When an ion-selective electrode for sulfate was immersed in 0.0300 M sodium sulfate, the measured potential was 0.0460 V. What is the concentration of sulfate when the potential is 0.0610 V? Assume that the electrode follows the Nernst equation, the temperature is at 25°C, and that the activity coefficient of sulfate is 1.
I have done this a couple different ways and it keeps saying it's incorrect.
First I got 0.0539M and the second time I got 0.0167M. Both of which are wrong.
To determine the concentration of sulfate when the potential is 0.0610 V, we can use the Nernst equation:
E = E° - (RT / nF) * ln(Q)
Where:
- E is the measured potential
- E° is the standard reduction potential (given)
- R is the gas constant (8.314 J/(mol•K))
- T is the temperature in Kelvin (25°C = 298 K)
- n is the number of electrons involved in the reaction (assuming 2 for sulfate)
- F is Faraday's constant (96485 C/mol)
- Q is the reaction quotient, which can be calculated as the concentration of sulfate divided by the concentration of sodium sulfate
Given:
- E° = standard reduction potential = unknown
- E = measured potential = 0.0610 V
- R = 8.314 J/(mol•K)
- T = 298 K
- n = 2 (since sulfate has a 2- charge)
- F = 96485 C/mol
- [Na2SO4] = 0.0300 M
Let's solve for the standard reduction potential (E°) first.
0.0610 V = E° - (8.314 J/(mol•K) * 298 K / (2 * 96485 C/mol)) * ln(0.0300 M / [SO4^2-])
Now, rearrange the equation to solve for ln([SO4^2-]):
ln([SO4^2-]) = ( E° - 0.0610 V ) / [(8.314 J/(mol•K)) * 298 K / (2 * 96485 C/mol)] + ln(0.0300 M / [SO4^2-])
Now that we have the value of ln([SO4^2-]), we need to convert it back to concentration [SO4^2-].
Exponentiate both sides of the equation:
[SO4^2-] = exp(( E° - 0.0610 V ) / [(8.314 J/(mol•K)) * 298 K / (2 * 96485 C/mol)] + ln(0.0300 M / [SO4^2-]))
Now, we can substitute the measured potential (0.0610 V) to find the concentration of sulfate. However, to find the standard reduction potential (E°), we need more information—specifically, the standard reduction potential for the sulfate ion. If you provide the missing value for E°, I can help you calculate the concentration of sulfate.