(a) When ammonium hydroxide (NH4OH) is added to zinc nitrate solution [Zn(NO3)2], a gelatinous white ppt of zinc hydroxide [Zn(OH)2] is obtained which is soluble in excess of NH4OH.
(With excess NH4OH ppt. dissolves)
On the other hand, calcium nitrate solution [Ca(NO3)2] does not give any ppt. even when excess of ammonium hydroxide is added.
(b) When dil. sulphuric acid is added to sodium carbonate and heated, colourless, odourless gas is evolved which turns lime water milky and has no effect on KMnO4 or K2Cr2O7 solutions.
Na2CO3 + 2HCl ⟶ 2NaCl + H2O + CO2 ↑
When dil. sulphuric acid is added to sodium sulphite and heated, colourless gas with suffocating odour is evolved which turns lime water milky. It turns acidified K2Cr2O7 from orange to clear green and pink coloured KMnO4 to clear colourless.
Na2SO3 + 2HCl ⟶ 2NaCl + H2O + SO2 ↑
Hence, the two compounds can be distinguished.