What amount of heat (in kJ) is required to convert 14.7 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/g °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:**
*What amount of heat (in kJ) is required to convert 14.7 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/g·°C
- ΔHvap = 22.5 kJ/mol
- Normal boiling point, Tb = 57.3 °C
**Explanation of Terms:**
- **MM (Molar Mass):** The mass of one mole of a substance, provided as 83.21 g/mol.
- **Specific Heat Capacity:** The amount of heat required to raise the temperature of 1 gram of a substance by 1 °C. It is given for both the liquid and gas phases.
- **ΔHvap (Enthalpy of Vaporization):** The amount of heat required to convert one mole of a liquid into its vapor without a temperature change, provided as 22.5 kJ/mol.
- **Normal Boiling Point (Tb):** The temperature at which the liquid boils under a pressure of 1 atmosphere, given as 57.3 °C.
**Solution Approach:**
To solve this problem, you need to calculate the total heat required in three steps:
1. **Heating the Liquid from 19.2 °C to 57.3 °C (Boiling Point):**
- Use the formula \( q = m \times c \times \Delta T \) where \( m \) is mass, \( c \) is specific heat capacity, and \( \Delta T \) is the change in temperature.
2. **Vaporizing the Liquid at Boiling Point:**
- Use the formula \( q = n \times \Delta H_{vap} \) where \( n \) is the number of moles and \( \Delta H_{vap} \) is the enthalpy of vaporization.
3. **Heating the Gas from 57.3 °C to 93.5 °C:**
- Again, use the formula \( q = m \times c \times \Delta T \).
Make sure the units are consistent throughout the calculations, converting grams to moles where necessary and joules to kilojoules for the final](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0c7c0e9-1042-4b47-9e78-c6aaeaae6479%2Fbde918c6-9eff-4c4a-949a-5659f9e168bb%2F9jyongk_processed.png&w=3840&q=75)
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