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Chapter 6: Problem 14

Thermal decomposition of 5.0 metric tons of limestone to lime and carbon dioxide absorbs \(9.0 \times 10^{6} \mathrm{~kJ}\) of heat. Convert this energy to (a) joules; (b) calories; (c) British thermal units.

Short Answer

Expert verified
a) 9.0 × 10^9 J b) 2.15 × 10^9 cal c) 8.53 × 10^6 BTU

Step by step solution

01

Convert Metric Tons to Kilograms

First, convert 5.0 metric tons (tonnes) to kilograms. 1 metric ton = 1000 kg Therefore, 5.0 metric tons = 5.0 × 1000 kg = 5000 kg
02

Understand the Given Heat in Kilojoules

The given heat absorbed is 9.0 × 10^6 kJ.
03

Convert Kilojoules to Joules

Since 1 kilojoule (kJ) is equal to 1000 joules (J), convert 9.0 × 10^6 kJ to joules. 9.0 × 10^6 kJ × 1000 J/kJ = 9.0 × 10^9 J.
04

Convert Joules to Calories

Use the conversion factor where 1 calorie (cal) = 4.184 joules (J). Now convert joules to calories. 9.0 × 10^9 J ÷ 4.184 J/cal ≈ 2.15 × 10^9 cal.
05

Convert Joules to British Thermal Units (BTU)

Finally, use the conversion factor where 1 BTU ≈ 1055 joules (J) to convert joules to BTUs. 9.0 × 10^9 J ÷ 1055 J/BTU ≈ 8.53 × 10^6 BTU.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

thermal decomposition
Thermal decomposition is a chemical reaction where a compound breaks down into two or more simpler substances when heated. A common example is the decomposition of limestone (calcium carbonate, CaCO3) into lime (calcium oxide, CaO) and carbon dioxide (CO2). This process absorbs a significant amount of heat energy.
In our exercise, 5.0 metric tons of limestone undergo thermal decomposition, and the process absorbs 9.0 × 10^6 kilojoules (kJ) of heat.
kilojoules to joules
Energy is frequently measured in joules (J) and kilojoules (kJ) in chemistry. These units help quantify the amount of work done or the amount of heat absorbed or released in a reaction.
1 kilojoule (1 kJ) is equal to 1000 joules (J). To convert kilojoules to joules, you simply multiply by 1000. In our exercise, we converted 9.0 × 10^6 kJ to joules. The calculation is: 9.0 × 10^6 kJ × 1000 J/kJ = 9.0 × 10^9 J.
joules to calories
Calories are another unit of energy, commonly used in nutrition and chemistry. The relationship between joules and calories is essential for various conversions.
1 calorie (cal) is equal to 4.184 joules (J). To convert joules to calories, you divide by 4.184. In our example, we used this conversion to find out how many calories 9.0 × 10^9 joules corresponds to:
  • 9.0 × 10^9 J ÷ 4.184 J/cal ≈ 2.15 × 10^9 cal.
joules to BTU
BTU, or British Thermal Unit, is a unit of heat energy in the Imperial system commonly used in heating and air conditioning industries.
1 BTU is approximately equal to 1055 joules (J). To convert from joules to BTUs, you divide the energy in joules by 1055. For our exercise:
  • 9.0 × 10^9 J ÷ 1055 J/BTU ≈ 8.53 × 10^6 BTU.

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Most popular questions from this chapter

Kerosene, a common space-heater fuel, is a mixture of hydrocarbons whose "average" formula is \(\mathrm{C}_{12} \mathrm{H}_{26}\) (a) Write a balanced equation, using the simplest whole-number coefficients, for the complete combustion of kerosene to gases. (b) If \(\Delta H_{\mathrm{rn}}^{\circ}=-1.50 \times 10^{4} \mathrm{~kJ}\) for the combustion equation as written in part (a), determine \(\Delta H_{\mathrm{f}}^{\circ}\) of kerosene. (c) Calculate the heat released by combustion of 0.50 gal of kerosene \((d\) of kerosene \(=0.749 \mathrm{~g} / \mathrm{mL})\) (d) How many gallons of kerosene must be burned for a kerosene furnace to produce \(1250 .\) Btu \((1 \mathrm{Btu}=1.055 \mathrm{~kJ}) ?\)

The nutritional calorie (Calorie) is equivalent to 1 kcal. One pound of body fat is equivalent to about \(4.1 \times 10^{3}\) Calories. Express this quantity of energy in joules and kilojoules.

A mercury mirror forms inside a test tube as a result of the thermal decomposition of mercury(II) oxide: $$2 \mathrm{HgO}(s) \longrightarrow 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g) \quad \Delta H=181.6 \mathrm{~kJ}$$ (a) How much heat is absorbed to decompose \(555 \mathrm{~g}\) of the oxide? (b) If \(275 \mathrm{~kJ}\) of heat is absorbed, how many grams of \(\mathrm{Hg}\) form? 6.65 Most ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right),\) the starting material for producing polyethylene, comes from petroleum processing. It also occurs naturally as a fruit-ripening hormone and as a component of natural gas. (a) The heat transferred during combustion of \(\mathrm{C}_{2} \mathrm{H}_{4}\). is \(-1411 \mathrm{~kJ} / \mathrm{mol} .\) Write a balanced thermochemical equation. (b) How many grams of \(\mathrm{C}_{2} \mathrm{H}_{4}\) must burn to give \(70.0 \mathrm{~kJ}\) of heat?

When a \(2.150-\mathrm{g}\) sample of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) is burned in a bomb calorimeter with a heat capacity of \(6.317 \mathrm{~kJ} / \mathrm{K}\), the temperature of the calorimeter increases from \(23.446^{\circ} \mathrm{C}\) to \(28.745^{\circ} \mathrm{C}\). Calculate \(\Delta E\) for the combustion of glucose in \(\mathrm{kJ} / \mathrm{mol}\).

The chemistry of nitrogen oxides is very versatile. Given the following reactions and their standard enthalpy changes,(1) \(\mathrm{NO}(g)+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{3}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-39.8 \mathrm{~kJ}\) (2) \(\mathrm{NO}(g)+\mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}(g) \Delta H_{\mathrm{rxn}}^{0}=-112.5 \mathrm{~kJ}\) (3) \(2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)\) \(\Delta H_{\mathrm{ran}}^{0}=-57.2 \mathrm{~kJ}\) (4) \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) \(\Delta H_{\mathrm{rxn}}^{0}=-114.2 \mathrm{~kJ}\) (5) \(\mathrm{N}_{2} \mathrm{O}_{5}(s) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}(g)\) $$\Delta H_{\mathrm{ran}}^{\circ}=54.1 \mathrm{~kJ}$$calculate the standard enthalpy of reaction for$$\mathrm{N}_{2} \mathrm{O}_{3}(g)+\mathrm{N}_{2} \mathrm{O}_{5}(s) \longrightarrow 2 \mathrm{~N}_{2} \mathrm{O}_{4}(g) $$
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