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Chapter 8: Problem 8

Urea, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\), is used in the manufacture of resins and glues. When \(5.00 \mathrm{~g}\) of urea is dissolved in \(250.0 \mathrm{~mL}\) of water \((d=1.00 \mathrm{~g} / \mathrm{mL})\) at \(30.0^{\circ} \mathrm{C}\) in a coffee-cup calorimeter, \(27.6 \mathrm{~kJ}\) of heat is absorbed. (a) Is the solution process exothermic? (b) What is \(q_{\mathrm{H}_{2} \mathrm{O}}\) ? (c) What is the final temperature of the solution? (Specific heat of water is \(4.18 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\).) (d) What are the initial and final temperatures in \({ }^{\circ} \mathrm{F}\) ?

Short Answer

Expert verified
What are the initial and final temperatures of the solution in 掳C and 掳F? Answer: The solution process is endothermic as it absorbs heat. The heat absorbed by water during the dissolution is 27,600 J. The initial temperature is 30.0掳C (86.0掳F) and the final temperature is 56.4掳C (133.5掳F).

Step by step solution

01

(a) Identifying the process as exothermic or endothermic

Since the heat is absorbed (instead of being released) during the solution process, the process is endothermic (not exothermic).
02

(b) Finding the heat absorbed by water, \(q_{H_2O}\)

Since the process is endothermic and absorbs 27.6 kJ (or 27600 J) of heat, the heat absorbed by the water during the solution process can be represented as: \(q_{H_2O} = 27600 \ \text{J}\).
03

(c) Calculating the final temperature of the solution

To find the final temperature of the solution, we can use the formula for heat transfer: \(q = mc螖T\), where \(q\) is the heat absorbed or released, \(m\) is the mass of the substance, \(c\) is the specific heat, and \(螖T\) is the change in temperature. In this case, the mass of water (\(m\)) is 250.0 g (since the density of water is 1.00 g/mL), the initial temperature (\(T_i\)) is 30.0掳C, and the specific heat of water (\(c\)) is 4.18 J/g路掳C. We can rearrange the formula to solve for the change in temperature (\(螖T\)): \(螖T = \frac{q}{mc} = \frac{27600 \ \text{J}}{250.0 \ \text{g} \cdot 4.18 \ \text{J/g} \cdot{ }^{\circ} \mathrm{C}} = \frac{27600}{1045} = 26.4{ }^{\circ} \mathrm{C}\) Now we can find the final temperature (\(T_f\)) by adding the change in temperature to the initial temperature: \(T_f = T_i + 螖T = 30.0{ }^{\circ} \mathrm{C} + 26.4{ }^{\circ} \mathrm{C} = 56.4{ }^{\circ} \mathrm{C}\)
04

(d) Converting the initial and final temperatures to 掳F

To convert the initial and final temperatures from 掳C to 掳F, we can use the formula: \(T_{(掳F)} = T_{(掳C)} \cdot \frac{9}{5} + 32\) For the initial temperature: \(T_i{(}^\circ F{)} = 30.0{ }^\circ C \cdot \frac{9}{5} + 32 = 54{ }^\circ F\) For the final temperature: \(T_f{(}^{\circ}F{)} = 56.4{ }^{\circ} \mathrm{C} \cdot \frac{9}{5} + 32 = 133.5{ }^{\circ} \mathrm{F}\)

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Key Concepts

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

Endothermic Process
An endothermic process is one in which the system absorbs heat from its surroundings. Imagine you're dissolving urea in water and the solution feels cold鈥攊t means the system took in heat. This absorption of heat is a hallmark of an endothermic process.
The energy required is absorbed rather than released, as is typical in exothermic processes. In the context of the provided exercise, since 27.6 kJ of heat was absorbed when dissolving urea, we can confidently say this is an endothermic process.
Here's the takeaway:
  • If the heat flows into a system, it's endothermic.
  • The surroundings will lose heat as the system absorbs it.
Understanding this helps us classify chemical processes and predict how systems will behave in various conditions.
Heat Transfer Calculations
In thermodynamics, calculating heat transfer involves understanding how heat energy moves through substances. To determine the heat absorbed or released, we utilize the formula: \[ q = mc\Delta T \] where \(q\) is the heat transferred, \(m\) is the mass of the substance, \(c\) is the specific heat capacity, and \(\Delta T\) is the temperature change.
In the example of our urea solution, the heat absorbed by the water was 27.6 kJ, translating to 27600 J. This is the direct heat transfer during the process.
Key points to note:
  • Use this formula to calculate how much heat is exchanged.
  • Make sure to convert all units to match鈥攋oules for energy and grams for mass, for example.
  • Understanding the context: knowing if a process is exothermic or endothermic can guide your calculation direction (i.e., increase or decrease in temperature).
These calculations help predict temperature changes resulting from chemical reactions or physical changes.
Specific Heat Capacity
Specific heat capacity is the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius. It's an intrinsic property that varies among different substances.
Water, for instance, has a specific heat capacity of 4.18 J/g路掳C, meaning it takes 4.18 Joules of energy to raise the temperature of 1 gram of water by 1掳C. This high capacity plays a crucial role in everyday phenomena and also in scientific experiments.
In practical terms:
  • A higher specific heat capacity means a substance can absorb more heat without drastically changing its temperature.
  • Substances with lower specific heat can heat up or cool down rapidly.
By understanding this concept, one can predict how different substances will respond to thermal energy inputs in various processes.
Temperature Conversion
Temperature conversions are useful when comparing measurements taken in different units. The most common conversions involve Fahrenheit and Celsius, two widely used temperature scales.
For converting Celsius to Fahrenheit, use the formula:\[ T_{(掳F)} = T_{(掳C)} \times \frac{9}{5} + 32 \]This formula converts a temperature from degrees Celsius to degrees Fahrenheit. In the exercise, the initial and final temperatures needed conversion:
  • The initial 30掳C converts to 54掳F.
  • The final 56.4掳C converts to approximately 133.5掳F.
Key points for conversion:
  • Always ensure you have the correct conversion formula for the scales you're dealing with.
  • Check your calculations鈥攕mall errors can lead to significant inaccuracies in scientific contexts.
  • Understanding this allows seamless communication across different scientific communities that may prefer one scale over another.
Temperature conversion helps provide easily understandable data across various metric systems.

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Most popular questions from this chapter

Which statement(s) is/are true about bond enthalpy? (a) Energy is required to break a bond. (b) \(\Delta H\) for the formation of a bond is always a negative number. (c) Bond enthalpy is defined only for bonds broken or formed in the gaseous state. (d) Because the presence of \(\pi\) bonds does not influence the geometry of a molecule, the presence of \(\pi\) bonds does not affect the value of the bond enthalpy between two atoms either. (e) The bond enthalpy for a double bond between atoms \(A\) and \(B\) is twice that for a single bond between atoms \(\mathrm{A}\) and \(\mathrm{B}\).

A typical fat in the body is glyceryl trioleate, \(\mathrm{C}_{57} \mathrm{H}_{104} \mathrm{O}_{6}\). When it is metabolized in the body, it combines with oxygen to produce carbon dioxide, water, and \(3.022 \times 10^{4} \mathrm{~kJ}\) of heat per mole of fat. (a) Write a balanced thermochemical equation for the metabolism of fat. (b) How many kilojoules of energy must be evolved in the form of heat if you want to get rid of five pounds of this fat by combustion? (c) How many nutritional calories is this? (1 nutritional calorie = \(1 \times 10^{3}\) calories)

Nitrogen oxide (NO) has been found to be a key component in many biological processes. It also can react with oxygen to give the brown gas \(\mathrm{NO}_{2}\). When one mole of NO reacts with oxygen, \(57.0 \mathrm{~kJ}\) of heat is evolved. (a) Write the thermochemical equation for the reaction between one mole of nitrogen oxide and oxygen. (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.)

To produce silicon, used in semiconductors, from sand \(\left(\mathrm{SiO}_{2}\right)\), a reaction is used that can be broken down into three steps: $$ \begin{aligned} \mathrm{SiO}_{2}(s)+2 \mathrm{C}(s) \longrightarrow \mathrm{Si}(s)+2 \mathrm{CO}(g) & & \Delta H=689.9 \mathrm{~kJ} \\ \mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SiCl}_{4}(g) & & \Delta H=-657.0 \mathrm{~kJ} \\ \mathrm{SiCl}_{4}(g)+2 \mathrm{Mg}(s) \longrightarrow 2 \mathrm{MgCl}_{2}(s)+\mathrm{Si}(s) & & \Delta H=-625.6 \mathrm{~kJ} \end{aligned} $$ (a) Write the thermochemical equation for the overall reaction for the formation of silicon from silicon dioxide; \(\mathrm{CO}\) and \(\mathrm{MgCl}_{2}\) are byproducts. (b) What is \(\Delta H\) for the formation of one mole of silicon? (c) Is the overall reaction exothermic?

Titanium is a metal used in jet engines. Its specific heat is \(0.523 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\). If \(5.88 \mathrm{~g}\) of titanium absorbs \(4.78 \mathrm{~J}\), what is the change in temperature?
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