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

Explanation:

As it is known that $SF_{6}$ molecule is a non-linear molecule. Therefore, its isochoric heat capacity will be as follows.

              $C_{v} = \frac{3}{2}R + \frac{3}{2}R + (3 \times 7 - 6)R$

                         = $\frac{3}{2}R + \frac{3}{2}R + 15R$

                         = 18 R

Also,    $C_{V} = M \times C_{v}$

where,     $C_{V}$ = molar heat capacity

                    M = molecular mass

               $C_{v}$ = specific heat

Hence, calculate the value of $C_{v}$ as follows.

                 $C_{V} = M \times C_{v}$

               $8 \times 8.314 \times 10^{7} = 146.06 \times C_{v}$

               $C_{v} = 10.2 \times 10^{6} erg. K^{-1}. gm^{-1}$

This means that value of isochoric specific heat is $10.2 \times 10^{6} erg. K^{-1}. gm^{-1}$.

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

                         dU = $nC_{v}dT$

Whereas for real gases "$\frac{an^{2}}{V^{2}}$" has to be added here.