CHEMISTRY: What is the pH if 50.0 mL of 0.100 M HCN is mixed with 50.0 mL of 0.100 M NaOH?

Question

kittybasil · Answer

$$K_a\text{ for HCN }=1.00\times10^{-6}$$ I know this is wrong, but they are telling me to work with that value.

Logic007 · Answer

Logic007 · Answer

clas.sa.ucsb.edu/staff/Resource%20folder/Chem109ABC/Acid,%20Base%20Strength/Table%20of%20Acids%20w%20Kas%20and%20pKas.pdf

Vocaloid · Answer

In this case you have equal moles acid and base

So all of the weak acid gets converted to its conjugate base

Calculate the concentration of the weak base solution using stoichiometry (moles of weak base/total volume, make sure to add the volumes of weak acid and strong base)

Then use the Kb to find the pH

kittybasil · Answer

Thank you to both! @Logic007 that is a very useful resource :)

Michael · Answer

$\color{#0cbb34}{\text{Originally Posted by}}$ @Michael
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pH = 10.43

Start with the equation:

$$HCN+NaOH\rightarrow NaCN+H_2O$$

This tells us that 1 mole of HCN reacts with 1 mole NaOH

$$n_{HCN} = c\times v = 0.100\times\frac{50.0}{1000} =0.00500$$

$$n_{NaOH} = c\times v =0.100\times \frac{50.0}{1000} = 0.00500$$

From the equation you can see that the no. moles NaCN = 0.00500

The nitrile ion is the co-base of a weak acid and undergoes hydrolysis:

$$CN^{-} + H_2O\rightleftharpoons HCN + OH^{-}$$

$$K_b = 1.00\times10^{-6}$$

$$pK_{b} = -logK_{b} = -\log(10^{-6}) = 6$$

This means the residual solution is slightly alkaline and occurs when a weak acid is neutralised by a strong base.

From the equilibrium expression you can set up an ICE table and derive this expression for the pOH of a weak base of concentration "b":

$$pOH = \frac{1}{2} [pK_{b}-logb]$$

To find the concentration of the co - base we can say:

$$c_{CN^{-}} = \frac{n}{v} = \frac{0.00500}{0.100} = 0.0500\ \text{mol/l}$$

Note that the total volume = 50.0 ml + 50.0 ml = 0.100 L

$$pOH=\frac{1}{2}[6-\log(0.05)]$$

$$pOH = \frac{1}{2}[6-(-1.301)] = 3.565$$

$$pH + pOH = pK_{w} = 14$$

$$pH = 14 - pOH = 14 - 3.565 = 10.43$$

In reality the Kb value is much less so you would expect the pH to be a bit lower, I've gone with the value you have been given.
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kittybasil · Answer

... are you from Socratic? @Michael :P

Michael · Answer

I have answered questions on that site before but it is about to close down.