Thermochemistry

1.a. Determine the oxidation number of Cl in NaOCl.

1.b. Calculate the number of grams of $Na_2S_2O_3$ needed to prepare 100.00 mL of 0.500 M $Na_2S_2O_3(aq)$.

1.c. Using the balanced equation for the oxidation-reduction reaction and the information in the table above, determine which reactant is the limiting reactant. Justify your answer.

1.d. According to the graph, what is the temperature change of the reaction mixture?

1.e. The mass of the reaction mixture inside the calorimeter is 15.21 g.

1.e.i. Calculate the magnitude of the heat energy, in joules, that is released during the reaction. Assume that the specific heat of the reaction mixture is 3.94 J/(g·°C) and that the heat absorbed by the calorimeter is negligible.

1.e.ii. Using the balanced equation for the oxidation-reduction reaction and your answer to part (c), calculate the value of the enthalpy change of the reaction, $\Delta H_{rxn}$, in kJ/mol$_{rxn}$. Include the appropriate algebraic sign with your answer.

1.f. The magnitude of the enthalpy change, $\Delta H_{rxn}$, in kJ/mol$_{rxn}$, calculated from the results of the second experiment is the same as the result calculated in part (e)(ii). Explain this result.

1.g. Write the balanced net ionic equation for the given reaction.

4.a) A student investigates a reaction used in hand warmers, represented above. The student mixes $Fe(s)$ with a catalyst and sand in a small open container. The student measures the temperature of the mixture as the reaction proceeds. The data are given in the following table.

|Time (min) |Temperature of Mixture (°C)|
|---|---|
|0 |22.0 |
|1 |25.1 |
|2 |34.6 |
|3 |37.3 |
|4 |39.7 |
|5 |39.4 |

    4.a.i) The mixture (<math-inline>Fe(s)</math-inline>, catalyst, and sand) has a total mass of 15.0 g and a specific heat capacity of 0.72 J/(g×°C). Calculate the amount of heat absorbed by the mixture from 0 minutes to 4 minutes. (2 points)

    <math-inline>q = mcΔT = (15.0 g)(0.72 J/(g°C))(39.7°C - 22.0°C) = 190 J</math-inline>

    4.a.ii) Calculate the mass of <math-inline>Fe(s)</math-inline>, in grams, that reacted to generate the amount of heat calculated in part (a). (2 points)

    $190 J = 0.190 kJ$
    <math-inline>\frac{0.190 kJ}{-1650 kJ/mol\_{rxn}} = -1.15 \times 10^{-4} mol\_{rxn}</math-inline>
    <math-inline>-1.15 \times 10^{-4} mol\_{rxn} \times \frac{4 mol Fe}{1 mol\_{rxn}} = -4.61 \times 10^{-4} mol Fe</math-inline>
    <math-inline>-4.61 \times 10^{-4} mol Fe \times 55.85 g/mol = 0.0257 g Fe</math-inline>

4.b) In a second experiment, the student uses twice the mass of iron as that calculated in part (b) but the same mass of sand as in the first experiment. Would the maximum temperature reached in the second experiment be greater than, less than, or equal to the maximum temperature in the first experiment? Justify your answer. (2 points)

The maximum temperature reached in the second experiment would be greater than the maximum temperature in the first experiment. Since the mass of the iron is doubled, the amount of heat released by the reaction will be doubled. The total mass of the mixture is higher, but the heat released is doubled. The specific heat capacity remains the same, so the temperature increase will be greater.

2.a) How many grams of Cl($g$) can be formed from 1.25 mol of AlCl$_3$($g$) ?

2.b) Calculate the value of ΔH$_1$, in kJ/mol$_{rxn}$, for reaction 1 above using reactions 2, 3, and 4.

2.c.i) Based on the graph, what is the bond length, in picometers, for Cl$_2$ ? 2.c.ii) A student finds that the average Al − Cl bond length is 220 picometers and the average bond energy is 425 kJ/mol. Draw the potential energy curve for the average Al − Cl bond on the preceding graph.

2.d.i) The AlCl$_3$($g$) molecule has a trigonal planar geometry. Which diagram (1, 2, or 3) can be eliminated based on geometry? Justify your choice based on VSEPR theory. 2.d.ii) Which of the three diagrams is the best representation for the bonding in AlCl$_3$ ? Justify your choice based on formal charges.

2.e) Write the expression for the equilibrium constant, K$_p$, for this reaction.

2.f) Using the particle-level diagram, calculate the value of K$_p$ for the reaction if the total pressure in the container is 22.1 atm.

4.a) What should the student report as the highest temperature of the water?

4.b) A particle-level representation of water molecules in the calorimeter before and after the metal cube was added is shown. The length of the arrows in the Before diagram represents the speed of the water molecules in the system. In the After diagram, draw an arrow for each molecule to indicate how the speed of each of the molecules changes after the metal cube is added.

4.c) Assuming the metal transfers 2940 J of thermal energy to the water, calculate the specific heat of the metal in J/(g·°C).

4.d) In a second experiment, 2940 J of thermal energy is transferred from 98.1 g of aluminum, which has a specific heat capacity of 0.897 J / (g·° C). Explain how the magnitude of the temperature change of the aluminum, Δ$T_{Al}$, compares with the magnitude of the temperature change of the metal in the original experiment.