# Step-by-Step Solution ## 1. Freundlich Adsorption Isotherm Equation The Freundlich adsorption isotherm is given by: \[ \frac{x}{m} = k P^{1/n} \] where \(\frac{x}{m}\) = mass of gas adsorbed per unit mass of adsorbent, \(k\) = Freundlich constant, \(P\) = equilibrium pressure, \(n\) = constant related to adsorption intensity. ## 2. Assign Known Values You are given: At \(P = 1\, \text{atm}\), \(\frac{x}{m} = .5\, \text{g}\), \(1/n = .5\), so \(n = 2\). ## 3. Find the Freundlich Constant \(k\) Substitute the known values into the equation: \[ .5 = k \times (1)^{1/2} \] \[ .5 = k \] So, \(k = .5\). ## 4. Calculate \(\frac{x}{m}\) at \(P = 4\, \text{atm}\) Now, use the equation for \(P = 4\, \text{atm}\): \[ \frac{x}{m} = .5 \times (4)^{1/2} \] Calculate \((4)^{1/2}\): \[ (4)^{1/2} = 2 \] So, \[ \frac{x}{m} = .5 \times 2 = 1.\, \text{g} \] ## 5. Final Answer The mass of gas adsorbed per unit mass of adsorbent at \(4\, \text{atm}\) is **1. g**.