Verified Solution • 2025–26 Session moderate

QJEEM25Cha3dd: JEE Main 2025 Chemistry - Class 11 JEEM25Cha3dd Solution: If 1 mM solution of ethylamine produces , then the ionization…

If 1 mM solution of ethylamine produces pH=9\mathrm{pH}=9 , then the ionization constant (Kb)\left(\mathrm{K}_{\mathrm{b}}\right) of ethylamine is 10−x10^{-x} . The value of xx is _________ (nearest integer).

[The degree of ionization of ethylamine can be neglected with respect to unity.]

Step-by-Step Verified Solution

C2H5NH2(aq)+H2O⇌C2H2NH3++O⊖H\mathrm{C}_2 \mathrm{H}_5 \mathrm{NH}_2(\mathrm{aq})+\mathrm{H}_2 \mathrm{O} \rightleftharpoons \mathrm{C}_2 \mathrm{H}_2 \mathrm{NH}_3^{+}+\stackrel{\ominus}{\mathrm{O}} \mathrm{H}

C=10−3M−−C(1−α)CαCα⇒C=10−3=10−5=10−5

1−α≃11-\alpha \simeq 1

Given, PH=9⇒POH=5⇒[O⊖H]=10−5M\mathrm{P}^{\mathrm{H}}=9 \Rightarrow \mathrm{P}^{\mathrm{OH}}=5 \Rightarrow[\stackrel{\ominus}{\mathrm{O}} \mathrm{H}]=10^{-5} \mathrm{M}

Now, Kb=[C2H5NH3+][O⊖H][C2H5NH2]K_b=\frac{\left[\mathrm{C}_2 \mathrm{H}_5 \mathrm{NH}_3^{+}\right][\stackrel{\ominus}{\mathrm{O}} \mathrm{H}]}{\left[\mathrm{C}_2 \mathrm{H}_5 \mathrm{NH}_2\right]}

⇒Kb=10−5×10−510−3=10−7

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