⁵ molecules in 1 L of water - just divide these numbers to see one in how many dissociated.

 

[LearninDaMath]

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Thanks just did that. Got 1 out of every 5.58x10^{9} H2O molecules will dissociate into H^{+} and OH^{-}

I also did $\frac{55.5molH2O}{10^{-7}}= 5.5x10^{9}$

Since both values are the same, I take it that for the first result, I can say 1 molecule out of every 5.5E9 molecules is dissociate. And guess that for the second result, I can say 1 mol out of 5.5E9 moles will dissociate.

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If the above is correct, there is another aspect that is not making much sense.

There is this equation $10^{-14}M =10^{-7}M +10^{-7}M$. Does this mean that out of 1 Liter of H2O there will be 10^{-14} H2O molecules that dissociate into H and OH?

If so, is it correct to say that out of 55.5 moles of H2O, there will be $10^{14}moles$ which dissociate.

For some reason, it feels as though if $10^{-7}H$ and $10^{-7}OH$ are dissociated, then logically there can only be $10^{-7}$ original H2O molecules that could have dissociated.

What I think I mean is, if you have 10 H2O molecules, then you can only have 10 H and 10 OH molecules in total. If you split all 10 H2O molecules, you get 10 H and 10 OH. So,

10(H2O) →10(H) + 10(OH), Not 10(H2O) →5(H)+5(OH). So why then do we have:

$10^{-14}molH2O/L → 10^{-7}molH/L + 10^{-7}molOH/L$ instead of

$10^{-7}molH2O/L →10^{-7}molH/L + 10^{-7}molOH/L$ ?

 

[Borek]

Wrong again. It is not a sum:

$$K_w = [OH^-][H^+] = 10^{-14}$$

This is so called water ion product.

 

[JohnRC]

Wrong again. It is not a sum:

$$K_w = [OH^-][H^+] = 10^{-14}$$

This is so called water ion product.

In fact, the product should even have units -- 10^–14 M² -- which makes it even clearer that the two concentrations must be multiplied together