a.
HC2O\(_4^-\) ⇌ H+ + C2O\(_4^{2-}\)
\[K_\mathrm{a, HC_2O_4^-} = \frac {\mathrm{[H^+][C_2O_4^{2-}]}}{\mathrm{[HC_2O_4^-}]}\]
|
| [HC2O\(_4^-\)] | [H+] | [C2O\(_4^{2-}\)] |
|
| f.r. | \[0,100\] | \[0\] | \[0\] | M |
| ∆ | \[-x\] | \[+x\] | \[+x\] | M |
| v.j. | \[0,100-x\] | \[x\] | \[x\] | M |
\[5,1 \cdot 10^{-5} = \frac {x \cdot x}{0,100 - x}\]
\(pq\)-formeln ger:
\[\begin{aligned}x &= 0,00223296 = \mathrm{[H^+]} \\ \mathrm{pH} &= -\lg[\mathrm{H^+}] = -\lg 0,00223296 = 2,65111906 ≈ 2,65\end{aligned}\]
b.
HSO\(_4^-\) ⇌ H+ + SO\(_4^-\)
\[K_\mathrm{a, HSO_4^-} = \frac {\mathrm{[H^+][SO_4^{2-}]}}{\mathrm{[HSO_4^-]}}\]
|
| [HSO\(_4^-\)] | [H+] | [SO\(_4^-\)] |
|
| f.r. | \[0,100\] | \[0\] | \[0\] | M |
| ∆ | \[-x\] | \[+x\] | \[+x\] | M |
| v.j. | \[0,100-x\] | \[x\] | \[x\] | M |
\[\begin{aligned}K_\mathrm{a, HSO_4^-} &= 10^{-\mathrm{p}K_\mathrm{a, HSO_4^-}}\mathrm{M} = 10^{-2,00}\mathrm{M} \\ 10^{-2,00} &= \frac {x \cdot x}{0,100 - x}\end{aligned}\]
\(pq\)-formeln ger:
\[\begin{aligned}x &= 0,0270156 = \mathrm{[H^+]} \\ \mathrm{pH} &= -\lg[\mathrm{H^+}] = -\lg 0,0270156 = 1,56838538 ≈ 1,57\end{aligned}\]
c.
Al(H2O)\(_6^{3+}\) ⇌ H+ + Al(OH)(H2O)\(_5^{2+}\)
\[K_\mathrm{a, Al(H_2O)_6^{3+}} = \frac {\mathrm{[H^+][Al(OH)(H_2O)_6^{2+}]}}{[\mathrm{Al(H_2O)_6^{3+}}]}\]
|
| [Al(H2O)\(_6^{3+}\)] | [H+] | [Al(OH)(H2O)\(_5^{2+}\)] |
|
| f.r. | \[0,100\] | \[0\] | \[0\] | M |
| ∆ | \[-x\] | \[+x\] | \[+x\] | M |
| v.j. | \[0,100-x\] | \[x\] | \[x\] | M |
\[\begin{aligned}K_\mathrm{a, Al(H_2O)_6^{3+}} &= 10^{-\mathrm{p}K_\mathrm{a, Al(H_2O)_6^{3+}}}\mathrm{M} = 10^{-5,00}\mathrm{M} \\ 10^{-5,00} &= \frac {x \cdot x}{0,100 - x} ≈ \frac {x^2}{0,100} \\ 10^{-5,00} \cdot 0,100 &= x^2 \\ x &= \sqrt{10^{-5,00} \cdot 0,100} = 0,001 = \mathrm{[H^+]} \\ \mathrm{pH} &= -\lg [\mathrm{H^+}] = -\lg 0,001 = 3,00\end{aligned}\]
