The determination of 4.000 mmol of ZnCl2 is performed gravimetrically by the addition of NaCN solution in a Total volume of 200.00ml. Ksp = 3.0X10^-16 for Zn(CN)2. State and verify all assumption. Assume cyanide does not hydrolyze.
a. Derive the COC and COM equations for the solubility of Zn(CN)2.
b. Using the eqution your derive in part (a) calculate the mass loss of Zn(CN)2 if a 10% excess of NaCN is used taking activity into account. Is the mass Loss significant?
To solve this problem, we will follow these steps:
a. Deriving the COC and COM equations for the solubility of Zn(CN)2:
1. The COC (concentration of ions multiplied by their coefficients) equation for the reaction is:
ZnCl2 (s) ↔ Zn²⁺ (aq) + 2Cl⁻ (aq)
2. The COM (solubility product constant) equation for the formation of Zn(CN)2 (s) is:
Zn²⁺ (aq) + 2CN⁻ (aq) ↔ Zn(CN)2 (s)
b. Calculating the mass loss of Zn(CN)2:
1. Considering a 10% excess of NaCN, we assume that there is an excess of CN⁻ ions in the solution. So, the total concentration of CN⁻ ions will be the sum of original CN⁻ concentration plus 10% of that concentration.
2. The initial concentration of CN⁻ ions can be calculated using the equation:
C1 = n1 / V
where C1 is the initial concentration, n1 is the moles of CN⁻ ions, and V is the volume in liters.
3. Since NaCN is a salt, it dissociates completely in water, so the initial concentration of CN⁻ ions will be equal to the initial concentration of NaCN.
4. The initial concentration of NaCN is calculated using:
C1 = n1 / V
where C1 is the initial concentration, n1 is the moles of NaCN, and V is the volume in liters. Since the question did not provide the concentration or volume of NaCN solution, we will assume the concentration is 1 mol/L.
5. The moles of NaCN can be calculated using the equation:
n1 = C1 * V
where C1 is the initial concentration of NaCN and V is the volume of NaCN solution.
6. The moles of CN⁻ ions will be equal to the moles of NaCN since NaCN dissociates to one CN⁻ ion.
7. The new concentration of CN⁻ ions will be 1.1 times the initial concentration of CN⁻ ions.
8. To calculate the mass loss of Zn(CN)2, we will use the COM equation. Assuming the solubility of Zn(CN)2 is "s", the initial concentration of Zn²⁺ ions can be expressed as "s" and the concentration of CN⁻ ions will be 2s (according to the balanced equation of COM).
9. The new concentration of Zn²⁺ ions can be calculated using:
C2 = C1 - 2s
where C2 is the new concentration of Zn²⁺ ions, C1 is the initial concentration of Zn²⁺ ions, and s is the solubility of Zn(CN)2.
10. The mass loss of Zn(CN)2 can be calculated using the equation:
mass loss = (C1 - C2) * V * molar mass
where C1 is the initial concentration of Zn²⁺ ions, C2 is the new concentration of Zn²⁺ ions, V is the volume in liters, and molar mass is the molar mass of Zn(CN)2.
11. Compare the calculated mass loss to determine if it is significant. You can consider a mass loss significant if it is within a certain percentage threshold of the original mass of Zn(CN)2.
It's important to note that in this explanation, we made assumptions based on the information given in the question. Please cross-check the information and calculations with the actual values provided in your problem.