Calculate the total amount of heat that must be added to convert 15.7g of ice at its melting point to steam at 100.0°C
q1 = heat needed to melt the ice at zero to form liquid water at zero.
q1 = mass ice x heat fusion = ?
q2 = heat needed to raise T of liquid H2O at zero to liquid water at 100 C.
q2 = mass H2O x specific heat H2O x (Tfinal-Tinitial)
q3 = heat needed to turn liquid water @ 100 C into steam at 100 C.
q3 = mass H2O x heat vaporization.
Total heat = q1 + q2 + q3.
To calculate the total amount of heat required to convert ice to steam, we need to consider three separate steps and calculate the heat required for each step.
Step 1: Heating ice to its melting point.
To heat the ice from its initial temperature, which is at or below 0°C, to its melting point, we need to calculate the heat using the formula:
Q1 = m * C1 * ΔT1
Where:
Q1 = heat required
m = mass of the ice (15.7g)
C1 = specific heat capacity of ice (2.09 J/g°C)
ΔT1 = change in temperature (melting point of ice - initial temperature)
The melting point of ice is 0°C, so ΔT1 = 0 - initial temperature.
Step 2: Melting the ice.
To convert the ice at its melting point to water without changing its temperature, we need to calculate the heat using the formula:
Q2 = m * ΔHf
Where:
Q2 = heat required
m = mass of the ice (15.7g)
ΔHf = heat of fusion of ice (334 J/g)
Step 3: Heating the water from the melting point to boiling point.
To heat the water from its melting point to its boiling point, we need to calculate the heat using the formula:
Q3 = m * C2 * ΔT2
Where:
Q3 = heat required
m = mass of water (calculated from the mass of ice used in previous steps)
C2 = specific heat capacity of water (4.18 J/g°C)
ΔT2 = change in temperature (boiling point of water - melting point)
The boiling point of water is 100°C, so ΔT2 = boiling point - melting point.
Finally, to get the total amount of heat required, we sum up the values calculated in each step:
Total heat = Q1 + Q2 + Q3
Let's calculate the values and get the final result.