To rank the acids according to their acid strength, we need to compare their equilibrium constants (Ka values). The acid with the smallest Ka value is the weakest acid (it dissociates the least in solution), while the acid with the largest Ka value is the strongest acid (it dissociates the most in solution).
Here are the given acids and their Ka values:
1. [tex]\( C_6H_5OH \)[/tex]: [tex]\[ K_{a} = 1.3 \times 10^{-10} \][/tex]
2. [tex]\( HCO_2H \)[/tex]: [tex]\[ K_{a} = 1.8 \times 10^{-4} \][/tex]
3. [tex]\( HC_2O_4^- \)[/tex]: [tex]\[ K_{a} = 6.4 \times 10^{-5} \][/tex]
Let's compare these values:
- [tex]\( 1.3 \times 10^{-10} \)[/tex] (for [tex]\( C_6H_5OH \)[/tex]) is the smallest value.
- [tex]\( 6.4 \times 10^{-5} \)[/tex] (for [tex]\( HC_2O_4^- \)[/tex]) is larger than [tex]\( 1.3 \times 10^{-10} \)[/tex] but smaller than [tex]\( 1.8 \times 10^{-4} \)[/tex].
- [tex]\( 1.8 \times 10^{-4} \)[/tex] (for [tex]\( HCO_2H \)[/tex]) is the largest value.
Therefore, the ranking from weakest to strongest acid based on the Ka values is:
[tex]\[ C_6H_5OH < HC_2O_4 < HCO_2H \][/tex]
So the order from weakest to strongest acid is:
[tex]\[ C _6 H _5 OH, \, HC _2 O _4, \, HCO _2 H \][/tex]
