Answer
The addition of $1.25g$ $HBr$ would not exceed the buffer capacity.
Work Step by Step
1. Calculate the molar mass $(HBr)$:
1.01* 1 + 79.9* 1 = 80.91g/mol
2. Calculate the number of moles $(HBr)$
$n(moles) = \frac{mass(g)}{mm(g/mol)}$
$n(moles) = \frac{1.25}{ 80.91}$
$n(moles) = 0.0154$
3. Find the concentration in mol/L $(HBr)$:
$C(mol/L) = \frac{n(moles)}{volume(L)}$
$ C(mol/L) = \frac{ 0.0154}{ 0.5} $
$C(mol/L) = 0.0309$
4. Drawing the ICE table we get these concentrations at the equilibrium:
$HNO_2(aq) + H_2O(l) \lt -- \gt N{O_2}^-(aq) + H_3O^+(aq)$
Remember: Reactants at equilibrium = Initial Concentration - x
And Products = Initial Concentration + x
$[HNO_2] = 0.1 M - x$
$[N{O_2}^-] = 0.15M + x$
$[H_3O^+] = 0 + x$
5. Calculate 'x' using the $K_a$ expression.
$ 4.6\times 10^{- 4} = \frac{[N{O_2}^-][H_3O^+]}{[HNO_2]}$
$ 4.6\times 10^{- 4} = \frac{( 0.15 + x )* x}{ 0.1 - x}$
Considering 'x' has a very small value.
$ 4.6\times 10^{- 4} = \frac{ 0.15 * x}{ 0.1}$
$ 4.6\times 10^{- 4} = 1.5x$
$\frac{ 4.6\times 10^{- 4}}{ 1.5} = x$
$x = 3.07\times 10^{- 4}$
Percent dissociation: $\frac{ 3.07\times 10^{- 4}}{ 0.1} \times 100\% = 0.307\%$
x = $[H_3O^+]$
6. Calculate the pH Value
$pH = -log[H_3O^+]$
$pH = -log( 3.07 \times 10^{- 4})$
$pH = 3.513$
7. Since we are adding a strong acid, this reaction will occur:
$N{O_2}^-(aq) + H_3O^+(aq) -- \gt HNO_2(aq) + H_2O(l)$
And these are the concentrations after this reaction:
Remember: Reactants at equilibrium = Initial Concentration - y
And Products = Initial Concentration + y
Since $HBr$ is a strong base, y = $[HBr] = 0.0309M$
$[HNO_2] = 0.1 M + 0.0309 = 0.131M$
$[N{O_2}^-] = 0.15M - 0.0309 = 0.119M$
8. Now, calculate the hydronium ion concentration after the addition of the $HBr$:
$[H_3O^+] = Ka * (\frac{[HNO_2]}{[N{O_2}^-]})$
$[H_3O^+] = 4.7 \times 10^{-4} * \frac{0.131}{0.119}$
$[H_3O^+] = 4.7 \times 10^{-4} * 1.1$
$[H_3O^+] = 5.06 \times 10^{-4}$
9. Calculate the pH Value
$pH = -log[H_3O^+]$
$pH = -log( 5.06 \times 10^{- 4})$
$pH = 3.296$
10. Calculate the pH difference:
$3.513 - 3.296 = 0.217$
Since it is smaller than 1, we consider that, it did not exceed the buffer capacity.
