The work done by a gas when its 0.5 mole at 27°C expands from 5 lit to 25 lit reversibly and isothermally is -x kJ. Find value of x ?

To find the value of x, we can use the formula for the work done by a gas during an isothermal expansion:

Work = -nRT ln(V2/V1)

Where:

• n is the number of moles of the gas (0.5 mol in this case)
• R is the ideal gas constant (8.314 J/mol·K)
• T is the temperature in Kelvin (27°C = 300 K)
• V1 is the initial volume (5 L)
• V2 is the final volume (25 L)

Plugging in the values, we have:

Work = -(0.5 mol)(8.314 J/mol·K)(300 K) ln(25 L/5 L)

Simplifying further:

Work = -1247.1 J ln(5)

Using the natural logarithm of 5:

Work ≈ -1247.1 J (1.609)

Calculating the value:

Work ≈ -2004.4 J

Since the question asks for the value of x in kJ, we convert the result to kJ:

x = 2004.4 J / 1000 = 2.0044 kJ

Therefore, the value of x is approximately 2.0044 kJ.