Question

Predict (to 3 sig figs) the isochoric specific heat of gaseous SF6 (molar mass 146.06 g/mol) at 1200 K, assuming that at this temperature all translational, rotational and vibrational degrees of freedom are accessible, and assuming no electronic degrees of freedom are accessible at all. Do you need to assume ideal fully gas behavior?

Answer 1

Step-by-step explanation:

As it is known that
`SF_(6)` molecule is a non-linear molecule. Therefore, its isochoric heat capacity will be as follows.

`C_(v) = (3)/(2)R + (3)/(2)R + (3 * 7 - 6)R`

=
`(3)/(2)R + (3)/(2)R + 15R`

= 18 R

Also,
`C_(V) = M * C_(v)`

where,
`C_(V)` = molar heat capacity

M = molecular mass

`C_(v)` = specific heat

Hence, calculate the value of
`C_(v)` as follows.

`C_(V) = M * C_(v)`

`8 * 8.314 * 10^(7) = 146.06 * C_(v)`

`C_(v) = 10.2 * 10^(6) erg. K^(-1). gm^(-1)`

This means that value of isochoric specific heat is
`10.2 * 10^(6) erg. K^(-1). gm^(-1)`.

Yes, we have to assume ideal gas behavior because for ideal gas:

dU =
`nC_(v)dT`

Whereas for real gases "
`(an^(2))/(V^(2))`" has to be added here.