Sulfur dichloride dioxide has an apparent molecular mass of 96.5g mol-1 at 400oC and a volume of 10dm3. Calculate the equilibrium constant kc of the reaction at this temperature.
\begin {aligned}
SO_2Cl_2\rightleftharpoons SO_2+Cl_2
\end {aligned}When reading this question it is obvious that neither of the molecules mentioned have a molar mass of 96.5g. This means that in this question the mass given is an average of all the gases present, since the SO2Cl2 would decompose.
An ICE table can then be used to find the molar mass, assuming that 1 mole of SO2Cl2 was present in the beginning at that the degree of dissociation is the amount that would have dissociated of the SO2Cl2.
Using the values obtained from the ICE table, one can find the degree of dissociation (α).
\begin {aligned}
\frac{135(1-\alpha)+64(\alpha)+71(\alpha)}{1+\alpha}=96.5
\end {aligned}where α can be found to be 0.400.
\begin {aligned}
k_c=\frac{[SO_2][Cl_2]}{[SOCl_2]}
\end {aligned}The kc equation is:
In order to find kc it is important to find the concentration where the concentrations can be found as:
\begin {aligned}
[SO_2Cl_2]=\frac{0.6}{10}=0.06M
\end {aligned}\begin {aligned}
[SO_2]=[Cl_2]=\frac{0.04}{10}=0.04M
\end {aligned}
Once the concentrations are found, then it is just a matter of placing each value in the kc equation as follows:
\begin {aligned}
k_c=\frac{[0.04][0.04]}{[0.06]}
\end {aligned}where kc would be found to be: 0.026mol dm-3