A 50.0 g sample of Chromium metal was heated to 103 degrees Celcius and then dropped into a beaker containing 76.0 g of water at 25.0 degrees Celcius. If the specific heat of Chromium metal is 0.110 cal/g C, what will be the equilibrium temperature of the Chromium-Water mixture? (Cwater = 1 cal/g °C)
Thermochemistry
Thermochemistry can be considered as a branch of thermodynamics that deals with the connections between warmth, work, and various types of energy, formed because of different synthetic and actual cycles. Thermochemistry describes the energy changes that occur as a result of reactions or chemical changes in a substance.
Exergonic Reaction
The term exergonic is derived from the Greek word in which ‘ergon’ means work and exergonic means ‘work outside’. Exergonic reactions releases work energy. Exergonic reactions are different from exothermic reactions, the one that releases only heat energy during the course of the reaction. So, exothermic reaction is one type of exergonic reaction. Exergonic reaction releases work energy in different forms like heat, light or sound. For example, a glow stick releases light making that an exergonic reaction and not an exothermic reaction since no heat is released. Even endothermic reactions at very high temperature are exergonic.
![**Problem Statement:**
A 50.0 g sample of Chromium metal was heated to 103 degrees Celsius and then dropped into a beaker containing 76.0 g of water at 25.0 degrees Celsius. If the specific heat of Chromium metal is 0.110 cal/g°C, what will be the equilibrium temperature of the Chromium-Water mixture? (C_water = 1 cal/g°C)
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In this physics and chemistry problem, you're asked to find the final equilibrium temperature when a hot metal (Chromium) is mixed with cooler water. Below are the relevant details extracted from the problem for clarity:
- Mass of Chromium (m_Cr): 50.0 g
- Initial temperature of Chromium (T_initial_Cr): 103°C
- Specific heat of Chromium (C_Cr): 0.110 cal/g°C
- Mass of water (m_water): 76.0 g
- Initial temperature of water (T_initial_water): 25°C
- Specific heat of water (C_water): 1 cal/g°C
The goal is to determine the final equilibrium temperature (T_final) of the combined Chromium-Water mixture.
To solve this, you would typically use the formula for heat transfer and assume that the heat lost by the Chromium equals the heat gained by the water:
\[ q_{Cr} = -q_{water} \]
Where:
- \( q = mc\Delta T \)
- \( \Delta T = T_{final} - T_{initial} \)
### Detailed Solution Process:
1. Write the heat loss equation for Chromium:
\[ q_{Cr} = m_{Cr} \cdot C_{Cr} \cdot (T_{final} - T_{initial_{Cr}}) \]
2. Write the heat gain equation for water:
\[ q_{water} = m_{water} \cdot C_{water} \cdot (T_{final} - T_{initial_{water}}) \]
3. Set the heat loss equal to the heat gain and solve for \( T_{final} \):
\[ m_{Cr} \cdot C_{Cr} \cdot (T_{final} - T_{initial_{Cr}}) = - (m_{water} \cdot C_{water} \cdot (T_{final} - T_{initial_{water}})) \]
### Substitute the given values and solve:
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