Can someone just get me started on this im not sure of how to go about solving this.
The heat of vaporization of carbon disulfide, CS2, at 25° C is 27.2 kJ/mol. 1.00 mol of carbon disulfide vapor condenses to liquid at 25° C. The entropy of this vapor at 25° C is 243 J/(mol•K). What is the entropy of the liquid at this temperature? Express your answer in j/k
To find the entropy of the liquid at 25° C, we need to consider the change in entropy during the phase transition from vapor to liquid.
The change in entropy (ΔS) during a phase transition can be calculated using the formula:
ΔS = ΔH/T
Where:
ΔS = change in entropy
ΔH = heat of vaporization
T = temperature
In this case, we have the heat of vaporization of carbon disulfide (CS2) at 25° C, which is 27.2 kJ/mol. To convert it to joules, we multiply by 1000, so ΔH = 27.2 × 1000 = 27,200 J/mol.
The temperature (T) is given as 25° C, which needs to be converted to Kelvin by adding 273.15: T = 25 + 273.15 = 298.15 K.
Using the formula, we can find the change in entropy during the phase transition:
ΔS = 27,200 J/mol / 298.15 K
Calculating this gives us ΔS = 91.32 J/(mol•K).
Therefore, the entropy of the liquid at 25° C is 91.32 J/(mol•K).
To find the entropy of the liquid at 25° C, you can apply the concept of the phase transition of a substance.
Step 1: Determine the phase transition occurring
In this case, the phase transition is the vapor condensing to a liquid.
Step 2: Calculate the change in entropy during the phase transition
The change in entropy during the phase transition, ΔS, can be calculated using the formula:
ΔS = ΔH / T
where ΔH is the heat of vaporization and T is the temperature.
Step 3: Plug in the given values
Given:
Heat of vaporization (ΔH) = 27.2 kJ/mol
Temperature (T) = 25° C
Convert the heat of vaporization to J/mol:
27.2 kJ/mol = 27.2 × 10^3 J/mol
Convert the temperature to Kelvin:
25° C = 25 + 273 = 298 K
Step 4: Calculate the change in entropy
Using the formula mentioned in step 2, we can plug in the values:
ΔS = (27.2 × 10^3 J/mol) / 298 K
Step 5: Calculate the entropy of the liquid
Since the process is a phase transition from vapor to liquid, the change in entropy is the negative of the entropy of the vapor. Therefore, the entropy of the liquid is:
Entropy of liquid = -ΔS
Substitute the value of ΔS into the equation:
Entropy of liquid = -(27.2 × 10^3 J/mol) / 298 K
Step 6: Calculate the final entropy of the liquid
Perform the calculation to find the final entropy of the liquid.
After performing the calculations, you will get the entropy of the liquid at 25° C expressed in J/K.