# Thermodynamics questions

#### Dhamnekar Winod

##### Active member
Hello,
Here are the questions with unknown answers. (These chemistry questions are other math topics.)
1) At 1 bar, the boiling point of water is 372.78 K. At this temperature and pressure, the density of liquid water is $958.66 kg/m^3$ and that of gaseous water is $0.59021 kg/m^3.$ What are the molar volumes. in $m^3 mol^{-1}$ of liquid and gaseous water at this temperature and pressure? in Liters/mol?

2) Refer to the answer to 1) question. Assuming that a water molecule excludes the other water molecules from a cubic region centered on itself, estimate the average distance between nearest-neighbor water molecules in the liquid and in the gas.

3)Calculate the molar volume and gaseous water at 1 bar and 372.78 K from ideal gas equation. What is the error, expressed as a percentage of the value, you calculated in question 1).

4) At 372.78 K, the virial coefficient B* for water is $-1.487 × 10^{-7} Pa^{-1}$. Calculate the molar volume of gaseous water at 1 bar and 372.78 K from the virial equation: $Z=P\overline{V}/RT= 1+B^*P.$ What is the error, expressed as a percentage of the value, you computed in question 1).

5) Compute the molar volume of gaseous water at 1 bar and 372.78 K from van der Waals' equation. The van der Waals' parameters for water are $a=5.537 bar L^2 mol^{-1}$ and $b=0.0305 L mol^{-1}$. What is the error, expressed as the percentage of the value, you computed in question 1)?

6)What are your comments on the results in questions 3,4 and 5? At this temperature, would you expect the accuracy to increase or decrease at lower pressure?

#### Dhamnekar Winod

##### Active member
Hello,
Here are the questions with unknown answers. (These chemistry questions are other math topics.)
1) At 1 bar, the boiling point of water is 372.78 K. At this temperature and pressure, the density of liquid water is $958.66 kg/m^3$ and that of gaseous water is $0.59021 kg/m^3.$ What are the molar volumes. in $m^3 mol^{-1}$ of liquid and gaseous water at this temperature and pressure? in Liters/mol?

2) Refer to the answer to 1) question. Assuming that a water molecule excludes the other water molecules from a cubic region centered on itself, estimate the average distance between nearest-neighbor water molecules in the liquid and in the gas.

3)Calculate the molar volume and gaseous water at 1 bar and 372.78 K from ideal gas equation. What is the error, expressed as a percentage of the value, you calculated in question 1).

4) At 372.78 K, the virial coefficient B* for water is $-1.487 × 10^{-7} Pa^{-1}$. Calculate the molar volume of gaseous water at 1 bar and 372.78 K from the virial equation: $Z=P\overline{V}/RT= 1+B^*P.$ What is the error, expressed as a percentage of the value, you computed in question 1).

5) Compute the molar volume of gaseous water at 1 bar and 372.78 K from van der Waals' equation. The van der Waals' parameters for water are $a=5.537 bar L^2 mol^{-1}$ and $b=0.0305 L mol^{-1}$. What is the error, expressed as the percentage of the value, you computed in question 1)?

6)What are your comments on the results in questions 3,4 and 5? At this temperature, would you expect the accuracy to increase or decrease at lower pressure?
Hello,
Answer to question 1)

Molar volume of liquid water is $0.00001879m^3/mol$

Molar volume of gaseous water is $0.030589 m^3/mol$ using charles' law for temperature-volume relationship.

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Hey Dhamnekar Winod,
What is it that you really want to know?
After all, so far you have merely posted a set of problem statements. And you followed up with what appears to be text book answers without explanation.
Either way, there are plenty of those in various text books.
Is there something that you are stuck on? If so, what is it?

#### Dhamnekar Winod

##### Active member
Hey Dhamnekar Winod,
What is it that you really want to know?
After all, so far you have merely posted a set of problem statements. And you followed up with what appears to be text book answers without explanation.
Either way, there are plenty of those in various text books.
Is there something that you are stuck on? If so, what is it?
Hi,
I don't know the correct answers to all of these question for verifications. I also don't know how to answer question 2), 5). As question 5) is still unsolved, I can't go further to consider answering question 6).

So, i am studying answers given by learned science professors to similar types of questions. It took much time to answer 1), because i was not knowing that molar mass of gaseous water and liquid water is one and the same, that is 18.02g/mol.