Specific heat capacity of solid ethanol is 2.419 J/g C. Melting point temperature of ethanol is -114.4 C/ 158.8 K. Enthalpy of fusion of ethanol is 106.4 J/g. Specific heat capacity of liquid ethanol is 2.440 J/g C. 44.0 g of solid ethanol at -134.4 C is dropped into a Dewar flask containing 325 g of ethanol at -82.5 C. How much energy is transferred from the liquid ethanol to the solid ethanol to raise its temperature from -134.4 C to its melting point temperature, -114.4 C?
at what temperature will 45g of solid dissolve
To find the energy transferred from the liquid ethanol to the solid ethanol to raise its temperature, you need to calculate the heat absorbed by the solid ethanol during this process.
The energy transferred can be calculated using the formula: Q = m * c * ΔT, where:
Q is the energy transferred (in joules),
m is the mass of the substance (in grams),
c is the specific heat capacity of the substance (in J/g°C),
and ΔT is the change in temperature (in °C).
Given data:
Specific heat capacity of solid ethanol (c_s) = 2.419 J/g°C
Mass of solid ethanol (m_s) = 44.0 g
Initial temperature of solid ethanol (T_s_initial) = -134.4°C
Final temperature of solid ethanol (T_s_final) = -114.4°C
Calculating the energy transferred (Q):
ΔT = T_s_final - T_s_initial
ΔT = (-114.4°C) - (-134.4°C)
ΔT = 20°C
Q = m_s * c_s * ΔT
Q = 44.0 g * 2.419 J/g°C * 20°C
Now, substitute the values and calculate Q:
Q = 44.0 g * 2.419 J/g°C * 20°C
Q ≈ 2150.15 J
Therefore, approximately 2150.15 joules of energy is transferred from the liquid ethanol to the solid ethanol to raise its temperature from -134.4°C to -114.4°C.
To calculate the amount of energy transferred from the liquid ethanol to the solid ethanol to raise its temperature from -134.4°C to its melting point temperature (-114.4°C), we'll need to consider the following steps:
Step 1: Calculate the energy required to increase the temperature of solid ethanol from -134.4°C to 0°C (its melting point temperature).
Step 2: Calculate the energy required to melt the solid ethanol at 0°C.
Step 3: Calculate the energy required to increase the temperature of the liquid ethanol from 0°C to -114.4°C.
Step 1: Calculate the energy required to increase the temperature of solid ethanol from -134.4°C to 0°C (its melting point temperature).
Given:
- Specific heat capacity of solid ethanol = 2.419 J/g°C
- Mass of solid ethanol = 44.0 g
- Change in temperature = (0°C - (-134.4°C)) = 134.4°C
Energy required = Mass × Specific heat capacity × Change in temperature
= 44.0 g × 2.419 J/g°C × 134.4°C
≈ 137,791.36 J
Step 2: Calculate the energy required to melt the solid ethanol at 0°C.
Given:
- Enthalpy of fusion of ethanol = 106.4 J/g
- Mass of solid ethanol = 44.0 g
Energy required = Mass × Enthalpy of fusion
= 44.0 g × 106.4 J/g
= 4,681.6 J
Step 3: Calculate the energy required to increase the temperature of the liquid ethanol from 0°C to -114.4°C.
Given:
- Specific heat capacity of liquid ethanol = 2.440 J/g°C
- Mass of liquid ethanol = 325 g
- Change in temperature = (-114.4°C - 0°C) = -114.4°C
Energy required = Mass × Specific heat capacity × Change in temperature
= 325 g × 2.440 J/g°C × (-114.4°C)
≈ -87,883.6 J (negative because energy is transferred from the liquid ethanol)
The total energy transferred from the liquid ethanol to the solid ethanol to raise its temperature from -134.4°C to its melting point temperature of -114.4°C is determined by adding up the energies calculated in each step:
Total energy transferred = Energy for temperature increase (Step 1) + Energy for melting (Step 2) + Energy for temperature decrease (Step 3)
= 137,791.36 J + 4,681.6 J + -87,883.6 J
≈ 54,589.36 J
Therefore, approximately 54,589.36 Joules (J) of energy are transferred from the liquid ethanol to the solid ethanol to raise its temperature from -134.4°C to the melting point temperature of -114.4°C.