Respuesta :
Answer:
For a: The ionic strength of lead sulfate solution is 0.1 mol/kg and for magnesium chloride is 0.03 mol/kg
For b: The activity coefficient of [tex]Pb^{2+}\text{ and }SO_4^{2-}[/tex] ions in lead sulfate solution is 0.352 and 0.324 respectively and the activity coefficient of [tex]Mg^{2+}\text{ and }Cl^{-}[/tex] ions in magnesium chlorirde solution is 0.500 and 0.843 respectively
Explanation:
- For a:
To calculate the ionic strength, we use the equation:
[tex]I=\frac{1}{2}\sum_{i=1}^n(C_iZ_i^2)[/tex]
where,
[tex]C_i[/tex] = concentration of i-th ions.
[tex]Z_i[/tex] = charge of i-th ions.
Taking [tex]PbSO_4[/tex] solution:
The chemical equation for the ionization of lead sulfate follows:
[tex]PbSO_4(aq.)\rightarrow Pb^{2+}(aq.)+SO_4^{2-}(aq.)[/tex]
For the ions:
[tex]C_{SO_4^{2-}}=0.025mol/kg\\C_{Pb^{2+}}=0.025mol/kg\\Z_{SO_4^{2-}}=-2\\Z_{Pb^{2+}}=+2[/tex]
Putting values in above equation, we get:
[tex]I=\frac{1}{2}[(0.025\times (+2)^2)+(0.025\times (-2)^2)]\\\\I=0.1mol/kg[/tex]
Taking [tex]MgCl_2[/tex] solution:
The chemical equation for the ionization of lead sulfate follows:
[tex]MgCl_2(aq.)\rightarrow Mg^{2+}(aq.)+2Cl^{-}(aq.)[/tex]
For the ions:
[tex]C_{Cl^{-}}=0.02mol/kg\\C_{Mg^{2+}}=0.01mol/kg\\Z_{Cl^{-}}=-1\\Z_{Mg^{2+}}=+2[/tex]
Putting values in above equation, we get:
[tex]I=\frac{1}{2}[(0.01\times (+2)^2)+(0.02\times (-1)^2)]\\\\I=0.03mol/kg[/tex]
Hence, the ionic strength of lead sulfate solution is 0.1 mol/kg and for magnesium chloride is 0.03 mol/kg
- For b:
To calculate the activity coefficient, we use the equation:
[tex]-\log \gamma_i=\frac{0.509Z_i^2\sqrt{I}}{1+3.3(\alpha_i \sqrt{I})}[/tex]
where,
[tex]Z_i[/tex] = charge on i-th specie
I = ionic strength
[tex]\alpha[/tex] = effective hydrated radius of i-th specie (in nm)
- Taking [tex]PbSO_4[/tex] solution:
For [tex]Pb^{2+}[/tex] ions:
We know that:
[tex]\alpha_{Pb^{2+}}=0.401nm\\I=0.1mol/kg\\Z_{Pb^{2+}}=+2[/tex]
Putting values in above equation, we get:
[tex]-\log \gamma_{Pb^{2+}}=\frac{0.509\times (+2)^2\sqrt{0.1}}{1+3.3(0.401\sqrt{0.1})}\\\\-\log \gamma_{Pb^{2+}}=0.454\\\\\gamma_{Pb^{2+}}=10^{-0.454}=0.352[/tex]
For [tex]SO_4^{2-}[/tex] ions:
We know that:
[tex]\alpha_{SO_4^{2-}}=0.300nm\\I=0.1mol/kg\\Z_{SO_4^{2-}}=-2[/tex]
Putting values in above equation, we get:
[tex]-\log \gamma_{SO_4^{2-}}=\frac{0.509\times (-2)^2\sqrt{0.1}}{1+3.3(0.300\sqrt{0.1})}\\\\-\log\gamma_{SO_4^{2-}}=0.490\\\\\gamma_{SO_4^{2-}}=10^{-0.490}=0.324[/tex]
- Taking [tex]MgCl_2[/tex] solution:
For [tex]Mg^{2+}[/tex] ions:
We know that:
[tex]\alpha_{Mg^{2+}}=0.300nm\\I=0.03mol/kg\\Z_{Mg^{2+}}=+2[/tex]
Putting values in above equation, we get:
[tex]-\log \gamma_{Mg^{2+}}=\frac{0.509\times (+2)^2\sqrt{0.03}}{1+3.3(0.300\sqrt{0.03})}\\\\-\log\gamma_{Mg^{2+}}=0.301\\\\\gamma_{Mg^{2+}}=10^{-0.301}=0.500[/tex]
For [tex]Cl^{-}[/tex] ions:
We know that:
[tex]\alpha_{Cl^{-}}=0.330nm\\I=0.03mol/kg\\Z_{Cl^{-}}=-1[/tex]
Putting values in above equation, we get:
[tex]-\log \gamma_{Cl^{-}}=\frac{0.509\times (-1)^2\sqrt{0.03}}{1+3.3(0.330\sqrt{0.03})}\\\\-\log\gamma_{Cl^{-}}=0.0742\\\\\gamma_{Cl^{-}}=10^{-0.0742}=0.843[/tex]
Hence, the activity coefficient of [tex]Pb^{2+}\text{ and }SO_4^{2-}[/tex] ions in lead sulfate solution is 0.352 and 0.324 respectively and the activity coefficient of [tex]Mg^{2+}\text{ and }Cl^{-}[/tex] ions in magnesium chlorirde solution is 0.500 and 0.843 respectively