Answer:
kb = 2,0x10⁻⁵
Explanation:
The ka for HCN is:
HCN ⇄ H⁺ + CN⁻; ka = 4,9x10⁻¹⁰ <em>(1)</em>
The inverse reaction has an equilibrium constant of:
H⁺ + CN⁻ ⇄ HCN k = 1/4,9x10⁻¹⁰ = 2,0x10⁹ <em>(2)</em>
As the equilibrium of the water is:
H₂O ⇄ H⁺ + OH⁻; kw = 1x10⁻¹⁴ <em>(3)</em>
The sum of (2) + (3) gives:
H₂O + CN⁻ ⇄ HCN + OH⁻; kb = kw×k = 1x10⁻¹⁴×2,0x10⁹ =
2,0x10⁻⁶; <em>kb = 2,0x10⁻⁵</em>
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<em>-In fact, the general formula to convert from ka to kb is:</em>
<em>kb = kw / ka-</em>
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I hope it helps!