Given that the specific heat capacities of ice and steam are 2.06 J/g degrees celsius and 2.03 J/g degrees celsius, respectively, and considering the information about water given, calculate the total quantity of heat evolved when 10.0g of steam at 200degrees. celsius is consensed, cooled, and frozen to ice at 50 degrees celsius.
I assume this is frozen to ice at -50C.
These are best worked in pieces.
Within a phase; i.e. change of T in steam or water or ice is
q = mass x specific heat in that phase x (Tfinal-Tinitial),
Example:
q for moving steam from 200 C to 100 C.
q = 10.0g x 2.03 J/g x (100-200) = ?
q at a phase change.
q = mass x heat vaporization at 100C or
q = mass x heat fusion at zero C.
example:
10.0 g x heat vaporization = ?
Then add q for each segment of the problem to find the total q for the problem.
To calculate the total quantity of heat evolved when steam is condensed, cooled, and frozen to ice, we need to consider the following steps:
Step 1: Calculate the heat evolved when steam is condensed to liquid water.
Step 2: Calculate the heat evolved when the liquid water is cooled to 0 degrees Celsius.
Step 3: Calculate the heat evolved when the liquid water freezes to ice at 0 degrees Celsius.
Step 4: Calculate the heat evolved when the ice is further cooled from 0 degrees Celsius to -10 degrees Celsius.
Let's calculate each step:
Step 1: Heat evolved when steam is condensed to liquid water:
To calculate the heat evolved when 10.0g of steam is condensed, we use the formula: q = m * ΔHvap, where q is the heat evolved, m is the mass, and ΔHvap is the heat of vaporization.
The heat of vaporization for water is approximately 40.7 kJ/mol or 40,700 J/mol. Therefore, the heat of vaporization for 1 gram of water is:
ΔHvap = (40,700 J/mol) / (18 g/mol) = 2,261 J/g
q = m * ΔHvap = 10.0g * 2,261 J/g = 22,610 J
Step 2: Heat evolved when liquid water is cooled to 0 degrees Celsius:
The specific heat capacity of liquid water is 4.18 J/g degrees Celsius. To calculate the heat evolved when liquid water is cooled from 200 degrees Celsius to 0 degrees Celsius, we use the formula:
q = m * Cp * ΔT, where q is the heat evolved, m is the mass, Cp is the specific heat capacity, and ΔT is the change in temperature.
ΔT = 200 degrees Celsius - 0 degrees Celsius = 200 degrees Celsius
q = m * Cp * ΔT = 10.0g * 4.18 J/g degrees Celsius * 200 degrees Celsius = 8360 J
Step 3: Heat evolved when the liquid water freezes to ice at 0 degrees Celsius:
The specific heat capacity of ice is 2.06 J/g degrees Celsius. To calculate the heat evolved when the liquid water freezes to ice at 0 degrees Celsius, we use the formula:
q = m * Cp * ΔT, where q is the heat evolved, m is the mass, Cp is the specific heat capacity, and ΔT is the change in temperature.
ΔT = 0 degrees Celsius - 0 degrees Celsius = 0 degrees Celsius
q = m * Cp * ΔT = 10.0g * 2.06 J/g degrees Celsius * 0 degrees Celsius = 0 J
Step 4: Heat evolved when the ice is further cooled from 0 degrees Celsius to -10 degrees Celsius:
The specific heat capacity of ice is 2.06 J/g degrees Celsius. To calculate the heat evolved when the ice is further cooled from 0 degrees Celsius to -10 degrees Celsius, we use the formula:
q = m * Cp * ΔT, where q is the heat evolved, m is the mass, Cp is the specific heat capacity, and ΔT is the change in temperature.
ΔT = 0 degrees Celsius - (-10) degrees Celsius = 10 degrees Celsius
q = m * Cp * ΔT = 10.0g * 2.06 J/g degrees Celsius * 10 degrees Celsius = 206 J
Now, add up the heat evolved in each step to get the total quantity of heat evolved:
Total quantity of heat evolved = q1 + q2 + q3 + q4
= 22,610 J + 8360 J + 0 J + 206 J
= 31,176 J
Therefore, the total quantity of heat evolved when 10.0g of steam at 200 degrees Celsius is condensed, cooled, and frozen to ice at 50 degrees Celsius is 31,176 J.