91影视

The four equilibrium reactions are given by: \(1): \mathrm{Be}^{2+}(a q)+\mathrm{F}^{-}(a q) \rightleftharpoons \mathrm{BeF}^{+}(a q) \quad K_{1}=7.9 \times 10^{4}\) \(2): \mathrm{BeF}^{+}(a q)+\mathrm{F}^{-}(a q) \rightleftharpoons \mathrm{BeF}_{2}(a q) \quad K_{2}=5.8 \times 10^{3}\) \(3): \operatorname{BeF}_{2}(a q)+\mathrm{F}^{-}(a q) \rightleftharpoons \mathrm{BeF}_{3}^{-}(a q) \quad K_{3}=6.1 \times 10^{2}\) \(4): \mathrm{BeF}_{3}^{-}(a q)+\mathrm{F}^{-}(a q) \rightleftharpoons \mathrm{BeF}_{4}^{2-}(a q) \quad K_{4}=2.7 \times 10^{1}\)

We are given the initial concentrations of Be(NO3)鈧� (1.0 x 10鈦烩伌 M) and NaF (8.0 M). Therefore, the initial concentrations of Be虏鈦� and F鈦� are: [Be虏鈦篯鈧� = 1.0 x 10鈦烩伌 M [F鈦籡鈧� = 8.0 M Since the solution volume doubles, the concentrations will be halved: [Be虏鈦篯鈧� = 0.5 x 10鈦烩伌 M [F鈦籡鈧� = 4.0 M

Since the equilibria occur sequentially, the concentration of the successive anions will be lower than the previous anion. Let [F鈦籡 = [F鈦籡鈧� - x - 2y - 3z, where x, y, z are the concentrations of BeF鈦�, BeF鈧�, and BeF鈧冣伝, respectively. The concentration of Be虏鈦�, BeF鈦�, BeF鈧�, BeF鈧冣伝 and BeF鈧劼测伝 decrease successively and we can approximate: \[x << y, y << z, z << [F鈦籡\] Using the approximation, we can find x, y, and z from the equilibrium constants: \(K_{1} = \frac{[BeF^{+}][F^{-}]}{[Be^{2+}]} = \frac{x(4 - x)}{0.5\times10^{-4}}\) \(K_{2} = \frac{[BeF_{2}][F^{-}]}{[BeF^{+}]} = \frac{y(4 - x)}{x}\) \(K_{3} = \frac{[BeF_{3}^{-}][F^{-}]}{[BeF_{2}]} = \frac{z(4 - x)}{y}\) From equation (1): x 鈮� \(\frac{0.5\times10^{-4} \times K_1}{4}\) From equation (2): y 鈮� \(\frac{x \times K_2}{4}\) From equation (3): z 鈮� \(\frac{y \times K_3}{4}\) Now calculate x, y, and z: x 鈮� 9.875 x 10鈦烩伓 M y 鈮� 8.415 x 10鈦烩伖 M z 鈮� 3.212 x 10鈦宦孤� M The equilibrium concentrations of each species are as follows: [F鈦籡 鈮� 4.0 M - x - 2y - 3z 鈮� 3.99987 M [Be虏鈦篯 鈮� 0 - x 鈮� 0.5 x 10鈦烩伌 M - 9.875 x 10鈦烩伓 M 鈮� 0.490125 x 10鈦烩伌 M [BeF鈦篯 鈮� x 鈮� 9.875 x 10鈦烩伓 M [BeF鈧俔 鈮� y 鈮� 8.415 x 10鈦烩伖 M [BeF鈧冣伝] 鈮� z 鈮� 3.212 x 10鈦宦孤� M [BeF鈧劼测伝] 鈮� K_4 脳 z 鈮� 8.673 x 10鈦宦孤� M These are the equilibrium concentrations of the species in the solution.