The thermite process is used for welding railway track together. In this reaction, aluminum reduces iron(III) oxide to metallic iron:

$$2 AI(s) + Fe2O3(s)→2 Fe(s) + Al2O3(s)$$

Igniting a small charge of barium peroxide mixed with aluminum triggers the reaction of a mixture of aluminum powder and iron (III) oxide; the molten iron produced flows into the space between the steel rails that are to bejoined. (a) Calculate the standard enthalpy change ΔH° for this reaction, using data from Appendix D. (b) Calculate the heat given off when 3.21 g iron(III) oxide is reduced by aluminum at constant pressure.

“Thermite” reactions have been used for welding metal parts such as railway rails and in metal refining. One such thermite reaction is $\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(s) \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Fe}(s)$). Is the reaction spontaneous at room temperature under standard conditions? During the reaction, the surroundings absorb 851.8 kJ/mol of heat.

Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent? If it is convergent, find the sum. If it is divergent, explain why.

$$^∞∑n=1 cos^n$$

Name the property illustrated in each statement.

$$1 \cdot ( a b c ) = a b c$$

Solve each equation.

$$- 4 ( - 5 - . b ) = \frac { 1 } { 3 } ( b + 16 )$$

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Differentiate between rhombic sulfur and monoclinic sulfur.

In her bag, a photographer is carrying three exchange-able camera lenses with focal lengths of 400.0 mm, 50.0 mm, and 28.0 mm. Which lens should she use for (a) wide angle shots (a cathedral, takes from the square in front). (b) everyday use (children at play), and (c) telephoto work (lions in Africa takes from across the river)?

The enthalpy change of combu stion of monoclinic sulfur to SO2(g) is -9 .376 kJ g^-1. Under the same conditions, the rhombic form of sulfur has an enth alpy change of combust ion to SO2(g) of -9.293 kJ g^-1. Comput e the ΔH of the reaction

$$S(monocl inic) - S(rhombic)$$

per gram of sulfur reacting.

A cone-shaped paper drinking cup (like the kind used at water fountains) has a radius R and a height H. If the water height in the cup is h, the water volume is given by

$$V = \frac { 1 } { 3 } \pi \left( \frac { R } { H } \right) ^ { 2 } h ^ { 3 }$$

Suppose that the cup's dimensions are R=1.5 in. and H = 4 in. a. If the flow rate from the fountain into the cup is 2 in. 3$/$ sec, use Simulink to determine how long will it take to ll the cup to the brim. b. If the flow rate from the fountain into the cup is given by 2$\left( 1 - e ^ { - 2 t } \right)$ in. 3$/$ sec, use Simulink to determine how long will it take to ll the cup to the brim.

Sulfur dioxide is one of the major contributors to acid rain. Sulfur dioxide can react with oxygen and water in the atmosphere to form sulfuric acid, as shown in the following equation:

$$2 \mathrm { H } _ { 2 } \mathrm { O } ( l ) + \mathrm { O } _ { 2 } ( g ) + 2 \mathrm { SO } _ { 2 } ( g ) \rightarrow 2 \mathrm { H } _ { 2 } \mathrm { SO } _ { 4 } ( a q )$$

If 50.0 g of sulfur dioxide from pollutants reacts with water and oxygen found in the air, how many grams of sulfuric acid can be produced? How many grams of oxygen are used in the process?

For each of the following reactions, the enthalpy change given is that measured when the numbers of moles of reactants and products taking part in the reaction are as given by their coefficents in the equation. Calculate the enth alpy change when 1.00 gram of the underlined substance is consumed or produced. (a)

$$Ca(s) + Br2(l) → CaBr2(s).ΔH = - 683 kJ$$

(b)

$$6 Fe2O3 (s)→4 Fe3O4 (s) + O2 (g). ΔH = +472 kJ$$

(c)

$$2 NaHSO4(s)→2 NaOH (s) + 2SO2(g) + O2(g). ΔH = +806 kJ$$

(a) Calculate the change in enthalpy when 20 0 grams of aluminum metal is heated from 298 K to 573 K at constant pressure of 1 atm. (b) Calculate the change in enthalpy when 20.0 grams of metallic lead is taken through the same process. In both cases assume the heat capacity values predicted by equipartiti on are valid thro gh the temperature range stated.

Divide.

$$\left( 12 x ^ { 4 } + 9 x ^ { 3 } - 10 x ^ { 2 } \right) \div 3 x ^ { 3 }$$

Determine whether the improper integral converges or diverges.

$$∫_1^∞ 1 / (x² + 5) dx$$