Finding amount of NaN02 needed to raise the a solution's pH to 5

[rokku]

What amount of sodium Nitrate must be added to 500 ml of .200 M solution of HN02. Ka=4.0^-4


Ka=(H+)(A-)
--------
(HA)



Ph of 5 = 1.0^-5 (H+) so, (1.0^-5)(x)
---------- = 4.0^-4 , however X turns out to be way too big
.200

 

[Borek]

Sorry, it is barely unreadable, try to use LaTeX to format the equation.

If I understand correctly what you did, your approach looks OK. Nothing strange in high amount of nitrate required - you want to get to pH which is 1.6 unit from the pKa, that requires around 10^1.6 more nitrate than there is nitrous acid.

 

[rokku]

Sorry about that, let me try again. Besides the obvious spacing issues I incorrectly mention Sodium Nitrate when it really should be Sodium Nitrite.

At first the pH of the undisturbed weak acid HN02 is around .69. I found it using a simple ICE table and the initial concentration HN02 (.200 Molar) plus the Ka (4.0^-4). When Sodium Nitrite is added, the salt completely dissociates and you end up with a common ion (NO2-) which would push the equilibrium to the left and result in less (H+) ions and a higher pH. Because we know what the desired pH is (5.00) we know that at equilibrium there should be the Antilog of 5, or 1.0^-5 M of H+. We also know that there has to be a new concentration of NO2- ions which is designated as X. Here is where I get stuck, what would the equilibrium concentration of HN02 be?

The formula to use would be Ka= (H+)(A-)/(HA)----> 4.0^-4=(1.0^-5)(X)/(equilibrium concentration of HN02?)

 

[Borek]

You can reasonably safely assume equilibrium concentration of HNO₂ to be 0.2. High excess of NO₂^- shifts the dissociation far to the left.

My approximate calculations show that you need around 8.5M of NaNO₂ (that ignoring ionic strength of the solution, which is pretty high).

 

[rokku]

You can reasonably safely assume equilibrium concentration of HNO₂ to be 0.2. High excess of NO₂^- shifts the dissociation far to the left.

If High excess of NO2- shifts the dissociation far to the left, wouldn't the equilibrium concentration of HNO2 be significantly larger than its initial of .200?

 

[Borek]

No, you don't have a source of H⁺ (other than water, but it is an acid many orders of magnitude weaker than HNO₂ itself).

 

[rokku]

Ah I see, thank you.