The fluorocarbon compound C2Cl3F3 has a normal boiling point of 47.6 °C. The specific heat of this compound in the liquid state is 0.91 J/g-K and in the gas state is 0.67 J/g-K. The heat of vaporization is 27.5 kJ/mol. What is the amount of heat required to convert 5.6 g of the compound from a liquid at 30.0 °C to a gas at 60.5 °C?
q within the liquid state from T of 30 C to T of 47.6 is
q = mass x specific heat liquid x (Tf-Ti) or
q1 = 5.6 g x 0.91 J/g.K x (47.6 - 30) = ? J
q2 to convert liquid to gas @ the boiling point is
q2 = delta H x mol = 27.5 kJ/mol x 5.6g/molar mass = ? kJ
q3 within the gas phase is
q3 = mass x specific heat x (Tfinal-Tinitial) =
q3 = 5.6 g x 0.67 J/g.K x (60.5 - 47.6) = ? in J
Total = qtotal = q1 + q2 + q3 = ?
To calculate the amount of heat required to convert 5.6 g of the compound from a liquid at 30.0 °C to a gas at 60.5 °C, we need to consider three steps:
Step 1: Heating the liquid from 30.0 °C to its boiling point
Step 2: Vaporizing the liquid at its boiling point
Step 3: Heating the gas from its boiling point to 60.5 °C
Let's calculate each step:
Step 1: Heating the liquid from 30.0 °C to its boiling point
The specific heat of the compound in the liquid state is 0.91 J/g-K.
The temperature change (∆T) for this step is:
∆T = final temperature - initial temperature
= 47.6 °C - 30.0 °C
= 17.6 °C
The amount of heat required to heat the liquid is:
q1 = mass × specific heat × ∆T
= 5.6 g × 0.91 J/g-K × 17.6 °C
Step 2: Vaporizing the liquid at its boiling point
The heat of vaporization is 27.5 kJ/mol.
To convert grams to moles, we need the molar mass of the compound. The molar mass of C2Cl3F3 can be found by adding up the atomic masses of each element:
C: 2 atoms × atomic mass of carbon
Cl: 3 atoms × atomic mass of chlorine
F: 3 atoms × atomic mass of fluorine
After finding the molar mass, we can convert grams to moles:
moles = mass / molar mass
The amount of heat required to vaporize the liquid is:
q2 = moles × heat of vaporization
Step 3: Heating the gas from its boiling point to 60.5 °C
The specific heat of the compound in the gas state is 0.67 J/g-K.
The temperature change (∆T) for this step is:
∆T = final temperature - boiling point
= 60.5 °C - 47.6 °C
The amount of heat required to heat the gas is:
q3 = mass × specific heat × ∆T
Finally, the total amount of heat required is the sum of q1, q2, and q3:
total heat = q1 + q2 + q3
Calculate all the values and add up the results to find the total heat required.
To find the amount of heat required to convert the compound from a liquid to a gas, we need to consider the different steps involved:
1. Heating the liquid from 30.0 °C to its boiling point (47.6 °C).
2. Changing the liquid to a gas at its boiling point (47.6 °C).
3. Heating the gas from the boiling point (47.6 °C) to 60.5 °C.
Let's break down each step and calculate the heat required for each.
Step 1: Heating the liquid from 30.0 °C to the boiling point (47.6 °C)
The heat required for this step can be calculated using the formula:
Q = m * c * ΔT
where:
Q is the heat transferred
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
Q1 = 5.6 g * 0.91 J/g-K * (47.6 °C - 30.0 °C)
Step 2: Changing the liquid to a gas at its boiling point (47.6 °C)
The heat required for this step is equal to the heat of vaporization, which is given as 27.5 kJ/mol. However, we need to convert the mass (in grams) to moles using the molar mass of the compound. The molar mass of C2Cl3F3 can be calculated as follows:
C: 2 atoms * atomic mass of C
Cl: 3 atoms * atomic mass of Cl
F: 3 atoms * atomic mass of F
Once you have the molar mass, you can calculate the number of moles (n) using the formula:
n = m / M
where:
n is the number of moles
m is the mass
M is the molar mass
Q2 = n * ΔHvap
where:
Q2 is the heat required for the phase change (vaporization)
ΔHvap is the heat of vaporization
Step 3: Heating the gas from the boiling point (47.6 °C) to 60.5 °C
The heat required for this step can be calculated using the same formula as in Step 1:
Q3 = 5.6 g * 0.67 J/g-K * (60.5 °C - 47.6 °C)
Finally, we can find the total heat required by summing up the heat required for each step:
Total heat (Q total) = Q1 + Q2 + Q3
Now, you can plug in the values and calculate the answer.