Problem 170 - Introductory Chemistry Atoms First

Question

Convert to cal \(/ \mathrm{g} \cdot{ }^{\circ} \mathrm{C}:\) (a) \(1.04 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\) (the specific heat of nitrogen gas) (b) \(0.84 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\) (the specific heat of carbon dioxide gas)

Step-by-Step Solution

Answer

(a) The specific heat of nitrogen gas in cal/g°C is approximately 0.2486 cal/g°C. (b) The specific heat of carbon dioxide gas in cal/g°C is approximately 0.2008 cal/g°C.

Step 1: Identify the given value

The specific heat of nitrogen gas is given as 1.04 J/g°C.

Step 2: Apply the conversion factor

Divide the given specific heat value by the conversion factor: Specific heat in cal/g°C = \(\frac{1.04 \mathrm{~J}}{4.184 \mathrm{~J/cal}}\)

Step 3: Calculate the specific heat in cal/g°C

Perform the division: Specific heat in cal/g°C = 1.04 / 4.184 ≈ 0.2486 (b) Conversion of 0.84 J/g°C to cal/g°C (specific heat of carbon dioxide gas)

Step 1: Identify the given value

The specific heat of carbon dioxide gas is given as 0.84 J/g°C.

Step 2: Apply the conversion factor

Divide the given specific heat value by the conversion factor: Specific heat in cal/g°C = \(\frac{0.84 \mathrm{~J}}{4.184 \mathrm{~J/cal}}\)

Step 3: Calculate the specific heat in cal/g°C

Perform the division: Specific heat in cal/g°C = 0.84 / 4.184 ≈ 0.2008 In conclusion: (a) The specific heat of nitrogen gas in cal/g°C is approximately 0.2486 cal/g°C. (b) The specific heat of carbon dioxide gas in cal/g°C is approximately 0.2008 cal/g°C.

Key Concepts

Energy Conversion in Thermochemistry

Understanding energy conversion is crucial when studying thermochemistry, a branch of chemistry that deals with the heat involved during chemical reactions and phase changes. Energy can be measured in various units, with joules (J) and calories (cal) being common. One calorie is defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius at a pressure of one atmosphere.

To draw parallels, imagine energy as currency that can be exchanged in different forms; like dollars to euros, energy units can be converted too. In thermochemistry, we often need to convert energy units to align with the standard or preferred units used in a given context, such as converting joules to calories in calorimetry. This allows for a more standardized interpretation of heat energy changes associated with chemical processes.

Calorimetry and Its Importance

Delving into the intricacies of calorimetry, it's a method that enables us to measure the heat of chemical reactions or physical changes as well as heat capacity. The core apparatus for this experimental technique is a calorimeter, which basically isolates a system to accurately determine the transfer of energy as heat.

Calorimetry falls under the study of thermodynamics and directly concerns the first law of thermodynamics, which deals with the conservation of energy. The process involves careful attention to temperature changes that occur during the experiment, which are then used to calculate the specific heat capacity of substances or the enthalpy changes in reactions. Remember, specific heat capacity is a property that indicates how much heat energy a substance needs for its temperature to increase by one degree.

Thermochemistry: Specific Heat

In the realm of thermochemistry, the concept of specific heat plays a vital role in understanding how substances interact with heat. It's the amount of heat per unit mass required to raise the temperature of a substance by one degree Celsius. Various substances have unique specific heat values, which is indicative of how they absorb and transfer heat. For instance, water has a relatively high specific heat capacity, which is why it's great at regulating temperatures.

When solving problems like the given exercise, it's important to note that the specific heat can be expressed in different units and converting between them (J/g°C to cal/g°C) requires the use of a conversion factor (1 cal = 4.184 J). This fundamental understanding paves the way for students to not merely apply conversion factors, but also appreciate the principles of energy changes that govern the physical world.