pH of acids, bases and salts

Exercise 22

    

Vanadium chloride (III) is a salt having brilliants purple crystals but hygroscopic. Its aqueous solution is green in an acid medium. At what value should we adjust the $pH$ to be sure to get there 4 times more hexaquavanadium(III) than hydroxopentaquavanadium(III)

$V(H_2O)_6^{3+} $: weak acid $\frac{[V(H_2O)_6^{3+}]}{[V(H_2O)_5OH^{2+}]}\gt 4$ $\frac{[V(H_2O)_6^{3+}]}{[V(H_2O)_5OH^{2+}]}$ $=$ $\frac{[H_3O^+]}{K_a}$ so: $[H_3O^+]\gt 4K_a$ $-log[H_3O^+]$ $\lt$ $-$ $logK_a$ $-$ $log4$ $pH\lt pK_a$ $-$ $log4$ $pH\lt 2.32$