Given that the specific heat capacities of ice and steam are 2.06 J/g°C and 2.03 J/g°C, the molar heats of fusion and vaporization for water are 6.02 kJ/mol and 40.6 kJ/mol, respectively, and the specific heat capacity of water is 4.18 J/g°C, calculate the total quantity of heat evolved when 25.6 g of steam at 194°C is condensed, cooled, and frozen to ice at -50.°C.
It's best to work this in stages.
q1 = heat released in moving steam from 194 C to 100 C.
q1 = mass x specific heat steam x (Tfinal-Tinitial)
q2 = heat released to condense steam at 100 C to liquid water at 100 C.
q2 = mass steam x heat vaporixation.
q3 = heat released to move T of liquid water from 100 C to zero C.
q3 = mass x specific heat water x (Tfinal-Tinitial).
q4 = heat released to freeze water at zero C to ice at zero C.
q4 = mass water x heat fusion.
q5 = heat released to move solid ice from zero C to -50 C.
q5 = mass ice x specific heat ice x (Tfinal-Tinitial).
Total q = q1 + q2 + q3 + q4 + q5
To calculate the total quantity of heat evolved when 25.6 g of steam at 194°C is condensed, cooled, and frozen to ice at -50.°C, we need to consider the different processes involved and the corresponding heat exchanges.
First, let's calculate the heat exchanged during the condensation process:
1. Calculate the heat exchanged during condensation:
The heat exchanged during the condensation process can be calculated using the equation:
Q = m × ΔH_vap
Where:
Q is the heat exchanged (in joules),
m is the mass of the substance (in grams), and
ΔH_vap is the molar heat of vaporization (in joules per mole).
Converting the mass of steam to moles:
molar mass of steam = 18.015 g/mol
moles of steam = mass of steam / molar mass of steam
moles of steam = 25.6 g / 18.015 g/mol
Next, we convert moles of steam to joules using the molar heat of vaporization:
Q_condensation = moles of steam × ΔH_vap
2. Calculate the heat exchanged during the cooling process:
Q_cooling = m × c × ΔT
Where:
m is the mass of the substance (in grams),
c is the specific heat capacity (in joules per gram per degree Celsius), and
ΔT is the change in temperature (in degrees Celsius).
To calculate the heat exchanged during the cooling process, we need to consider that water will be cooled from 194°C to 0°C, and then further cooled from 0°C to -50°C.
For the cooling from 194°C to 0°C:
ΔT1 = 0°C - 194°C
Q_cooling1 = m × c × ΔT1
For the cooling from 0°C to -50°C:
ΔT2 = -50°C - 0°C
Q_cooling2 = m × c × ΔT2
3. Calculate the heat exchanged during the freezing process:
Q_freezing = m × ΔH_fus
Where:
ΔH_fus is the molar heat of fusion (in joules per mole).
Converting the mass of ice to moles:
molar mass of ice = 18.015 g/mol
moles of ice = mass of ice / molar mass of ice
moles of ice = 25.6 g / 18.015 g/mol
Next, we convert moles of ice to joules using the molar heat of fusion:
Q_freezing = moles of ice × ΔH_fus
Finally, we can calculate the total quantity of heat evolved by summing up the individual heat exchanges:
Total heat evolved = Q_condensation + Q_cooling1 + Q_cooling2 + Q_freezing
Note: Make sure to use the correct units for all calculations.
Plug in the values into the respective equations, perform the calculations, and sum up the results to find the total quantity of heat evolved.
To calculate the total quantity of heat evolved, we need to consider the different steps involved in the process and find the heat transferred at each step.
Let's break down the process into three steps:
Step 1: Condensing steam to water at 100°C
Step 2: Cooling water from 100°C to 0°C
Step 3: Freezing water to ice at -50°C
Step 1: Condensing steam to water at 100°C
To calculate the heat transferred during this step, we'll use the formula:
q = m × ΔHvap
where q is the heat transferred, m is the mass, and ΔHvap is the molar heat of vaporization.
Given:
Mass of steam (m) = 25.6 g
ΔHvap = 40.6 kJ/mol = 40.6 × 10³ J/mol
Since we are given the mass in grams and the molar heat of vaporization in joules per mole, we need to convert the mass to moles to use the equation.
Using the molar mass of water (18.015 g/mol), the number of moles (n) can be calculated as:
n = m / M
= 25.6 g / 18.015 g/mol
Now we can calculate the heat transferred during step 1:
q1 = n × ΔHvap
= (25.6 g / 18.015 g/mol) × (40.6 × 10³ J/mol)
Step 2: Cooling water from 100°C to 0°C
To calculate the heat transferred during this step, we'll use the formula:
q = m × c × ΔT
where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Given:
Mass of water (m) = 25.6 g
Specific heat capacity of water (c) = 4.18 J/g°C
Change in temperature (ΔT) = 100°C - 0°C = 100°C
Using the formula:
q2 = m × c × ΔT
= 25.6 g × 4.18 J/g°C × 100°C
Step 3: Freezing water to ice at -50°C
To calculate the heat transferred during this step, we'll use the formula:
q = m × ΔHfus
where q is the heat transferred, m is the mass, and ΔHfus is the molar heat of fusion.
Given:
Mass of ice (m) = 25.6 g
ΔHfus = 6.02 kJ/mol = 6.02 × 10³ J/mol
Since we are given the mass in grams and the molar heat of fusion in joules per mole, we need to convert the mass to moles to use the equation.
Using the molar mass of water (18.015 g/mol), the number of moles (n) can be calculated as:
n = m / M
= 25.6 g / 18.015 g/mol
Now we can calculate the heat transferred during step 3:
q3 = n × ΔHfus
= (25.6 g / 18.015 g/mol) × (6.02 × 10³ J/mol)
Finally, we can calculate the total quantity of heat evolved by summing up the heat transferred in each step:
Total heat evolved = q1 + q2 + q3