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Khouuu · Jun 10, 2009, 03:18 PM

In a titration of 100 mL 0.10M nitrous acid HNO2 against 0.10M sodium hydroxide, calculate the pH at the following stages:
K(a) for the nitrous acid = 4.5 x 10-4

a) before any base has been added to reach the acid solution.

b) after 25% of the base necessary to reach the equivalence point has been added.

c) at the equivalence point.

Perito · Jun 10, 2009, 08:21 PM

In a titration of 100 mL 0.10M nitrous acid HNO2 against 0.10M sodium hydroxide, calculate the pH at the following stages:
K(a) for the nitrous acid = 4.5 x 10-4

a) before any base has been added to reach the acid solution.

a. Calculate the concentration of H+

$HNO_2 \rightleftharpoons H^+ + NO_2^-$

Take the negative log of that concentration to find the pH.

0.1M HNO2. You immediately know the concentration.

$\frac {[H^+][NO_2^-]}{[HNO_2]}=4.5 \times 10^{-4}$ (Equation 1)

$\frac {x^2}{0.1-x}=4.5 \times 10^{-4}$ where x is the amount that's dissociated.

$x^2+4.5 \times 10^{-4}x - 4.5 \times 10^{-5}=0$

$x= \frac {-4.5 \times 10^{-4} \pm \sqrt {( 2.025 \times 10^{-9} + 1.8 \times 10^{-4} )}}{2} \approx \frac {-4.5 \times 10^{-4} \pm 1.34 \times 10^{-2}}{2}$

the negative root makes no chemical sense so

$x \approx 1.30 \times 10^{-2}$

x is both the hydrogen ion concentration and the nitrite ion concentration.

$pH = -log(1.30 \times 10^{-2}) \approx 1.89$

b) after 25% of the base necessary to reach the equivalence point has been added.

b. Add the base. Figure out the concentration of NO2 -- don't forget to add the volume of base that's added. Assume that the volumes add. Then, do the same calculation as in #1.

In a titration of 100 mL 0.10M nitrous acid HNO2 against 0.10M sodium hydroxide, calculate the pH at the following stages:
K(a) for the nitrous acid = 4.5 x 10-4

c) at the equivalence point.

c. Here the amount of acid equals the amount of base. You have only sodium nitrite (NaNO2). Nitrous acid is a weak acid:

$NO_2^- + H_2O \rightleftharpoons HNO_2 + OH^-$

This is really not all that different from Equation 1 since $[H^+][OH^-]=10^{-14}$

Figure out the concentration of Nitrite. Create an equation like I did in problem #1. In this case, the conc of HNO2 equals the conc of OH-

$\frac {(10^{-14} - [OH^-])[NO_2^-]}{[HNO_2]}=4.5 \times 10^{-4}$ (Equation 1b)

if C is the concentration of HNO2 before dissociation

$\frac {(10^{-14} - x)(C-x)}{x}=4.5 \times 10^{-4}$ (Equation 1b)

Solve for x and calculate the pH.