- #1
demander
- 26
- 0
Hi to all, hope you can help me with a problem that took me almost all the week
To find The Pka of Neutral Red, i had to use this expression [tex]\frac{A-A_{HNR}}{A_{NR}-A}[/tex]
So Now I Have to show that [tex]\frac{[NR]}{[HNR^{+}]}=\frac{A-A_{HNR}}{A_{NR}-A}[/tex]
i tried backwards and i did it, but starting from the concnetrations is far more dificult
i Have to prove that equallity using only this equations
[tex]C_{HNR^{+}} + C_{NR}=C_{Total}[/tex](1)
[tex]A_{HNR^{+}}=\epsilon_{HNR^{+}}.b.C_{total}[/tex](2)
[tex]A_{NR}=\epsilon_{NR}.b.C_{total}[/tex](3)
[tex]A=\epsilon_{HNR^{+}}.b.C_{HNR^{+}} + \epsilon_{NR}.b.C_{NR}[/tex] (4)
I tried to solve 4 in order to [tex]C_{HNR^{+}}[/tex] first and then in order to [tex]C_{NR}[/tex].
I arrive to
[tex]C_{HNR^{+}}=\frac{A-\epsilon_{NR}.b.C_{NR}}{\epsilon_{HNR^{+}}.b}[/tex]
[tex]C_{NR}=\frac{A-\epsilon_{HNR^{+}}.b.C_{HNR^{+}}}{\epsilon_{NR}.b}[/tex]
then i did the following, added and subtracted the same value in the fraction numerator, like this:
[tex]C_{NR}=\frac{A+\epsilon_{HNR^{+}}.b.C_{NR}-\epsilon_{HNR^{+}}.b.C_{HNR^{+}}-\epsilon_{HNR^{+}}.b.C_{NR}}{\epsilon_{NR}.b}[/tex]
so i could do:
[tex]C_{NR}=\frac{A+\epsilon_{HNR^{+}}.b.C_{NR}-\epsilon_{HNR^{+}}.b.(C_{HNR^{+}}+C_{NR}}{\epsilon_{NR}.b}[/tex]
and using equation 1 it came
[tex]C_{NR}=\frac{A+\epsilon_{HNR^{+}}.b.C_{NR}-\epsilon_{HNR^{+}}.b.(C_{t})}{\epsilon_{NR}.b}[/tex]
then using equation 2:
[tex]C_{NR}=\frac{A+\epsilon_{HNR^{+}}.b.C_{NR}-A_{HNR^{+}}}{\epsilon_{NR}.b}[/tex]
doing the same thing to HNR it came:
[tex]C_{HNR}=\frac{A+\epsilon_{NR}.b.C_{HNR}-A_{NR}}{\epsilon_{HNR^{+}}.b}[/tex]
So doing the reason
[tex]\frac{[NR]}{[HNR^{+}]}[/tex]=[tex]\frac{\frac{A+\epsilon_{HNR^{+}}.b.C_{NR}-A_{HNR^{+}}}{\epsilon_{NR}.b}}{\frac{A+\epsilon_{NR}.b.C_{HNR}-A_{NR}}{\epsilon_{HNR^{+}}.b}}[/tex]
and it's here where i can't see how can i arrive to the final equation
am i going for the worst way? i thought about this all week and can't find a way to prove what i should
hope someone can help me, it's kind of urgent
Homework Statement
To find The Pka of Neutral Red, i had to use this expression [tex]\frac{A-A_{HNR}}{A_{NR}-A}[/tex]
So Now I Have to show that [tex]\frac{[NR]}{[HNR^{+}]}=\frac{A-A_{HNR}}{A_{NR}-A}[/tex]
i tried backwards and i did it, but starting from the concnetrations is far more dificult
Homework Equations
i Have to prove that equallity using only this equations
[tex]C_{HNR^{+}} + C_{NR}=C_{Total}[/tex](1)
[tex]A_{HNR^{+}}=\epsilon_{HNR^{+}}.b.C_{total}[/tex](2)
[tex]A_{NR}=\epsilon_{NR}.b.C_{total}[/tex](3)
[tex]A=\epsilon_{HNR^{+}}.b.C_{HNR^{+}} + \epsilon_{NR}.b.C_{NR}[/tex] (4)
The Attempt at a Solution
I tried to solve 4 in order to [tex]C_{HNR^{+}}[/tex] first and then in order to [tex]C_{NR}[/tex].
I arrive to
[tex]C_{HNR^{+}}=\frac{A-\epsilon_{NR}.b.C_{NR}}{\epsilon_{HNR^{+}}.b}[/tex]
[tex]C_{NR}=\frac{A-\epsilon_{HNR^{+}}.b.C_{HNR^{+}}}{\epsilon_{NR}.b}[/tex]
then i did the following, added and subtracted the same value in the fraction numerator, like this:
[tex]C_{NR}=\frac{A+\epsilon_{HNR^{+}}.b.C_{NR}-\epsilon_{HNR^{+}}.b.C_{HNR^{+}}-\epsilon_{HNR^{+}}.b.C_{NR}}{\epsilon_{NR}.b}[/tex]
so i could do:
[tex]C_{NR}=\frac{A+\epsilon_{HNR^{+}}.b.C_{NR}-\epsilon_{HNR^{+}}.b.(C_{HNR^{+}}+C_{NR}}{\epsilon_{NR}.b}[/tex]
and using equation 1 it came
[tex]C_{NR}=\frac{A+\epsilon_{HNR^{+}}.b.C_{NR}-\epsilon_{HNR^{+}}.b.(C_{t})}{\epsilon_{NR}.b}[/tex]
then using equation 2:
[tex]C_{NR}=\frac{A+\epsilon_{HNR^{+}}.b.C_{NR}-A_{HNR^{+}}}{\epsilon_{NR}.b}[/tex]
doing the same thing to HNR it came:
[tex]C_{HNR}=\frac{A+\epsilon_{NR}.b.C_{HNR}-A_{NR}}{\epsilon_{HNR^{+}}.b}[/tex]
So doing the reason
[tex]\frac{[NR]}{[HNR^{+}]}[/tex]=[tex]\frac{\frac{A+\epsilon_{HNR^{+}}.b.C_{NR}-A_{HNR^{+}}}{\epsilon_{NR}.b}}{\frac{A+\epsilon_{NR}.b.C_{HNR}-A_{NR}}{\epsilon_{HNR^{+}}.b}}[/tex]
and it's here where i can't see how can i arrive to the final equation
am i going for the worst way? i thought about this all week and can't find a way to prove what i should
hope someone can help me, it's kind of urgent