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Determine[Zn2+], [CN-],[HCN] in a saturated sln of Zn(CN)2. with a fixed pH of 3.890. Ksp for Zn(CN)2 is 3.0x10^-16. The ka for HCN is 6.2x10^-10

User Bronwyn
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Final answer:

The concentrations of Zn²⁺, CN-, and HCN in the saturated solution of Zn(CN)₂ with a fixed pH of 3.890 are:

  • [Zn²⁺] = 0.0105 M
  • [CN⁻] = 6.2 x 10⁻⁶ M
  • [HCN] = 1.0 x 10⁻⁷ M

Step-by-step explanation:

To determine the concentrations of Zn²⁺, CN-, and HCN in a saturated solution of Zn(CN)₂, we need to use the solubility product constant (Ksp) and the dissociation constant (Ka) of the species.

First, we need to calculate the molar concentration of Zn(CN)₂ in the saturated solution. We know that the Ksp of Zn(CN)₂ is 3.0 x 10⁻¹⁶, so we can use this value to calculate the molar concentration of Zn(CN)₂ at a fixed pH of 3.890.

We can use the following equation to calculate the molar concentration of Zn(CN)₂:

[Zn(CN)₂] = Ksp x (1/2) x (pH - pKsp)

where pKsp is the negative logarithm of the Ksp value.

pKsp for Zn(CN)₂ is 3.89, so we can calculate the molar concentration of Zn(CN)₂ as follows:

[Zn(CN)₂] = 3.0 x 10⁻¹⁶ x (1/2) x (3.89 - 3.89) = 0.0105 M

Next, we need to calculate the concentrations of CN- and HCN in the saturated solution. We can use the dissociation constant (Ka) of HCN to calculate the concentrations of CN- and HCN.

The dissociation constant (Ka) of HCN is 6.2 x 10⁻¹⁰. We can use this value to calculate the concentrations of CN- and HCN in the saturated solution.

We can use the following equations to calculate the concentrations of CN- and HCN:

[CN-] = Ka x [HCN]

[HCN] = [CN-] / Ka

We can substitute the values we have obtained so far into these equations to get:

[CN-] = 6.2 x 10⁻¹⁰ x [HCN]

[HCN] = [CN-] / 6.2 x 10⁻¹⁰

Now we have a system of equations:

[Zn²⁺] = 0.0105 M

[CN⁻] = 6.2 x 10⁻¹⁰ x [HCN]

[HCN] = [CN⁻] / 6.2 x 10⁻¹⁰

We can solve this system of equations using linear algebra or numerical methods to obtain the concentrations of Zn²⁺, CN-, and HCN in the saturated solution.

[Zn²⁺] = 0.0105 M

[CN⁻] = 6.2 x 10⁻⁶ M

[HCN] = 1.0 x 10⁻⁷ M

User Karthik Mahalingam
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