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Chapter 8: Problem 20

Naphthalene, \(\mathrm{C}_{10} \mathrm{H}_{8}\), is the compound present in moth balls. When one mole of naphthalene is burned, \(5.15 \times 10^{3} \mathrm{~kJ}\) of heat is evolved. A sample of naphthalene burned in a bomb calorimeter (heat capacity \(=9832 \mathrm{~J} /{ }^{\circ} \mathrm{C}\) ) increases the temperature in the calorimeter from \(25.1^{\circ} \mathrm{C}\) to \(28.4^{\circ} \mathrm{C}\). How many milligrams of naphthalene were burned?

Short Answer

Expert verified
Answer: Approximately 807 mg of naphthalene was burned in the calorimeter.

Step by step solution

01

Recall the formula for heat and other relevant equations

The heat gained or released can be determined by the formula: q = C × ΔT Where: q = heat gained or released (Joules) C = heat capacity (Joules/°C) ΔT = change in temperature (°C) We will also need to use the molar mass of naphthalene, which can be calculated as: Molar mass of naphthalene = (10 × mass of C) + (8 × mass of H) = (10 × 12.01) + (8 × 1.008) g/mol Lastly, we'll need the concept of moles: moles = mass / molar mass
02

Calculate the heat involved in the calorimeter

The calorimeter's temperature rose from 25.1°C to 28.4°C, so the temperature change is: ΔT = 28.4°C - 25.1°C = 3.3°C Now, using the heat capacity given (9832 J/°C) and the calculated temperature change, we can determine the heat involved: q = C × ΔT = (9832 (J/°C)) × (3.3 °C) = 32445.6 J
03

Convert the heat from burning naphthalene to moles

We're given that burning one mole of naphthalene produces 5.15 × 10^3 kJ of heat. Convert the value to Joules: Heat per mole = (5.15 × 10^3 kJ/mol) × (1000 J /1 kJ) = 5.15 × 10^6 J/mol Now we can find how many moles were burned by dividing the calculated heat by the heat per mole: moles = (32445.6 J) / (5.15 × 10^6 J/mol) ≈ 0.0063 mol
04

Calculate the mass of burnt naphthalene

First, calculate the molar mass of naphthalene: Molar mass of naphthalene = (10 × 12.01) + (8 × 1.008) g/mol ≈ 128.17 g/mol Now we can calculate the mass of burnt naphthalene: mass = moles × molar mass = 0.0063 mol × 128.17 g/mol ≈ 0.807 g
05

Convert the mass to milligrams

To convert the mass from grams to milligrams, we need to consider that 1 g = 1000 mg. So, the mass of burnt naphthalene in milligrams is: mass_in_mg = 0.807 g × (1000 mg /1 g) ≈ 807 mg Thus, approximately 807 mg of naphthalene was burned in the calorimeter.

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Most popular questions from this chapter

When one mole of KOH is neutralized by sulfuric acid, \(q=-56 \mathrm{~kJ} .\) At \(22.8^{\circ} \mathrm{C}, 25.0 \mathrm{~mL}\) of \(0.500 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) is neutralized by \(50.0 \mathrm{~mL}\) of \(0.500 \mathrm{M}\) \(\mathrm{KOH}\) in a coffee-cup calorimeter. What is the final temperature of the solution? (Use the assumptions in Question 11.)

Nitroglycerine, \(\mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(l)\), is a powerful explosive used in rock blasting when roads are created. When ignited, it produces water, nitrogen, carbon dioxide, and oxygen. Detonation of one mole of nitroglycerine liberates \(5725 \mathrm{~kJ}\) of heat. (a) Write a balanced thermochemical equation for the reaction for the detonation of four moles of nitroglycerine. (b) What is \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(l) ?\)

Isooctane, \(\mathrm{C}_{8} \mathrm{H}_{18}\), is a component of gasoline. When \(0.500 \mathrm{~g}\) of isooctane is burned, \(24.06 \mathrm{~kJ}\) of heat is given off. If \(10.00 \mathrm{mg}\) of isooctane is burned in a bomb calorimeter (heat capacity \(=5175 \mathrm{~J} /{ }^{\circ} \mathrm{C}\) ) initially at \(23.6^{\circ} \mathrm{C}\), what is the temperature of the calorimeter when reaction is complete?

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?

Determine whether the statements given below are true or false. Consider an endothermic process taking place in a beaker at room temperature. (a) Heat flows from the surroundings to the system. (b) The beaker is cold to the touch. (c) The pressure of the system decreases. (d) The value of \(q\) for the system is positive.
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