`2 dm^(3)` of methane under `600 kPa` and `300K` and `4 dm^(3)` of oxygen under `900k Pa` and `300K` are forced into `3 dm^(3)` evacuated vessel, the temperature being maintained at `300K`. Calculate the change in entropy of gases assuming that they are ideal.

Explanation

To calculate the change in entropy of the gases when 2 dm³ of methane and 4 dm³ of oxygen are mixed in a 3 dm³ evacuated vessel at 300 K, we can follow these steps:

### Step 1: Calculate the number of moles of methane (CH₄)
Using the ideal gas equation \( PV = nRT \):
- Given:
- Pressure of methane \( P_1 = 600 \, \text{kPa} = 600 \times 10^3 \, \text{Pa} \)
- Volume of methane \( V_1 = 2 \, \text{dm}^3 = 2 \times 10^{-3} \, \text{m}^3 \)
- Temperature \( T = 300 \, \text{K} \)
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