What amount of heat (in kJ) is required to convert 10.7 g of an unknown liquid (MM = 83.21 g/mol) at 19.2 °C to a gas at 93.5 °C? (specific heat capacity of liquid = 1.58 J/g. °C; specific heat capacity of gas = 0.932 J/9•°C; AHvap = 22.5 kJ/mol; normal boiling point, Tb = 57.3°C)
Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
![**Problem Statement for an Educational Website:**
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**Title: Calculating the Heat Required for Phase Transition and Temperature Change**
**Objective:**
Determine the amount of heat (in kJ) needed to convert 10.7 g of an unknown liquid to a gas, given the initial and final temperatures, specific heat capacities of both the liquid and gas phases, the enthalpy of vaporization, and the boiling point of the liquid.
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**Background Information:**
1. **Given Data:**
- Mass of liquid: 10.7 g
- Molar Mass (MM): 83.21 g/mol
- Initial Temperature: 19.2 °C
- Final Temperature: 93.5 °C
- Specific Heat Capacity of Liquid (c_liq): 1.58 J/g⋅°C
- Specific Heat Capacity of Gas (c_gas): 0.932 J/g⋅°C
- Enthalpy of Vaporization (ΔHvap): 22.5 kJ/mol
- Normal Boiling Point (Tb): 57.3 °C
2. **Concepts Used:**
- **Specific Heat Capacity**: Quantity of heat needed to change the temperature of 1 gram of a substance by 1°C.
- **Enthalpy of Vaporization (ΔHvap)**: Heat required to convert 1 mole of liquid to gas at its boiling point.
3. **Required Calculations:**
- Heat required to raise the temperature of the liquid to boiling point.
- Heat required for phase change from liquid to gas.
- Heat required to raise the temperature of the gas to the final temperature.
**Steps:**
1. Calculate the heat needed to raise the temperature of the liquid to its boiling point.
2. Calculate the heat required for the phase transition at the boiling point.
3. Calculate the heat needed to raise the temperature of the gas from the boiling point to the final temperature.
4. Sum all the calculated heats to find the total heat required.
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**Explanation Steps:**
1. **Heat to raise temperature of the liquid to boiling point (q1):**
\[
q_1 = m \cdot c_{liq} \cdot \Delta T_{liq}
\]
where \( \Delta T_{liq} = Tb - T_{initial} \).
2. **](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d924445-39e4-4bb2-9286-0ab6470dbf21%2F47f908b6-7898-44c3-8b9e-f5e2501cbc6a%2Frvk80p_processed.jpeg&w=3840&q=75)
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