How many kilojoules of heat is required to completely covert 60.0 grams of water at 32.0° C to steam at 100°C?
For water:
s = 4.179 J/g °C
(delta)H fusion = 6.01 kJ/mol
(delta)H vap = 40.7 kJ/mol
q1 = heat to move H2O from T = 32 C to 100 C.
q1 = mass water x specific heat water x (Tfinal-Tinitial)
q2 = heat to vaporize water at 100 to steam at 100.
q2 = mass water x delta Hvap.
Total heat required = q1 + q2.
To find the amount of heat required to convert 60.0 grams of water from 32.0°C to steam at 100°C, we need to calculate the heat required to raise the temperature of the water from 32.0°C to 100°C and then add the heat required to convert the water to steam.
Let's break down the calculation into two steps:
Step 1: Heating the water from 32.0°C to 100°C.
To calculate the heat required to raise the temperature of the water, we'll use the specific heat formula:
Q = m * s * ΔT
where:
Q = heat energy (in Joules)
m = mass of the substance (in grams)
s = specific heat capacity of the substance (in J/g °C)
ΔT = change in temperature (in °C)
Given:
m = 60.0 grams
s (specific heat capacity of water) = 4.179 J/g°C
ΔT = 100°C - 32.0°C = 68.0°C
Substituting these values into the formula, we get:
Q1 = 60.0 g * 4.179 J/g°C * 68.0°C
Step 2: Converting the water to steam.
To calculate the heat required to convert the water to steam, we'll use the heat of vaporization formula:
Q = moles * ΔH
where:
Q = heat energy (in Joules)
moles = mass of the substance (in grams) / molar mass of the substance (in g/mol)
ΔH = molar heat of vaporization (in J/mol)
First, we need to calculate the number of moles of water:
moles = mass of water / molar mass of water
Given:
mass of water = 60.0 grams
molar mass of water = 18.015 g/mol
moles = 60.0 g / 18.015 g/mol
Then, we can calculate the heat required for vaporization:
Q2 = moles * ΔH
Given:
ΔH (molar heat of vaporization) = 40.7 kJ/mol
Note: The value of ΔH is given in kJ/mol, so we need to convert it to J/mol by multiplying it by 1000.
Now, we can substitute the values into the formula:
Q2 = (60.0 g / 18.015 g/mol) * (40.7 kJ/mol * 1000 J/kJ)
Finally, to find the total heat required, we add Q1 and Q2:
Total heat required = Q1 + Q2
Calculating all the values and summing them up will give us the answer.