Question

EDTA^-4 binds metal ions to form complexes, thus can be used to determine concentrations of metal ions. Calculate the concentration of [Co^2+] in solution after the addition of 48.0mL of 0.05M EDTA4- to a 50mL sample of 0.048M [Co2+].
Co^2+ + EDTA^4- -----> [Co(EDTA)]^2-
Kf= 2.04x10^16

Answer 1

Answer on Question #66937, Chemistry - General Chemistry

EDTA⁴- binds metal ions to form complexes, thus can be used to determine concentrations of metal ions. Calculate the concentration of [Co²⁺] in solution after the addition of 48.0mL of 0.05M EDTA⁴- to a 50mL sample of 0.048M [Co²⁺].

$$\mathrm{K_f} = 2.04 \times 10^{16}$$

Solution:

1. $c(\mathrm{Co}^{2+}) = [\mathrm{Co}^{2+}] + [[\mathrm{Co}(EDTA)]^{2-}] = \frac{50 \times 0.048}{98} = 2.45 \times 10^{-2} \, \mathrm{M}$

2. $c(\mathrm{EDTA}^{4-}) = [\mathrm{EDTA}^{4-}] + [[\mathrm{Co}(EDTA)]^{2-}] = \frac{48 \times 0.05}{98} = 2.45 \times 10^{-2} \, \mathrm{M}$

3. $[[\mathrm{Co}(EDTA)]^{2-}] = c(\mathrm{Co}^{2+}) - [\mathrm{Co}^{2+}]$

4. $[EDTA^{4-}] = c(EDTA^{4-}) - [[\mathrm{Co}(EDTA)]^{2-}] = c(EDTA^{4-}) - c(\mathrm{Co}^{2+}) + [\mathrm{Co}^{2+}] = 2.45 \times 10^{-2} - 2.45 \times 10^{-2} + [\mathrm{Co}^{2+}] = [\mathrm{Co}^{2+}]$

5. $K_f = \frac{[[\mathrm{Co}(EDTA)]^{2-}]}{[\mathrm{Co}^{2+}] \times [EDTA^{4-}]}$

$$2.04 \times 10^{16} = \frac{[[\mathrm{Co}(EDTA)]^{2-}]}{[\mathrm{Co}^{2+}] \times [EDTA^{4-}]} = \frac{2.45 \times 10^{-2} - [\mathrm{Co}^{2+}]}{[\mathrm{Co}^{2+}] \times [\mathrm{Co}^{2+}]}$$ $$\begin{array}{l} 2.04 \times 10^{16} = \frac{2.45 \times 10^{-2}}{[\mathrm{Co}^{2+}] \times [\mathrm{Co}^{2+}]} = \frac{2.45 \times 10^{-2}}{[\mathrm{Co}^{2+}]^2} \Rightarrow [\mathrm{Co}^{2+}]^2 \\ = \frac{2.45 \times 10^{-2}}{2.04 \times 10^{16}} \\ [\mathrm{Co}^{2+}]^2 = 1.2 \times 10^{-18} \\ [\mathrm{Co}^{2+}] = 1.1 \times 10^{-9} \, \mathrm{M} \\ \end{array}$$

Answer: the concentration of $[\mathrm{Co}^{2+}]$ in solution is $1.1 \times 10^{-9} \, \mathrm{M}$.

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