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Explanation & Answer
First find the molarity of the salt:
1 NaOH & 1 HNO2 --> 1 NaNO2 & H2O
0.05 litres @ 0.25mol / litre HNO2 = 0.2 moles of HNO2
0.2 moles of HNO2 needs 0.2 moles of NaOH
0.2 moles of NaOH @ 1mol/litre = 0.2 litres of NaOH
your NaNO2 : 0.2 mol / 0.25 litres = 0.8 Molar
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the (NO2)- ion from the weak acid will do a hydrolysis with water, producing a basic solution :
NO2- in water --> HNO2 & OH-
the K hydrolysis = K water / K acid = 1e-14 / 5.1e-4 = 1.96e-11
1.96e-11 = [HNO2] [OH-] / [NO2-]
1.96e-11 = [x] [x] / [0.8]
x2 = 1.568e-11
x = [OH-] = 3.98e-6
pOH = 5.4
pH = 14 - pOH = 8.6
your answer: = 8.6
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