A solution is prepared by adding 4.50 mol of sodium hydroxide to 1.00 L of 1.00 M Co(NO₃)₂. What is the equilibrium concentration of cobalt ions? K_f = 5.0 *10⁹ for Co(OH)₄²¯ A) 1.1 * 10¯² M B) 1.4 * 10¯⁵ M C) 3.2 *10¯⁹ M D) 2.0* 10¯¹⁰ M E) 4.9* 10¯¹³ M

Question

Quizplus · Accepted Answer

First, let's write out the balanced chemical equation for the reaction between Co(NOS1U1B13S1U1B0)S1U1B12S1U1B0 and NaOH:

Co(NOS1U1B13S1U1B0)S1U1B12S1U1B0 + 2 NaOH → Co(OH)S1U1B14S1U1B0S1U1P12S1S1P0¯ + Na(NOS1U1B13S1U1B0)S1U1B12S1U1B0

We can use the equilibrium constant expression for this reaction to find the equilibrium concentration of Co2+ ions:

Kf = [Co(OH)S1U1B14S1U1B0S1U1P12S1S1P0¯]/[Co(NOS1U1B13S1U1B0)S1U1B12S1U1B0][OH¯]²

We are given the initial concentration and volume of Co(NOS1U1B13S1U1B0)S1U1B12S1U1B0, and we know that 4.50 moles of NaOH were added. The final volume of the solution will be 1.00 L + the volume of 4.50 moles of NaOH added. We can use this information to find the final concentration of OH¯ in the solution, which we can use to calculate the equilibrium concentration of Co2+ ions.

First, we need to find the final volume of the solution:

4.50 mol NaOH x (1 L/1 mol) = 4.50 L

Final volume = 1.00 L + 4.50 L = 5.50 L

Next, we can find the final concentration of OH¯ in the solution:

4.50 mol NaOH x (1 mol OH¯/1 mol NaOH) = 4.50 mol OH¯

[OH¯] = 4.50 mol / 5.50 L = 0.818 M

Now we can use the equilibrium constant expression to find the equilibrium concentration of Co2+ ions:

Kf = [Co(OH)S1U1B14S1U1B0S1U1P12S1S1P0¯]/[Co(NOS1U1B13S1U1B0)S1U1B12S1U1B0][OH¯]²

Kf = 5.0 F1F1F1S1F1F1F10 10S1U1P19S1S1P0

5.0 F1F1F1S1F1F1F10 10S1U1P19S1S1P0 = [Co2+]/(1.00 M)[0.818 M]²

[Co2+] = 3.17 F1F1F1S1F1F1F10 10¯S1U1P5S1S1P0 M ≈ 3.2 F1F1F1S1F1F1F10 10¯S1U1P5S1S1P0 M

Therefore, the equilibrium concentration of cobalt ions is approximately 3.2 F1F1F1S1F1F1F10 10¯S1U1P5S1S1P0 M. The best choice is C.

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