Fe3+(aq) + KSCN(s) → FeSCN2+(aq) + K+(aq) 5. To determine the moles of Fe3+(aq) in a 100. mL sample — Solutions Chemistry Question

STEPS:

1. Understand the core analytical concept (Beer's Law): The graph provided is a calibration curve that relates the absorbance ($A$) of the dark-red coordination complex $\text{FeSCN}^{2+}$ to its molar concentration ($M$) at a specific wavelength (453 nm). According to the Beer^-Lambert Law, absorbance is directly proportional to concentration ($A = \epsilon bC$), yielding a straight line of best fit passing through the origin.
2. Read the concentration of $\text{FeSCN}^{2+}$ from the best-fit line:
* Locate $0.20$ on the y-axis (Absorbance at 453 nm).
* Follow the grid line horizontally to the right until it intersects the solid line of best fit.
* From that intersection point, look vertically downward to read the concentration on the x-axis.
* The intersection lies exactly on the fourth grid line, which corresponds to a concentration of $4.0 \times 10^{-5}\text{ M}$ (since the major grid line is $5 \times 10^{-5}\text{ M}$ and has 5 subdivisions, each vertical grid line represents exactly $1.0 \times 10^{-5}\text{ M}$).
3. Apply the stoichiometry of the complexation reaction:
* Look at the balanced chemical equation representing the conversion:
$$\text{Fe}^{3+}(aq) + \text{KSCN}(s) \rightarrow \text{FeSCN}^{2+}(aq) + \text{K}^+(aq)$$
* Because an excess of solid $\text{KSCN}$ is added, the iron(III) ion ($\text{Fe}^{3+}$) is the limiting reactant and is completely converted into $\text{FeSCN}^{2+}$.
* The stoichiometric ratio between $\text{Fe}^{3+}$ and $\text{FeSCN}^{2+}$ is exactly $1:1$. Therefore:
$$\text{Moles of Fe}^{3+}\text{ initially present} = \text{Moles of FeSCN}^{2+}\text{ produced}$$
4. Convert the sample volume to liters:
* The volume of the sample is $100.\text{ mL}$.
* Converting to liters ($\text{L}$) gives:
$$100.\text{ mL} \times \frac{1\text{ L}}{1000\text{ mL}} = \mathbf{0.100\text{ L}}$$
5. Calculate the moles of $\text{Fe}^{3+}$ present:
* Use the molarity equation ($n = M \times V$) to find the total moles in the sample:
$$\text{Moles of FeSCN}^{2+} = (4.0 \times 10^{-5}\text{ mol/L}) \times (0.100\text{ L}) = \mathbf{4.0 \times 10^{-6}\text{ mol}}$$
* Since there is a 1:1 ratio, the initial moles of $\text{Fe}^{3+}$ are exactly $4 \times 10^{-6}\text{ mol}$, which identifies Option C as the correct answer.

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WHY_OTHERS_WRONG:

• Option A is incorrect ($4 \times 10^{-4}\text{ mol}$): This value is off by two orders of magnitude. A student might arrive at this option if they read the concentration correctly as $4.0 \times 10^{-5}\text{ M}$ but made a decimal error when converting $100.\text{ mL}$ to liters (e.g., multiplying by 10 instead of dividing by 1000).
• Option B is incorrect ($3 \times 10^{-4}\text{ mol}$): This option is off in both the coefficient and the exponent. It represents a combination of a misread concentration value (reading an outlier data point instead of the best-fit line) and a metric conversion/mathematical mistake.
• Option D is incorrect ($3 \times 10^{-6}\text{ mol}$): A student will arrive at this incorrect answer if they read the coordinate of the individual experimental data point closest to an absorbance of 0.20 (which sits near $3.0 \times 10^{-5}\text{ M}$) rather than reading from the solid line of best fit (which is at $4.0 \times 10^{-5}\text{ M}$). When performing calibration curve calculations in science, values must always be determined using the calibrated line of best fit rather than raw, unadjusted data points.