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Chapter 8: Problem 1

Titanium is a metal used in jet engines. Its specific heat is \(0.523 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\). If \(5.88 \mathrm{~g}\) of titanium absorbs \(4.78 \mathrm{~J}\), what is the change in temperature?

Short Answer

Expert verified
Answer: The change in temperature of the titanium is approximately 1.47°C.

Step by step solution

01

Write the given values.

We are given: Specific heat of titanium (c) = 0.523 J/g °C Mass of titanium (m) = 5.88 g Energy absorbed (q) = 4.78 J
02

Write the formula for calculating the change in temperature (ΔT).

The formula for calculating the change in temperature is: \(q = mcΔT\)
03

Rearrange the formula for ΔT.

We need to find ΔT, so we will rearrange the formula: \(ΔT = \frac{q}{mc}\)
04

Plug in the given values and calculate ΔT.

Now we will substitute the given values for q, m, and c in the formula: \(ΔT = \frac{4.78 \mathrm{~J}}{5.88 \mathrm{~g} \times 0.523 \mathrm{~J / g\cdot ^{\circ}C}}\)
05

Solve for ΔT.

Now, calculate the value of ΔT: \(ΔT = \frac{4.78 \mathrm{~J}}{ (5.88 \mathrm{~g}) \times (0.523 \mathrm{~J / g\cdot ^{\circ}C})} \approx 1.47^{\circ} C\) The change in temperature of the titanium is approximately 1.47°C.

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Most popular questions from this chapter

Calcium carbide, \(\mathrm{CaC}_{2}\), is the raw material for the production of acetylene (used in welding torches). Calcium carbide is produced by reacting calcium oxide with carbon, producing carbon monoxide as a byproduct. When one mole of calcium carbide is formed, \(464.8 \mathrm{~kJ}\) is absorbed. (a) Write a thermochemical equation for this reaction. (b) Is the reaction exothermic or endothermic? (c) Draw an energy diagram showing the path of this reaction. (Figure \(8.4\) is an example of such an energy diagram.) (d) What is \(\Delta H\) when \(1.00 \mathrm{~g}\) of \(\mathrm{CaC}_{2}(\mathrm{~g})\) is formed? (e) How many grams of carbon are used up when \(20.00 \mathrm{~kJ}\) of heat is absorbed?

Natural gas companies in the United States use the "therm" as a unit of energy. One therm is \(1 \times 10^{5} \mathrm{BTU}\). (a) How many joules are in one therm? \(\left(1 \mathrm{~J}=9.48 \times 10^{-4} \mathrm{BTU}\right)\) (b) When propane gas, \(\mathrm{C}_{3} \mathrm{H}_{8}\), is burned in oxygen, \(\mathrm{CO}_{2}\) and steam are produced. How many therms of energy are given off by \(1.00 \mathrm{~mol}\) of propane gas?

Salicylic acid, \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\), is one of the starting materials in the manufacture of aspirin. When \(1.00 \mathrm{~g}\) of salicylic acid burns in a bomb calorimeter, the temperature rises from \(23.11^{\circ} \mathrm{C}\) to \(28.91^{\circ} \mathrm{C}\). The temperature in the bomb calorimeter increases by \(2.48^{\circ} \mathrm{C}\) when the calorimeter absorbs \(9.37 \mathrm{~kJ}\). How much heat is given off when one mole of salicylic acid is burned?

To produce silicon, used in semiconductors, from sand \(\left(\mathrm{SiO}_{2}\right)\), a reaction is used that can be broken down into three steps: $$ \begin{aligned} \mathrm{SiO}_{2}(s)+2 \mathrm{C}(s) \longrightarrow \mathrm{Si}(s)+2 \mathrm{CO}(g) & & \Delta H=689.9 \mathrm{~kJ} \\ \mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SiCl}_{4}(g) & & \Delta H=-657.0 \mathrm{~kJ} \\ \mathrm{SiCl}_{4}(g)+2 \mathrm{Mg}(s) \longrightarrow 2 \mathrm{MgCl}_{2}(s)+\mathrm{Si}(s) & & \Delta H=-625.6 \mathrm{~kJ} \end{aligned} $$ (a) Write the thermochemical equation for the overall reaction for the formation of silicon from silicon dioxide; \(\mathrm{CO}\) and \(\mathrm{MgCl}_{2}\) are byproducts. (b) What is \(\Delta H\) for the formation of one mole of silicon? (c) Is the overall reaction exothermic?

Consider the reaction of methane with oxygen. Suppose that the reaction is carried out in a furnace used to heat a house. If \(q=-890 \mathrm{~kJ}\) and \(w=+5 \mathrm{~kJ}\), what is \(\Delta E ? \Delta H\) at \(25^{\circ} \mathrm{C} ?\)
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