How many joules of heat are required to completely covert 85.0 grams of water at 40.0° C to steam at 100°C?
For water: c = 4.179 J/g °C Hfusion = 6.01 kJ/mol Hvap = 40.7 kJ/mol
q1 = heat needed to raise T of liquid water from 40 C to liquid water at 100 C.
q1 = mass H2O x specific heat H2O x (Tfinal-Tinitial)
q2 = heat needed to convert water at 100 C to steam at 100 C.
q2 = mass H2O x heat vaporization.
Total q = q1 + q2.
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To determine the amount of heat required to convert water from a specified temperature to steam, we need to consider the following steps:
1. Calculate the heat required to raise the temperature of the water from 40.0°C to its boiling point, 100°C.
2. Calculate the heat required to convert the water at its boiling point to steam.
Step 1: Calculating the heat required to raise the temperature
The heat required to raise the temperature of a substance can be calculated using the formula:
q = m * c * ΔT
Where:
q is the heat (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)
Given:
m = 85.0 grams
c (specific heat capacity of water) = 4.179 J/g°C
ΔT = (100°C - 40.0°C) = 60.0°C
Using the formula, we can calculate the heat required to raise the temperature:
q1 = 85.0 g * 4.179 J/g°C * 60.0°C
Step 2: Calculating the heat required for phase change
The heat required for phase change can be calculated using the formula:
q = n * ΔH
Where:
q is the heat (in joules)
n is the number of moles of substance undergoing phase change
ΔH is the enthalpy change for the phase change (in kJ/mol)
First, we need to convert the mass of water to moles using the molar mass of water. The molar mass of water (H2O) is 18.015 g/mol.
n = m / M
Where:
m is the mass of water (in grams)
M is the molar mass of water (in g/mol)
Given:
m = 85.0 grams
M (molar mass of water) = 18.015 g/mol
n = 85.0 g / 18.015 g/mol
Next, we can calculate the heat required for the phase change from liquid water to water vapor:
q2 = n * ΔHvap
Where:
ΔHvap is the enthalpy of vaporization (in kJ/mol)
Given:
ΔHvap = 40.7 kJ/mol
Now, we can calculate q2:
q2 = (85.0 g / 18.015 g/mol) * 40.7 kJ/mol
Finally, we can find the total heat required by adding q1 and q2:
Total heat = q1 + q2
Remember to convert kJ to J when adding the two values.