Final answer:
To calculate the concentration of tartrate ion (C₄H₄O₆²⁻) in a 0.175 M solution of tartaric acid (H₂C₄H₄O₆), you can use the dissociation of tartaric acid into its ions and the acid dissociation constant (Ka).
Step-by-step explanation:
To calculate the concentration of tartrate ion (C₄H₄O₆²⁻) in a 0.175 M solution of tartaric acid (H₂C₄H₄O₆), we need to consider the dissociation of tartaric acid into its ions. Tartaric acid is a diprotic acid, so it can lose two hydrogen ions in a stepwise manner.
The dissociation of tartaric acid can be represented by the following equations:
H₂C₄H₄O₆ → H⁺ + HC₄H₄O₆⁻
HC₄H₄O₆⁻ → H⁺ + C₄H₄O₆²⁻
The concentration of tartrate ion (C₄H₄O₆²⁻) is equal to the concentration of HC₄H₄O₆⁻, which is the ion produced in the second dissociation step. The acid dissociation constant (Ka) for the second dissociation step is given as Ka₂= 4.6×10⁻⁵.
So, we can use the value of Ka₂ and the initial concentration of tartaric acid (0.175 M) to calculate the concentration of tartrate ion. This can be done using an ICE table and the expression for Ka. The final concentration of tartrate ion can be calculated as [C₄H₄O₆²⁻] = Ka₂ × [HC₄H₄O₆⁻].