A solution of Na2CO3 is added dropwise to a solution that contains 1.34×10−2M Fe^2+ and 1.33×10−2M Cd^2+ . What CO3^2- concentration of is need to initiate precipitation? Neglect any volume changes during the addition.
Look up Ksp for FeCO3.
Look up Ksp for CdCO3.
Write Ksp expression for FeCO3.
Write Ksp expression for CdCO3.
Solve FeCO3 expression for CO3^-2 using iron(II) given.
Solve CdCO3 expression for CO3^-2 using Cd^+2 given.
The smallest concn calculated will be the minimum concn of CO3^-2 needed to start pptn. Check my work.
To determine the CO3^2- concentration needed to initiate precipitation, we need to find the concentration of CO3^2- ions at which the solubility product (Ksp) of the solid precipitate is exceeded.
First, we need to write out the balanced chemical equation for the reaction between Na2CO3 and Fe^2+ and Cd^2+ ions:
Na2CO3 + Fe^2+ -> FeCO3 + 2Na+
Na2CO3 + Cd^2+ -> CdCO3 + 2Na+
Since FeCO3 and CdCO3 are both insoluble, they will precipitate out of solution when their product concentrations exceed their respective solubility products.
The solubility product (Ksp) expression for FeCO3 is:
Ksp = [Fe^2+][CO3^2-]
Let's assume x represents the concentration of CO3^2- ions that will react to form the FeCO3 precipitate.
At equilibrium, the concentration of Fe^2+ ions will be (1.34×10^-2 - x) M, and the concentration of Cd^2+ ions will be (1.33×10^-2 - x) M.
Since FeCO3 and CdCO3 are both formed from the reaction of Na2CO3 and CO3^2- ions, the concentration of CO3^2- ions will be 2x.
Now, let's substitute the given concentrations and the assumed concentration of CO3^2- ions into the Ksp expression:
Ksp = (1.34×10^-2 - x)(2x)
Ksp = 2.68×10^-2x - 2x^2
To find the CO3^2- concentration needed to initiate precipitation, we set the Ksp expression equal to the Ksp value of FeCO3:
2.68×10^-2x - 2x^2 = Ksp of FeCO3
The Ksp value for FeCO3 is usually very small, so we can neglect the x^2 term when compared to the x term. This simplifies the equation:
2.68×10^-2x ≈ Ksp of FeCO3
By substituting the Ksp value for FeCO3, we can solve for x:
2.68×10^-2x ≈ [Fe^2+][CO3^2-] = Ksp of FeCO3 = [Fe^2+][CO3^2-]
Plugging in the Fe^2+ concentration (1.34×10^-2 M), we have:
2.68×10^-2x ≈ (1.34×10^-2)(1.34×10^-2) = 1.7952×10^-4
Now, divide both sides of the equation by 2.68×10^-2:
x ≈ (1.7952×10^-4) / (2.68×10^-2)
x ≈ 6.70×10^-3 M
Therefore, a CO3^2- concentration of approximately 6.70×10^-3 M is needed to initiate precipitation.
To determine the CO3^2- concentration needed to initiate precipitation, we need to identify the ion that forms an insoluble precipitate with CO3^2-. In this case, we know that Na2CO3 is added dropwise to a solution containing Fe^2+ and Cd^2+ ions.
First, let's consider the solubility rules to identify which ion forms an insoluble precipitate with CO3^2-. According to the rules:
1. Most carbonates (CO3^2-) are insoluble, except for alkali metal carbonates (e.g., Na2CO3) and ammonium carbonate (NH4)2CO3.
2. Most hydroxides (OH^-) are insoluble, except for alkali metals (e.g., NaOH) and barium hydroxide (Ba(OH)2).
Based on these rules, it is clear that both Fe^2+ and Cd^2+ ions can potentially form insoluble precipitates with CO3^2-. Hence, we need to compare the solubility product constants (Ksp) of their respective carbonates to determine which one is less soluble.
The Ksp expression for the formation of a precipitate is given by:
Ksp = [M+][CO3^2-]
The solubility product constant for FeCO3 is approximately 4.87 × 10^-11, and for CdCO3, it is approximately 7.4 × 10^-12.
Comparing the two Ksp values, we can see that FeCO3 (4.87 × 10^-11) has a smaller Ksp compared to CdCO3 (7.4 × 10^-12). This implies that FeCO3 is less soluble than CdCO3 and thus would precipitate first when the concentration of CO3^2- ions exceeds a certain threshold.
Therefore, to initiate precipitation of FeCO3, we need to determine the concentration of CO3^2- ions at which the Ksp of FeCO3 is reached. The Ksp expression can be rearranged as follows:
Ksp = [Fe^2+][CO3^2-] = 4.87 × 10^-11
Using the given concentration of Fe^2+ (1.34 × 10^-2 M), we can rearrange the equation to find the CO3^2- concentration:
[CO3^2-] = Ksp / [Fe^2+]
[CO3^2-] = (4.87 × 10^-11) / (1.34 × 10^-2)
[CO3^2-] ≈ 3.64 × 10^-9 M
Therefore, a CO3^2- concentration of approximately 3.64 × 10^-9 M is needed to initiate the precipitation of FeCO3 in this solution.