Calculate the energy (in kJ) required to heat 25 g of liquid water from 25oC to 100.oC and change it to steam at 100oC. The specific heat capacity of liquid water is 4.18 J/goC, and the molar heat of vaporization of water is 40.6 kJ/mol.
To calculate the total energy required to heat liquid water from 25°C to 100°C and then change it to steam at 100°C, we need to consider two separate processes:
1. Heating the water from 25°C to 100°C:
To calculate the energy required for this process, we will use the equation:
q = m * c * ΔT
where:
q = energy (in Joules)
m = mass of the water (in grams)
c = specific heat capacity of water (in J/goC)
ΔT = change in temperature (in oC)
Given:
Mass (m) = 25 g
Specific heat capacity (c) = 4.18 J/goC
Initial temperature (T1) = 25°C
Final temperature (T2) = 100°C
We can now substitute these values into the equation:
q = 25 g * 4.18 J/goC * (100°C - 25°C)
By calculating the expression inside the brackets:
q = 25 g * 4.18 J/goC * 75°C
Now, multiply the mass by the specific heat capacity and the change in temperature to get the energy required to raise the temperature of the water:
q = 25 g * 4.18 J/goC * 75°C = 7825 J
To convert the energy to kilojoules, divide by 1000:
q = 7825 J / 1000 = 7.825 kJ
Therefore, the energy required to heat 25 g of liquid water from 25°C to 100°C is 7.825 kJ.
2. Changing the water at 100°C to steam:
To calculate the energy required for this process, we will use the equation:
q = n * ΔHvap
where:
q = energy (in Joules)
n = number of moles of water
ΔHvap = molar heat of vaporization of water
Given:
Mass (m) = 25 g
Molar mass of water (M) = 18.01528 g/mol (from periodic table)
Molar heat of vaporization (ΔHvap) = 40.6 kJ/mol
To find the number of moles of water, divide the mass by the molar mass:
n = 25 g / 18.01528 g/mol
Now calculate the energy required using the expression:
q = n * ΔHvap
q = (25 g / 18.01528 g/mol) * 40.6 kJ/mol
By simplifying the expression:
q ≈ 33.924 kJ
Therefore, the energy required to change 25 g of water at 100°C to steam is approximately 33.924 kJ.
To find the total energy required, add the results of the two processes:
Total energy = Heating energy + Vaporization energy
Total energy = 7.825 kJ + 33.924 kJ
Total energy ≈ 41.749 kJ
Therefore, the total energy required to heat 25 g of liquid water from 25°C to 100°C and change it to steam at 100°C is approximately 41.749 kJ.
To calculate the energy required to heat 25 g of liquid water from 25°C to 100°C and change it to steam at 100°C, we need to consider two steps:
Step 1: Heating the water from 25°C to 100°C.
Step 2: Converting the water at 100°C to steam at 100°C.
Step 1: Calculate the energy required to heat the water using the formula:
q = m * c * ΔT
Where:
q is the energy required (in Joules)
m is the mass of the water (in grams)
c is the specific heat capacity of water (in J/g°C)
ΔT is the change in temperature (in °C)
Given:
m = 25 g
c = 4.18 J/goC
ΔT = (100 - 25)°C = 75°C
Substituting the values:
q = 25 g * 4.18 J/goC * 75°C
q = 78,375 J
Since 1 kJ = 1000 J, we can convert this to kJ:
q = 78,375 J / 1000
q = 78.375 kJ
Step 2: Calculate the energy required to vaporize the water at 100°C using the formula:
q = n * ΔHvap
Where:
q is the energy required (in Joules)
n is the number of moles of water
ΔHvap is the molar heat of vaporization of water (in J/mol)
To find the number of moles of water, we can use the formula:
n = m / M
Where:
m is the mass of the water (in grams)
M is the molar mass of water (in g/mol)
Given:
m = 25 g
M = 18.015 g/mol (molar mass of water)
Substituting the values:
n = 25 g / 18.015 g/mol
n ≈ 1.3875 mol
Substituting the values into the equation for energy:
q = 1.3875 mol * 40.6 kJ/mol
q = 56.33875 kJ
Finally, sum up the energies from both steps:
Total energy = Energy from Step 1 + Energy from Step 2
Total energy = 78.375 kJ + 56.33875 kJ
Total energy ≈ 134.71 kJ
Therefore, the energy required to heat 25 g of liquid water from 25°C to 100°C and change it to steam at 100°C is approximately 134.71 kJ.
the molar mass of water is 18.0 g
E = [25 * (100 - 25) * .00418] +
... [(25 / 18) * 40.6]