Given:
- Amount of methane (ideal gas) = 1.6g
- Temperature = 400K
- Isothermal expansion (constant temperature)
- Volume increases ten times of the original value

To find:
- The work done by the gas in the process

Solution:

Step 1: Calculate the number of moles
- Calculate the molar mass of methane (CH4):
- Carbon (C) has a molar mass of 12.01 g/mol
- Hydrogen (H) has a molar mass of 1.01 g/mol
- Molar mass of methane = (4 * 1.01) + 12.01 = 16.05 g/mol

- Calculate the number of moles using the given mass of methane:
- Number of moles = Mass / Molar mass = 1.6 g / 16.05 g/mol = 0.0997 mol (approximately)

Step 2: Calculate the initial volume
- The volume of the gas can be calculated using the ideal gas equation:
- PV = nRT
- P = pressure (unknown)
- V = volume (unknown)
- n = number of moles (0.0997 mol)
- R = ideal gas constant (8.314 J/(mol·K))
- T = temperature (400K)

- Rearranging the equation:
- V = nRT / P

- Since the volume increases ten times, the initial volume can be calculated as:
- Initial volume = V / 10 = (0.0997 mol * 8.314 J/(mol·K) * 400K) / P

Step 3: Calculate the work done
- Work done by the gas in an isothermal process can be calculated using the equation:
- Work = -nRT * ln(Vf / Vi)

- Vi = initial volume (calculated in step 2)
- Vf = final volume (10 times the initial volume)
- n = number of moles (0.0997 mol)
- R = ideal gas constant (8.314 J/(mol·K))
- T = temperature (400K)

- Substituting the values:
- Work = -(0.0997 mol * 8.314 J/(mol·K) * 400K) * ln((10 * Vi) / Vi)

- Simplifying the equation:
- Work = -0.0997 mol * 8.314 J/(mol·K) * 400K * ln(10)

- Calculating the work done:
- Work = -0.0997 mol * 8.314 J/(mol·K) * 400K * ln(10) ≈ -1.03 kJ

Answer:
The work done by the gas in the process is approximately -1.03 kJ. The negative sign indicates that work is done on the gas during the expansion process.