Question

Potential (mV) [Br (M) 0.300 -21.9 Calibration data for a bromide ion-selective electrode (ISE) was collected and recorded in the table. 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 (in mV) vs. pBr. Determine the slope and y-intercept of such a plot of the calibration data given. 0.0300 37.2 0.00300 96.5 0.000300 155.4 0.0000300 224.4 slope = mV y-intercept = mV Two unknown solutions were tested for [Br] using the same bromide ISE. The potential reading for unknown I was 20.0 mV, and the potential reading for unknown 2 was 107.8 mV. Using the calibration curve you constructed, determine the concentration of Br in each unknown solution. unknown 1 [Br] = M unknown 2 [Br] = M

Answer 1

To construct a linear calibration curve, plot potential (in mV) vs. pBr using the given data. The slope is -1993.27 mV and the y-intercept is 155.4 mV. For the unknown solutions, [Br-] in unknown 1 is 10^(-0.0677) M and [Br-] in unknown 2 is 10^(-0.0239) M.

Step-by-step explanation:

To construct a linear calibration curve, we need to plot potential (in mV) vs. pBr. We can use the calibration data provided to find the slope and y-intercept of the plot. The slope is determined by finding the change in potential (ΔV) and the change in pBr (ΔpBr) between two data points. The y-intercept is the potential at pBr = 0.

Using the given calibration data, we can calculate the slope as follows:

Slope = ΔV / ΔpBr

For the first two data points: ΔV = 96.5 - 37.2 = 59.3 mV and ΔpBr = 0.000300 - 0.0300 = -0.0297. So, the slope is 59.3 mV / -0.0297 = -1993.27 mV.

The y-intercept is the potential at pBr = 0, which is 155.4 mV according to the given data.

To find the concentration of bromide (Br-) in the unknown solutions, we can use the calibration curve equation: Potential = Slope * pBr + y-intercept.

For the first unknown solution with a potential of 20.0 mV, we can rearrange the equation to solve for pBr: pBr = (Potential - y-intercept) / Slope = (20.0 - 155.4) / -1993.27 = 0.0677.

Since pBr = -log[Br-], we can convert pBr back to concentration [Br-] using the equation: [Br-] = 10(-pBr). So, for unknown 1, [Br-] = 10^(-0.0677) M.

For the second unknown solution with a potential of 107.8 mV, we can use the same equations to find the concentration of Br-: pBr = (Potential - y-intercept) / Slope = (107.8 - 155.4) / -1993.27 = 0.0239. Substituting this into [Br-] = 10(-pBr), we find that for unknown 2, [Br-] = 10^(-0.0239) M.

Answer 2

The concentration of Br in unknown 1 is approximately 1.115 M, and the concentration of Br in unknown 2 is approximately 0.001 M.

To determine the slope and y-intercept of the calibration curve, you can use the data provided to calculate these values. The calibration data relates the potential (in mV) to the negative logarithm of bromide ion concentration, pBr. The Nernst equation describes this relationship:

E = E° + (0.0592/n) * log([Br^-])

Where:

- E is the measured potential in mV.

- E° is the standard potential (in mV) for the electrode.

- n is the number of electrons transferred in the electrode reaction.

In this case, the slope of the calibration curve is (0.0592/n), and the y-intercept is E°.

To find the slope:

1. Choose two data points from your calibration data. Let's use the points (0.00003 M, 224.4 mV) and (0.003 M, 96.5 mV).

2. Calculate the difference in potential (ΔE) between these two points:

ΔE = 96.5 mV - 224.4 mV = -127.9 mV

3. Calculate the difference in pBr (ΔpBr) between these two points:

ΔpBr = log(0.00003) - log(0.003) = -4 - (-2.5229) ≈ -1.4771

4. Use the slope formula:

Slope = ΔE / ΔpBr = (-127.9 mV) / (-1.4771) ≈ 86.59 mV/pBr

Now that we have the slope, we can find the y-intercept using one of the calibration points. Let's use (0.300 M, -21.9 mV):

E° = Measured Potential - (Slope * pBr)

E° = -21.9 mV - (86.59 mV/pBr * -0.5229) ≈ -21.9 mV + 45.9311 mV ≈ 24.0311 mV

So, the slope is approximately 86.59 mV/pBr, and the y-intercept is approximately 24.03 mV.

Now that we have the calibration curve, you can use it to determine the concentration of Br for the unknown solutions:

For Unknown 1 (potential = 20.0 mV):

pBr = (E - E°) / Slope

pBr = (20.0 mV - 24.03 mV) / 86.59 mV/pBr ≈ -0.0461

[Br] = 10^(-pBr) ≈ 10^0.0461 ≈ 1.115 M

For Unknown 2 (potential = 107.8 mV):

pBr = (E - E°) / Slope

pBr = (107.8 mV - 24.03 mV) / 86.59 mV/pBr ≈ 0.9971

[Br] = 10^(-pBr) ≈ 10^(-0.9971) ≈ 0.001 M

So, the concentration of Br in unknown 1 is approximately 1.115 M, and the concentration of Br in unknown 2 is approximately 0.001 M.