For an isothermal reversible expansion of an ideal gas, the work done ($w$) is given by the formula: $w = -2.303 nRT \log\left(\frac{p_i}{p_f}\right)$ Given data: Number of moles, $n = 1 \text{ mole}$ Temperature, $T = 300 \text{ K}$ Initial pressure, $p_i = 5 \text{ atm}$ Final pressure, $p_f = 1 \text{ atm}$ Gas constant, $R = 8.314 \text{ J K}^{-1} \text{mol}^{-1}$ $\log 5 = 0.6989$ Substituting the values into the formula: $w = -2.303 \times 1 \times 8.314 \times 300 \times \log\left(\frac{5}{1}\right)$ $w = -2.303 \times 2494.2 \times \log 5$ $w = -5744.14 \times 0.6989 \approx -4014.6 \text{ J}$ The negative sign indicates that work is done by the system (expansion) .