At 1 atm, how much energy is required to heat 67.0 g of H2O(s) at –14.0 °C to H2O(g) at 115.0 °C?
Please explain, I'm not very good at Chemistry and this problem is giving me a headache. Thank you!
There are two equations you need and you do each in steps.
For moving from one T to another in the same phase, the formula is
q = heat needed = mass H2O x specific heat H2O x (Tfinal-Tinitial). For example, to move 67.0 g water from zero C to 100 C, heat needed is
q = 67.0 x 4.184 J/g*C x (100-0) = ?. Notice what I mean by the same phase. It is liquid from zero C to 100 C.
The other equation you need is ast the phase change. There are two phase changes in water for the temperatures in the problem. From ice at zero C to liquid H2O at zero C it is
q = mass H2 x heat fusion.
The other phase change is at 100 C. It changes from liquid water to steam at 100 C. That one is the same form but is
q = mass H2O x heat vaporization.
So you have same phase from -14 C to zero C(that's all ice phase or solid). Then a phase change at zero C from solid to liquid. Same phase from zero C to 100 C (all liquid). Phase change at 100 C to steam. Then same phase from 100 C steam to 115 C steam. Then add all of the qs together.
Any of the heat problems like this are worked the same way. Those two equations will work hundreds of questions.
To find the energy required to heat water from -14.0 °C to 115.0 °C, we need to use the specific heat formula and take into account the phase changes involved.
Step 1: Determine the energy required to heat the ice from -14.0 °C to 0 °C.
To do this, we need to use the formula Q = m * C * ΔT, where Q is the heat energy, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
The specific heat capacity of ice is 2.09 J/g°C, so we can calculate the energy required to heat the ice:
Q_ice = m * C * ΔT
Q_ice = 67.0 g * 2.09 J/g°C * (0 °C - (-14.0 °C))
Step 2: Determine the energy required to melt the ice.
To convert the ice at 0 °C to water at 0 °C, we need to calculate the heat energy required for the phase change using the formula:
Q_melt = m * ΔH_fusion
The enthalpy of fusion, ΔH_fusion, for water is 334 J/g. So, we can calculate the energy required to melt the ice:
Q_melt = 67.0 g * 334 J/g
Step 3: Determine the energy required to heat the water from 0 °C to 100 °C.
Once the ice has melted, we need to consider the energy required to heat the water from 0 °C to 100 °C:
Q_water = m * C * ΔT
Q_water = 67.0 g * 4.18 J/g°C * (100 °C - 0 °C)
Step 4: Determine the energy required to vaporize the water.
To convert the water at 100 °C to steam at 100 °C, we need to calculate the heat energy required for the phase change using the formula:
Q_vaporize = m * ΔH_vaporization
The enthalpy of vaporization, ΔH_vaporization, for water is 2260 J/g. So, we can calculate the energy required to vaporize the water:
Q_vaporize = 67.0 g * 2260 J/g
Step 5: Determine the energy required to heat the steam from 100 °C to 115 °C.
Finally, we need to consider the energy required to heat the steam from 100 °C to 115 °C:
Q_steam = m * C * ΔT
Q_steam = 67.0 g * 2.03 J/g°C * (115 °C - 100 °C)
Now that we have calculated the values for each step, we can add them together to find the total energy required:
Total energy required = Q_ice + Q_melt + Q_water + Q_vaporize + Q_steam
Simply plug in the values and perform the arithmetic to find the answer.