Question

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

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

Step-by-step solution

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

Understand the Given Heat in Kilojoules

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

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.

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.

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.

Key concepts

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.