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Question
Citric acid (H3A) is a polyprotic acid with K1,K2, and K3 equals to 7.4×10−4,1.7×10−5, and 4.0×10−7, respectively. Calculate the [H⊕],[H2A⊝],[HA2−], and [A3−] in 0.01M citric acid.
Citric acid (H3A) is a polyprotic acid with K1,K2, and K3 equals to 7.4×10−4,1.7×10−5, and 4.0×10−7, respectively. Calculate the [H⊕],[H2A⊝],[HA2−], and [A3−] in 0.01M citric acid.
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Solution
The correct option is A [H⊕]=[H2A⊝]=2.4×10−3M,[HA2−]=1.7×10−5,[A3−]=2.8×10−9
i. H3A+H2O⇌H2A⊝+H3O⊕
K1=[H2A⊝][H3O⊕][H3A]=7.4×10−4
K1=x20.01−x=7.4×10−4
or, x2+(7.4×10−4)x−(7.4×10−6)=0
∴x=−7.4×10−4+√(7.4×10−4)2+4(7.4×10−6)2
=2.4×10−3M=[H3O⊕]=[H2A⊝]
ii. H2A⊝+H2O⇌HA2−+H3O⊕
K2=[HA2−][H3O⊕][H2A−]
1.7×10−5=[HA2−][y]y⟹[HA2−]=1.7×10−5M
iii. HA2−+H2O⇌A3−+H3O⊕
K3=[A3−][H3O⊕][HA2−]
4.0×10−7=[A3−](2.4×10−3)1.7×10−5⇒[A3−]=2.8×10−9M
Hence. option A is correct.
i. H3A+H2O⇌H2A⊝+H3O⊕
K1=[H2A⊝][H3O⊕][H3A]=7.4×10−4
K1=x20.01−x=7.4×10−4
or, x2+(7.4×10−4)x−(7.4×10−6)=0
∴x=−7.4×10−4+√(7.4×10−4)2+4(7.4×10−6)2
=2.4×10−3M=[H3O⊕]=[H2A⊝]
ii. H2A⊝+H2O⇌HA2−+H3O⊕
ii. H2A⊝+H2O⇌HA2−+H3O⊕
K2=[HA2−][H3O⊕][H2A−]
1.7×10−5=[HA2−][y]y⟹[HA2−]=1.7×10−5M
iii. HA2−+H2O⇌A3−+H3O⊕
iii. HA2−+H2O⇌A3−+H3O⊕
K3=[A3−][H3O⊕][HA2−]
4.0×10−7=[A3−](2.4×10−3)1.7×10−5⇒[A3−]=2.8×10−9M
Hence. option A is correct.
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