How much heat is required to convert 6.78g of ice at − 14.0∘C to water at 24.0∘C ?
q1 = heat needed to raise T of ic from -14C to 0C.
q1 = mass ice x specific heat ice x (Tfinal-Tinitial)
q2 = heat needed to melt ice at zero C to liquid H2O at zero C.
q2 = mass ice x heat fusion
q3 = heat needed to raise T of liquid water from zero C to 24.0C
q3 = mass liquid H2O x specific heat H2O x (Tfinal-Tinitial)
qtotal = q1 + q2 + q3.
To determine the amount of heat required to convert the ice to water, you need to consider two parts: the heat required to raise the temperature of ice from -14.0°C to 0.0°C, and the heat required to melt the ice at 0.0°C and raise the temperature of the resulting water from 0.0°C to 24.0°C.
Let's break it down step by step:
1. Heat required to raise the temperature of ice from -14.0°C to 0.0°C:
The specific heat capacity of ice is 2.09 J/g°C. So, you need to calculate the heat using the formula:
heat = mass × specific heat capacity × temperature change
Given: mass of ice = 6.78g, specific heat capacity = 2.09 J/g°C, initial temperature = -14.0°C, final temperature = 0.0°C
heat = 6.78g × 2.09 J/g°C × (0.0°C - (-14.0°C))
2. Heat required to melt ice at 0.0°C and raise the temperature of the resulting water from 0.0°C to 24.0°C:
The heat of fusion (or melting) for ice is 333.5 J/g, and the specific heat capacity of water is 4.18 J/g°C.
First, calculate the heat required to melt the ice:
heat_1 = mass × heat of fusion
Given: mass of ice = 6.78g, heat of fusion = 333.5 J/g
heat_1 = 6.78g × 333.5 J/g
Next, calculate the heat required to raise the temperature of water from 0.0°C to 24.0°C:
heat_2 = mass × specific heat capacity × temperature change
Given: mass of water = mass of ice = 6.78g, specific heat capacity = 4.18 J/g°C, initial temperature = 0.0°C, final temperature = 24.0°C
heat_2 = 6.78g × 4.18 J/g°C × (24.0°C - 0.0°C)
Finally, add up the three calculated heats to find the total heat required:
total heat = heat + heat_1 + heat_2
Now you can substitute the values into the equation and calculate the total heat required.