Calculate the energy that must be removed to convert substance X from a gas at 115°C to a solid -50.7°C. Assume X has a molar mass of 75.0 g/mol.
Specific heat capacities
ΔHvap 20. kJ/mol C(s) 3.0 J/g · °C
ΔHfus 5.0 kJ/mol C(l) 2.5 J/g · °C
bp 75°C C(g) 1.0 J/g · °C
mp −15°C
If you can go step by step so I can understand how this is done That would be great! Thanks
You must know how many grams or how many moles you have initially. If moles, ok. If mass, convert mass to moles.
q1 = heat removed to move from 115 C to b.p.
q1 = mols x specific heat vapor x (Tfinal-Tinitial).
q2 = heat removed to convert vapor to liquid.
q2 = moles x heat vaporization.
q3 = heat removed to move from b.p. to melting point.
q3 = moles x specific heat liquid x (Tfinal - Tinitial).
q4 = heat removed to freeze liquid at m.p.
q4 = moles x heat fusion.
q5 = heat removed to move from m.p. to -50.7.
q5 = moles x specific heat solid x (Tfinal-Tinitial).
qtotal = q1+q2+q3+q4+q5
To calculate the energy required to convert substance X from a gas at 115°C to a solid at -50.7°C, we need to consider the following steps:
1. Determine the energy to cool the gas from 115°C to the boiling point.
2. Calculate the energy to condense the gas at the boiling point.
3. Determine the energy to cool the liquid from the boiling point to the melting point.
4. Calculate the energy to solidify the liquid at the melting point.
5. Determine the energy to cool the solid from the melting point to -50.7°C.
Step 1: Determine the energy to cool the gas from 115°C to the boiling point.
The specific heat capacity of the gas (C(g)) is given as 1.0 J/g · °C.
The boiling point (bp) of substance X is given as 75°C.
The energy required to cool the gas can be calculated using the formula:
q1 = m × C(g) × ΔT1
Where:
q1 = energy
m = mass of substance X
ΔT1 = change in temperature from 115°C to the boiling point (75°C)
Step 2: Calculate the energy to condense the gas at the boiling point.
The enthalpy of vaporization (ΔHvap) of substance X is given as 20.0 kJ/mol.
The energy required to condense the gas can be calculated using the formula:
q2 = n × ΔHvap
Where:
q2 = energy
n = number of moles of substance X
Step 3: Determine the energy to cool the liquid from the boiling point to the melting point.
The specific heat capacity of the liquid (C(l)) is given as 2.5 J/g · °C.
The melting point (mp) of substance X is given as -15°C.
The energy required to cool the liquid can be calculated using the formula:
q3 = m × C(l) × ΔT3
Where:
q3 = energy
m = mass of substance X
ΔT3 = change in temperature from the boiling point (75°C) to the melting point (-15°C)
Step 4: Calculate the energy to solidify the liquid at the melting point.
The enthalpy of fusion (ΔHfus) of substance X is given as 5.0 kJ/mol.
The energy required to solidify the liquid can be calculated using the formula:
q4 = n × ΔHfus
Where:
q4 = energy
n = number of moles of substance X
Step 5: Determine the energy to cool the solid from the melting point to -50.7°C.
The specific heat capacity of the solid (C(s)) is given as 3.0 J/g · °C.
The energy required to cool the solid can be calculated using the formula:
q5 = m × C(s) × ΔT5
Where:
q5 = energy
m = mass of substance X
ΔT5 = change in temperature from the melting point (-15°C) to -50.7°C
Finally, to calculate the total energy required to convert substance X from a gas at 115°C to a solid at -50.7°C, we need to sum up the energies from each step:
Total energy = q1 + q2 + q3 + q4 + q5
Please provide the mass or number of moles of substance X so that we can perform the calculations.
To calculate the energy required to convert substance X from a gas at 115°C to a solid at -50.7°C, we need to consider the energy changes at each step of the process: gas to liquid, liquid to solid, and temperature changes within each phase.
1. Energy to cool the gas from 115°C to its boiling point (bp) at 75°C:
To calculate this energy, we need to find the heat capacity of the gas phase, which is given as 1.0 J/g · °C. We also need to know the mass and the temperature change.
First, we need to convert the molar mass of X from g/mol to g/given mass. Given that the molar mass is 75.0 g/mol, we can convert it to g/g by dividing 75.0 g/mol by the given mass of X.
2. Energy to condense the gas at its boiling point to a liquid at -15°C:
To calculate this energy, we need to know the enthalpy of vaporization (ΔHvap), which is given as 20 kJ/mol, and the mass of X.
We can convert the mass of X to moles using the molar mass, which is 75.0 g/mol. Then, multiply the moles by the enthalpy of vaporization to find the energy required for the phase change.
3. Energy to cool the liquid from -15°C to its melting point (mp) at -50.7°C:
To calculate this energy, we need to find the heat capacity of the liquid phase, which is given as 2.5 J/g · °C. We also need to know the mass and the temperature change.
4. Energy to freeze the liquid at its melting point to a solid:
To calculate this energy, we need to know the enthalpy of fusion (ΔHfus), which is given as 5.0 kJ/mol, and the mass of X.
We can convert the mass of X to moles using the molar mass, which is 75.0 g/mol. Then, multiply the moles by the enthalpy of fusion to find the energy required for the phase change.
Once you have calculated each of these energies, you can sum them to find the total energy required to convert substance X from a gas at 115°C to a solid at -50.7°C.