Sulphuryl chloride breaks down in the gas phase at 593 K by a first order reaction: SO₂Cl₂(g) →…

Step 1. The pressure of the reactant. $p = 2 \times 0.480\ \text{bar} - 0.550\ \text{bar} = 0.410\ \text{bar}$.

Step 2. The rate constant. The time is $2.0 \times 3600\ \text{s} = 7200\ \text{s}$. Then $k = \dfrac{1}{7200\ \text{s}}\ln\dfrac{0.480}{0.410} = \dfrac{0.158}{7200\ \text{s}} = 2.19 \times 10^{-5}\ \text{s}^{-1}$. In one hour there are $3600\ \text{s}$, so $k = 0.0788\ \text{h}^{-1}$.

Step 3. The half-life. $t_{1/2} = \dfrac{0.693}{2.19 \times 10^{-5}\ \text{s}^{-1}} = 3.16 \times 10^4\ \text{s}$, which is $8.79\ \text{h}$.