The critical constants for water are `647 K`, `22.09 MPa`, and `0.0566 dm^(3) mol(-1)`. Calculate the values of `a`, `b` and `R` and explain the abnormal value of `R`.

Explanation

The given values are
`T_(c)=647 K`
`P_(c)=22.09 MPa=22.09xx10^(3)kPa`
`V_(c)=0.0566 dm^(3)mol^(-1)`
Thus `b=(V_(c))/(3)=(0.566 dm^(3)mol^(-1))/(3)`
`=0.0189 dm^(3)mol^(-1)`
`a=3P_(c)V_(c)^(2)`
`=3(22.09xx10^(3)kPa)(0.0566 dm^(3)mol^(-1))^(2)`
`=212.3kPa dm^(6)mol^(-2)`
`R=(8)/(3)(P_(c)V_(c))/(T_(c))`
`=(8)/(3)((22090kPa)(0.0566dm^(3)mol^(-1))/(647 K))`
`=5.153 JK^(-1)mol^(-1)`
The value of `R` is `8.314 JK^(-1) mol^(-1)`. The experimentally determined value is much different from this value. This is due to the fact that simple van der Waals attraction does not exist at the critical state.