At 1 atm, how much energy is required to heat 43.0 g of H2O(s) at –22.0 °C to H2O(g) at 169.0 °C?
Do this in steps.
Within a single phase use
q = mass x specific heat x (Tfinal-Tinitial).
For example. For ice at -22.0C to ice at 0C, it will be
q = 43.0g H2O x specific heat ice x [0-(-22] = ?
At a phase change use
q = mass x heat fusion (at melting point) or
q = mass x heat vaporization (at boiling point).
For example.
At zero C, the melting point of ice,
q = 43.0g x heat fusion = ?
Another within the phase from zero C to 100 C for liquid water.
Another phase change at 100 from liquid to vapor.
Another within the phase (gas at 100) from 100 C to 169.0C (gas at 169.0).
Then add all of the q values together.
To find the amount of energy required to heat a substance, we can use the equation:
Q = mcΔT
Where:
Q is the heat energy (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in J/g°C)
ΔT is the change in temperature (in °C)
First, let's calculate the heat energy required to heat the ice (H2O(s)) to its melting point of 0 °C. At this stage, the ice is still in a solid state.
Q1 = mcΔT
= (43.0 g) (2.09 J/g°C) (0 °C - (-22.0 °C)) [Using the specific heat capacity of ice]
Next, we calculate the heat energy required to melt the ice. The equation for this is:
Q2 = mL
= (43.0 g) (334 J/g) [Using the heat of fusion for water]
Now that the ice has melted to water (H2O(l)) at 0 °C, we calculate the heat energy required to raise the temperature of the water from 0 °C to 100 °C. This can be done using the specific heat capacity of liquid water.
Q3 = mcΔT
= (43.0 g) (4.18 J/g°C) (100 °C - 0 °C) [Using the specific heat capacity of water]
At this stage, the water is still in a liquid state. Now, we calculate the heat energy required to convert the water to steam (H2O(g)) at 100 °C, using the equation:
Q4 = mL
= (43.0 g) (2260 J/g) [Using the heat of vaporization for water]
Finally, we calculate the heat energy required to raise the temperature of steam from 100 °C to 169 °C, using the specific heat capacity of water vapor.
Q5 = mcΔT
= (43.0 g) (1.99 J/g°C) (169 °C - 100 °C) [Using the specific heat capacity of steam]
To find the total heat energy required, we sum up all the individual calculations:
Total heat energy = Q1 + Q2 + Q3 + Q4 + Q5
Simply substitute the values into the equations above and perform the necessary calculations to find the total heat energy required in joules.