At 1 atm, how much energy is required to heat 51.0 g of H2O(s) at –16.0 °C to H2O(g) at 125.0 °C?
heat= heat to heat ice to 0C + heat to melt ice +heat to heat water from 0 to100C+heat to change to vapor+heat to heat vap from 100 t0 125C
You have the mass of all. You need
specific heat of ice
heat of fusion ice
specific heat of water
heat of vaporization water
specific heat of steam
To determine the amount of energy required to heat a substance, you can use the specific heat equation. The specific heat equation is:
q = m * c * ΔT
Where:
q is the energy required (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, we need to calculate the energy required to heat the ice from -16.0 °C to 0 °C. Since this is a phase change from solid to liquid, we use the equation:
q1 = m * ΔHf
Where:
q1 is the energy required for the phase change (in Joules)
m is the mass of the substance (in grams)
ΔHf is the heat of fusion of water, which is 334 J/g
Calculating q1:
q1 = 51.0 g * 334 J/g = 17034 J
Next, we need to calculate the energy required to heat the liquid water from 0 °C to 100 °C. The specific heat capacity of liquid water is 4.18 J/g°C.
Calculating q2:
q2 = m * c * ΔT
q2 = 51.0 g * 4.18 J/g°C * (100 °C - 0 °C) = 21258 J
Now, we need to calculate the energy required to heat the water vapor from 100 °C to 125 °C. The specific heat capacity of water vapor is 2.03 J/g°C.
Calculating q3:
q3 = m * c * ΔT
q3 = 51.0 g * 2.03 J/g°C * (125 °C - 100 °C) = 1299 J
Finally, we can calculate the total energy required by summing up q1, q2, and q3:
Total energy required = q1 + q2 + q3
Total energy required = 17034 J + 21258 J + 1299 J = 39691 J
Therefore, at 1 atm, it requires 39,691 Joules of energy to heat 51.0 g of H2O(s) at -16.0 °C to H2O(g) at 125.0 °C.