Problem 90 - General Chemistry

Question

Hydrogen is an ideal fuel in many respects; for example, the product of its combustion, water, is nonpolluting. The heat given off in burning hydrogen to gaseous water is \(5.16 \times 10^{4}\) Btu per pound. What is this heat energy in joules per gram? ( 1 Btu = 252 cal; see also Table \(1.4 .\) )

Step-by-Step Solution

Answer

Heat energy is approximately 60000 J/g.

Step 1: Convert Btu to Calories

First, we need to convert the energy given in Btu to calories. Given: \[ \text{Heat energy in Btu} = 5.16 \times 10^4 \text{ Btu} \]\[ \text{1 Btu} = 252 \text{ calories} \]So,\[ \text{Heat energy in calories} = 5.16 \times 10^4 \times 252 \text{ cal} \]

Step 2: Convert Calories to Joules

Next, we need to convert the energy from calories to joules. Given:\[ \text{1 calorie} = 4.184 \text{ Joules} \]Calculating:\[ \text{Heat energy in joules} = (5.16 \times 10^4 \times 252) \times 4.184 \text{ J} \]

Step 3: Convert Pounds to Grams

We need to convert the mass from pounds to grams.Given:\[ 1 \text{ pound} = 453.592 \text{ grams} \]So,\[ \text{Mass in grams} = 453.592 \text{ grams} \]

Step 4: Calculate Heat Energy per Gram

Finally, we find the heat energy per gram by dividing the total energy in joules by the mass in grams.So,\[ \text{Heat energy per gram} = \frac{5.16 \times 10^4 \times 252 \times 4.184}{453.592} \text{ J/g} \]

Key Concepts

Calories to Joules

Energy can be expressed in various units, and understanding how to convert between them is essential in many scientific calculations. One common unit is the calorie, which is often used in areas like nutrition and chemistry. However, the joule is the international standard unit of energy. In the context of energy conversion, this might come up when you're dealing with heat energy calculations or biochemical energy exchanges.
To convert calories to joules, you use the conversion factor:

• 1 calorie = 4.184 joules.

This conversion is straightforward: simply multiply the number of calories by 4.184 to get the equivalent energy in joules. It's crucial in both scientific experiments and practical applications, especially when dealing with thermal processes or when performing calculations that require a common unit for accurate results.

Btu to Calories

British Thermal Units (Btu) are commonly used in heating and cooling applications, especially in engineering and some thermodynamics problems. However, often calculations might require or be more convenient in calories, which necessitates a conversion. The conversion factor between Btu and calories is:

• 1 Btu = 252 calories.

To convert energy expressed in Btu to calories, multiply the Btu value by 252. This is particularly useful in energy assessments, engineering projects, or when you're trying to align with specific scientific fields that predominantly use calories.

Hydrogen Combustion

Hydrogen combustion is a unique chemical reaction due to the fact that its only by-product is water, making it a clean energy source. This process involves hydrogen (H₂) reacting with oxygen (O₂) to form water (H₂O), releasing energy as heat.

• The reaction is: 2H₂ + O₂ → 2H₂O + Energy.

This energy release is characterized by its quantity, which is often quantified in energy units like Btu, calories, or joules. The high energy yield and non-polluting nature of hydrogen make it an attractive alternative fuel. Understanding its combustion process and energy output is key to leveraging hydrogen as a viable energy source, significantly impacting areas like renewable energy development and clean technology.

Mass Conversion

Mass conversion is a fundamental skill required when dealing with units in scientific calculations, particularly when you need to use consistent units across different parts of a problem. The conversion from pounds to grams, for instance, is necessary when you're working between the imperial and metric systems.

• 1 pound = 453.592 grams.

This conversion factor allows you to translate mass given in pounds to grams, a metric unit that is often used in scientific calculations. Converting units of mass is critical in ensuring the accuracy of calculations, especially in contexts like chemistry or physics, where precise measurements directly impact results and conclusions. It's an essential skill for correctly interpreting and working through problems in these disciplines.