№1
\[
\mathrm{MnO_2+4HBr\rightarrow MnBr_2+Br_2+2H_2O}
\]
№2
\[
\mathrm{Na_2CO_3+H_2SO_4\rightarrow Na_2SO_4+CO_2\uparrow+H_2O}
\]
\[
\mathrm{Na_2SO_4+BaCl_2\rightarrow BaSO_4\downarrow+2NaCl}
\]
№3
\[
m(\mathrm{Fe(NO_3)_3})=403{,}33\cdot0{,}4=161{,}332\text{ г}
\]
\[
n=\frac{161{,}332}{242}\approx0{,}667\text{ моль}
\]
\[
\mathrm{2Fe(NO_3)_3+3Ba(OH)_2\rightarrow2Fe(OH)_3\downarrow+3Ba(NO_3)_2}
\]
\[
m(\mathrm{Fe(OH)_3})=0{,}667\cdot107\approx\boxed{71{,}33\text{ г}}
\]
№4
\[
\mathrm{2Fe^{3+}+6H_2O\rightleftharpoons2Fe(OH)_3\downarrow+6H^+}
\]
