Which one is most ionic :

Solution :
TIPS/Formulae :
(i) Non metallic oxides are more covalent (or less ionic) as compared to metallic oxides.
(ii) Higher the polarising power of cation (higher for higher oxidation state of similar size cations) more will be covalent character.
(i) $${P_2}{O_5}$$  will be more covalent than other metallic oxides.
(ii) Oxidation state of $$Mn$$  is $$+7$$  in $$M{n_2}{O_7},$$  oxidation state of $$Cr$$  in $$Cr{O_3}$$  $$+6$$  and oxidation state of $$Mn$$  is $$+2$$  in $$MnO.$$
∴ $$MnO$$  is most ionic.
NOTE : $${P_2}{O_5},$$  being anon-metallic oxide will definitely be more covalent than the other metallic oxides. Further, we know that higher the polarising power of the cation ( higher for higher oxidation state of the similar size cations ) more will be the covalent character. Here $$Mn$$  is in $$+7\,O.S$$   in $$M{n_2}{O_7},Cr$$   in $$+6$$  in $$Cr{O_3}$$  and $$Mn$$  in $$+2$$  in $$MnO.$$  So $$MnO$$  is the most ionic and $$M{n_2}{O_7}$$  is the most covalent.