Directions :
For parts of the free-response question that require calculations , clearly show the method used and the steps involved in arriving at your answers . You must show your work to receive credit for your answer . Examples and equations may be included in your answers where appropriate .
A student determines the mass percent of iron in a sample of iron ore by doing a redox titration. The student finds the mass of the sample and then dissolves it in acid to a total volume of 25.00mL . Using a buret the student titrates the 25.00mL solution with 0.017MK_{2}Cr_{2}O_{7} The following reaction occurs during the titration Cr 2 O 1 ^ 2^ – (aq)+6Fe^ 2^ * (aq)+14H^ * (aq) 2Cr^ 3* (aq)+6Fe^ 3* (aq)+7H 7 O(l) The student collects the following data of iron ore in original sample Buret reading at end point45.52 mL Initial buret reading 15.05 mL (a) How many moles of Fe^ 2+ (aq) reacted with the ) ? ( 1Point ) (b) Assuming that all the iron in the ore was Fe^ 2+ , calculate the mass percent of iron in the ore sample . (1 Point ) (c) The student learns that the actual mass percent of iron in the ore sample is greater than the experimental value calculated in part (b). The student claims that the difference between the actual and experimental values could have been caused by rinsing the buret with distilled water just prior to filling it with 0.017MK_{2}Cr_{2}O_{2} Do you agree withthe student’s claim ? Explain your reasoning . ( 1 Point)
The Correct Answer and Explanation is:
To solve this problem, we will go through the parts step by step, starting with the data provided:
- Buret readings:
- Initial reading: 15.05 mL
- Final reading: 45.52 mL
- Volume of ( K_2Cr_2O_7 ) used:
[
\text{Volume} = \text{Final reading} – \text{Initial reading} = 45.52 \, \text{mL} – 15.05 \, \text{mL} = 30.47 \, \text{mL}
] - Molarity of ( K_2Cr_2O_7 ): 0.017 M
(a) Moles of ( Fe^{2+} ) that reacted
First, we need to calculate the moles of ( K_2Cr_2O_7 ) used in the titration.
Step 1: Convert volume to liters:
[
\text{Volume in L} = \frac{30.47 \, \text{mL}}{1000} = 0.03047 \, \text{L}
]
Step 2: Calculate moles of ( K_2Cr_2O_7 ):
[
\text{Moles of } K_2Cr_2O_7 = \text{Molarity} \times \text{Volume in L}
]
[
\text{Moles of } K_2Cr_2O_7 = 0.017 \, \text{M} \times 0.03047 \, \text{L} = 0.000518 \, \text{moles}
]
Step 3: Use stoichiometry from the balanced equation:
The balanced equation shows that 1 mole of ( K_2Cr_2O_7 ) reacts with 6 moles of ( Fe^{2+} ):
[
K_2Cr_2O_7 + 6Fe^{2+} + 14H^{+} \rightarrow 2Cr^{3+} + 6Fe^{3+} + 7H_2O
]
Thus, the moles of ( Fe^{2+} ) can be calculated as:
[
\text{Moles of } Fe^{2+} = 6 \times \text{Moles of } K_2Cr_2O_7 = 6 \times 0.000518 = 0.003108 \, \text{moles}
]
(b) Mass percent of iron in the ore sample
Step 1: Calculate the mass of ( Fe^{2+} ):
The molar mass of iron (( Fe )) is approximately 55.85 g/mol.
[
\text{Mass of } Fe^{2+} = \text{Moles of } Fe^{2+} \times \text{Molar mass of } Fe
]
[
\text{Mass of } Fe^{2+} = 0.003108 \, \text{moles} \times 55.85 \, \text{g/mol} \approx 0.173 \, \text{g}
]
Step 2: Calculate the mass percent of iron:
Assuming the total mass of the ore sample is ( m ) grams, the mass percent of iron can be calculated as:
[
\text{Mass percent of } Fe = \left( \frac{\text{Mass of } Fe^{2+}}{\text{Mass of sample}} \right) \times 100\%
]
If we let the mass of the sample be ( m = 1.000 \, \text{g} ) (for simplicity),
[
\text{Mass percent of } Fe = \left( \frac{0.173 \, \text{g}}{1.000 \, \text{g}} \right) \times 100\% = 17.3\%
]
(c) Analysis of the student’s claim
The student’s claim about the rinsing of the buret with distilled water affecting the results can be evaluated as follows:
Rinsing the buret with distilled water before filling it with ( K_2Cr_2O_7 ) would typically dilute the titrant, as any residual water left in the buret would mix with the titrant. Since the molarity of ( K_2Cr_2O_7 ) is 0.017 M, if water was left, the effective concentration of the titrant would be lower than intended, leading to fewer moles of ( K_2Cr_2O_7 ) reacting with ( Fe^{2+} ). This dilution could result in a lower amount of ( Fe^{2+} ) detected, leading to an underestimation of the iron content in the sample.
Thus, the student’s claim is plausible. If they had rinsed the buret and did not properly fill it with the titrant, the observed value of the mass percent of iron would indeed be lower than the actual value, since less ( K_2Cr_2O_7 ) would react with the iron. This could explain why the experimental mass percent of iron is less than the actual value found later. To ensure accurate titrations, it is essential to use titrant solutions without any dilution effects from previous rinsing.
Summary
- Moles of ( Fe^{2+} ) that reacted: 0.003108 moles
- Mass percent of iron in the ore sample (assuming 1 g sample): 17.3%
- The student’s claim about the effect of rinsing the buret is valid as it could lead to diluted titrant and underestimation of iron content.