Question

Calculate the pH for a 0.100 M Na₂CO₃ solution with a K_b1 of 2.1 x 10^-4 and a K_b2 of 2.2 x 10^-8

Answer 1

Answer о 1st: .O Construct two ICE table to calculate pH. co + H₂O HO + OH I (M): 0.1 C(M): –x +x +x E(M): 0.1-x [H205] [OH-] - - Kbi [co} ] (species under third bracket represent equilibrium concentration R X2 0.1-x = 2.1x104 or, x²+ (2.1x104)x - (2.1x10s) = 0 (2x1) - (2-1x104)+(2-4*109)2+(4x1x 2.1x105) x = - (ax² + bx + c = 0 => x= - b ± 1 6-9ac ; xxo ) [HCO3] = [OH-] = x= 4.479 × 103 M. 2a

2nd: Н0, + H20 I(M): (4.479x173) H, Co, tон" 0 (4-479x103) tx tx (4.479x109) + x C(M): x ECM): (4.479x103)-x X .: [H2603] [OH-] ] =k62 [HCO3 à x [(4-479x103)+x] = (2.2x108) (1.479x103) - X M a, x'+ (40479x103)x - (9.854810") - (2-2x178)x a x? +(4-479 x103)2 - (9.854x 10") = 0 .. x2 -(4.479x103) +14.479x103)2+(4*1*9.859x16") (2x1) - 2.2008 108m [OH] = (4.479x109) +8 M = (4:479x102)+(2-200x103M = (4.479 x103) M (Asige fiso) .. pH = 14-POH = 14+ log [OH-] = 18+ rog (4.479x103) = 11.7