How much heat is evolved in converting 1.00 mol of steam at 155.0 ∘C to ice at -45.0 ∘C? The heat capacity of steam is 2.01 J/(g⋅∘C) and of ice is 2.09 J/(g⋅∘C).
Let's see if you can do this yourself.
heat at phase change is
q = mass x heat vaporization at boiling point or
q = mass x heat fusion at freezing point.
Between phases it is
q = mass x specific heat x (Tfinal-Tinitial).
Now you have steam at 155 so it must go "within the phase" to 100 so that is equation 3.
Then you change from steam vapor to steam liquid. That's a phase change at the boiling point. Use equation 1.
Then you change T from 100 to zero C. That's equation 3 again.
At zero it freezes so that's a phase change from liquid to solid and you use equation 2.
Then you go from zero with a solid to -45 with a solid. That's equation again.
Then add all of the q values together.
I'm still not getting the correct answer.
I'm getting 5.65 kJ
Post your work for each step and I'll check it.
Check your arithmetic. I It looks like you have the right digits (close anyway) but off by a factor of 10. You don't show what you're using for delta H vap or delta H fusion. I used 18 g for a mole of H2O, 334J for delta H fusion and 2257J for heat vap and 4.18 for specific heat liquid water.
To find the amount of heat evolved in converting 1.00 mol of steam at 155.0 ∘C to ice at -45.0 ∘C, we can break down the process into two steps:
Step 1: Heat released when steam is cooled from 155.0 ∘C to 0 ∘C.
Step 2: Heat released when water at 0 ∘C is further cooled and converted to ice at -45.0 ∘C.
Step 1: To find the heat released when steam is cooled from 155.0 ∘C to 0 ∘C, we need to calculate the heat capacity of the steam and the mass of steam.
1. Calculate the mass of steam:
To determine the mass of steam, we need to know the molar mass of water. The molar mass of water is approximately 18.02 g/mol.
Given that we have 1.00 mol of steam:
mass of steam = molar mass of water × number of moles
mass of steam = 18.02 g/mol × 1.00 mol
mass of steam = 18.02 g
2. Calculate the heat released when steam is cooled to 0 ∘C:
The heat released can be calculated using the formula Q = m × C × ΔT, where Q is the heat, m is the mass of steam, C is the heat capacity of steam, and ΔT is the change in temperature.
Given:
m = 18.02 g
C = 2.01 J/(g⋅∘C)
ΔT = (0 ∘C - 155.0 ∘C) = -155.0 ∘C
Q1 = m × C × ΔT
Q1 = 18.02 g × 2.01 J/(g⋅∘C) × (-155.0 ∘C)
Q1 ≈ -5565.21 J (rounded to the nearest hundredth)
Step 2: To find the heat released when water at 0 ∘C is further cooled and converted to ice at -45.0 ∘C, we need to calculate the heat capacity of the ice and the mass of water.
1. Calculate the mass of water:
Since water has the same molar mass as steam, the mass of water is also 18.02 g.
2. Calculate the heat released when water is cooled to -45.0 ∘C:
The heat released can be calculated using the formula Q = m × C × ΔT, where Q is the heat, m is the mass of water, C is the heat capacity of ice, and ΔT is the change in temperature.
Given:
m = 18.02 g
C = 2.09 J/(g⋅∘C)
ΔT = (-45.0 ∘C - 0 ∘C) = -45.0 ∘C
Q2 = m × C × ΔT
Q2 = 18.02 g × 2.09 J/(g⋅∘C) × (-45.0 ∘C)
Q2 ≈ -1698.81 J (rounded to the nearest hundredth)
To find the total heat evolved, we need to add the heat released in both steps:
Total heat evolved = Q1 + Q2
Total heat evolved ≈ -5565.21 J + (-1698.81 J) ≈ -7264.02 J
Therefore, the heat evolved in converting 1.00 mol of steam at 155.0 ∘C to ice at -45.0 ∘C is approximately -7264.02 J (rounded to the nearest hundredth). Note that the negative sign indicates that the process releases heat.