The following data were obtained during the first order thermal decomposition of a gas A at constant volume:

The rate constant of the reaction is ______ $$\times 10^{-2} \text{ s}^{-1}$$ (nearest integer)

Using the total pressure at $$t = 115\text{ s}$$:

$$0.1 + 2x = 0.28$$ 

$$2x = 0.18 \implies x = 0.09 \text{ atm}$$

Now, find the remaining pressure of reactant $$\text{A}$$ at $$t = 115\text{ s}$$:

$$P_\text{A} = P_0 - x = 0.1 - 0.09 = 0.01 \text{ atm}$$

3. Calculate the Rate Constant ($$k$$)

Using the integrated first-order rate equation:

$$k = \frac{2.303}{t} \log_{10}\left(\frac{P_0}{P_\text{A}}\right)$$

Substitute the values ($$t = 115$$, $$P_0 = 0.1$$, $$P_\text{A} = 0.01$$):

$$k = \frac{2.303}{115} \log_{10}\left(\frac{0.1}{0.01}\right)$$

$$k = \frac{2.303}{115} \log_{10}(10) = \frac{2.303}{115} \times 1$$

$$k \approx 0.0200 \text{ s}^{-1}$$

$$0.0200 \text{ s}^{-1} = 2 \times 10^{-2}\text{ s}^{-1}$$