For Freundlich adsorption isotherm, a plot of log (x/m) (y - axis) and log p (x - axis) gives a stra — Surface Chemistry Chemistry Question

💡 Solution & Explanation

**Step 1: Recall the Freundlich adsorption isotherm equation** The Freundlich isotherm in logarithmic form is: $$\log\left(\frac{x}{m}\right) = \log k + n \log p$$ where x/m is mass of gas adsorbed per gram of adsorbent, k is the Freundlich constant, n is the slope, and p is pressure. **Step 2: Identify given values** - Intercept = log k = 0.4771 - Slope = n = 2 - Initial pressure = p = 0.04 atm **Step 3: Calculate the intercept value (k)** $$\log k = 0.4771$$ $$k = 10^{0.4771} = 3$$ **Step 4: Substitute values into the Freundlich equation** $$\log\left(\frac{x}{m}\right) = 0.4771 + 2 \times \log(0.04)$$ **Step 5: Calculate log(0.04)** $$\log(0.04) = \log(4 \times 10^{-2}) = \log 4 + \log 10^{-2}$$ $$= 0.6021 - 2 = -1.3979$$ **Step 6: Find x/m** $$\log\left(\frac{x}{m}\right) = 0.4771 + 2(-1.3979)$$ $$= 0.4771 - 2.7958 = -2.3187$$ $$\frac{x}{m} = 10^{-2.3187} = 0.048 \times 10^3 = 48$$ Therefore, the answer is 48.00.