Calculate the energy that must be removed to convert substance X from a gas at 116°C to a solid -44.6°C. Assume X has a molar mass of 75.0 g/mol.
ÄHvap 20. kJ/mol
C(s) 3.0 J/g·°C
ÄHfus 5.0 kJ/mol
C(l) 2.5 J/g·°C
bp 75°C
C(g) 1.0 J/g·°C
mp -15°C
please help! what formulas do i use?
For change of phase (example of vapor to liquid or liquid to a solid) use
q = mass x heat vaporization.
For the change in q with a single phase, (vapor or liquid or solid),
q = mass x specific heat x (delta T).
Then you add all of them together.
BUT, I don't think you can work this problem until you know how many grams (or how many mols) of substance X you have.
To solve this problem, you will need to calculate the energy needed to cool substance X from a gas at 116°C to a solid at -44.6°C. You can break down the problem into several steps and use the given data and formulas to calculate the energy at each step.
Step 1: Calculate the energy needed to cool substance X from a gas at 116°C to its boiling point of 75°C.
To calculate this energy, you can use the formula:
Q = mcΔT
Where Q is the energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, the specific heat capacity of substance X in the gaseous state is given as 1.0 J/g·°C, and the mass (molar mass) of substance X is given as 75.0 g/mol.
First, calculate the change in temperature (ΔT):
ΔT = Tf - Ti
ΔT = (75°C) - (116°C) = -41°C
Next, plug in the values into the formula:
Q1 = mcΔT
Q1 = (75.0 g/mol) x (1.0 J/g·°C) x (-41°C)
Q1 = -3075 J/mol
Step 2: Calculate the energy needed to vaporize substance X at its boiling point of 75°C.
To calculate this energy, you can use the given heat of vaporization (ÄHvap) value, which is given as 20 kJ/mol.
Q2 = ÄHvap
Q2 = 20 kJ/mol = 20000 J/mol
Note: Remember to convert the given value from kJ/mol to J/mol.
Step 3: Calculate the energy needed to cool substance X from a gas at the boiling point of 75°C to a gas at -15°C.
To calculate this energy, you can use the same formula as Step 1, but with different temperature values.
First, calculate the change in temperature (ΔT):
ΔT = Tf - Ti
ΔT = (-15°C) - (75°C) = -90°C
Next, plug in the values into the formula:
Q3 = mcΔT
Q3 = (75.0 g/mol) x (1.0 J/g·°C) x (-90°C)
Q3 = -6750 J/mol
Step 4: Calculate the energy needed to cool substance X from a gas at -15°C to a solid at -44.6°C.
To calculate this energy, you can use the formula as in Step 1.
First, calculate the change in temperature (ΔT):
ΔT = Tf - Ti
ΔT = (-44.6°C) - (-15°C) = -29.6°C
Next, plug in the values into the formula:
Q4 = mcΔT
Q4 = (75.0 g/mol) x (1.0 J/g·°C) x (-29.6°C)
Q4 = -2220 J/mol
Step 5: Calculate the energy needed to convert substance X from a gas at -44.6°C to a solid at -44.6°C.
To calculate this energy, you can use the given heat of fusion (ÄHfus) value, which is given as 5.0 kJ/mol.
Q5 = ÄHfus
Q5 = 5.0 kJ/mol = 5000 J/mol
Note: Remember to convert the given value from kJ/mol to J/mol.
Finally, to calculate the total energy needed for the entire process, you need to sum up all the energies calculated in the previous steps:
Total Energy = Q1 + Q2 + Q3 + Q4 + Q5
Total Energy = -3075 J/mol + 20000 J/mol - 6750 J/mol - 2220 J/mol + 5000 J/mol
Total Energy = 8755 J/mol
So, the total energy that must be removed to convert substance X from a gas at 116°C to a solid -44.6°C is 8755 J/mol.