Calibration data for a bromide ion-selective electrode (ISE) was collected and recorded below. The potential of the ISE was measured against a saturated calomel electrode (SCE). All solutions were buffered at a pH of 7.56. A linear calibration curve can be constructed from this data as a plot of potential vs. log[Br-]. Determine the slope and y-intercept of such a plot of the calibration data given.
Find the slope and the y-intercept.
Two unknown solutions were tested for [Br–] using the same bromide ISE. The potential reading for unknown 1 was 13.4 mV and the potential reading for unknown 2 was 181.9 mV. Using the calibration curve you constructed above, determine the concentration of Br– in each unknown solution.
I have done this problem multiple times (5 times) and I cannot figure out what I am doing wrong. I got the slope but not the intercept.
To find the slope and y-intercept for the linear calibration curve, you need two points on the curve. In this case, the potential readings for two different known concentrations of bromide ion ([Br-]) were measured against a saturated calomel electrode (SCE).
Let's assume the two solutions used for calibration have concentrations of [Br-]_1 and [Br-]_2, and their corresponding potential readings are V_1 and V_2, respectively.
To find the slope (m) of the calibration curve, you can use the formula:
m = (V_2 - V_1) / (log[Br-]_2 - log[Br-]_1)
To find the y-intercept (b), you can use one of the points on the curve and solve for b in the equation:
V = m * log[Br-] + b
Let's apply this to your specific problem:
Given the potential reading for unknown 1, V_1 = 13.4 mV, and the potential reading for unknown 2, V_2 = 181.9 mV.
Using the calibration curve equation, V = m * log[Br-] + b, we can substitute these values:
13.4 = m * log[Br-]_1 + b ---(1)
181.9 = m * log[Br-]_2 + b ---(2)
Since we know m, we can rearrange equation (1) to solve for b:
b = 13.4 - m * log[Br-]_1
Now, substitute this value of b into equation (2):
181.9 = m * log[Br-]_2 + (13.4 - m * log[Br-]_1)
Simplify by distributing the m term:
181.9 = m * log[Br-]_2 + 13.4 - m * log[Br-]_1
Now, rearrange the equation to solve for [Br-]_2:
m * log[Br-]_2 = 181.9 - 13.4 + m * log[Br-]_1
Finally, divide both sides of the equation by m to solve for [Br-]_2:
log[Br-]_2 = (181.9 - 13.4 + m * log[Br-]_1) / m
Using the same process, you can find the concentration [Br-]_1 for unknown 1. Just substitute the given values into the equations.
It's important to note that the slope and y-intercept of the calibration curve are specific to the particular electrode and conditions used in this experiment. If you're consistently getting the correct slope but incorrect y-intercept, double-check your calculations and make sure you've used the correct values for potential readings and concentrations.