the reaction Pb(OH)2 + HNO3 ---> Pb(OH)NO3 + H2O shows that Pb(OH)NO3 is :

a) acid salt b) basic salt c) a base d) an acid

base

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basic salt.

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And why?

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It is an acidic salt because Pb(OH)2 is a weak base and HNO3 being a strong acid .Simple presence of Hydroxyl group doesn't indicate basic character.eg.CH3COOH
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yes
 
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A basic salt
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the reaction Pb(OH)2 + HNO3 ---> Pb(OH)NO3 + H2O shows that Pb(OH)NO3 is a neutralization reaction
Pb(OH)2 is basic 
HNO3  is an acid
Pb(OH)NO3  is a basic salt as the combination of a strong base[Pb(OH)2] and a weak acid[HNO3] forms a basic salt[Pb(OH)NO3]
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