The mass of gas adsorbed, x, per unit mass of adsorbate, m, was measured at various pressures, p. A — Surface Chemistry Chemistry Question
Question
The mass of gas adsorbed, x, per unit mass of adsorbate, m, was measured at various pressures, p. A graph between and log p gives a straight line with slope equal to 2 and the intercept equal to 0.4771. The value of at a pressure of 4 atm is : (Given log3 = 0.47771)
💡 Solution & Explanation
**Step 1: Identify the Freundlich Adsorption Equation** The linear relationship between x/m and log p follows the Freundlich isotherm: $$\frac{x}{m} = k \cdot p^{1/n}$$ Taking logarithm: $\log\frac{x}{m} = \log k + \frac{1}{n}\log p$ **Step 2: Extract Parameters from Given Information** From the graph: - Slope = 1/n = 2, so n = 0.5 - Intercept = log k = 0.4771 Therefore: k = 10^0.4771 = 3 (since log 3 = 0.4771) **Step 3: Set Up the Equation** $$\log\frac{x}{m} = 0.4771 + 2\log p$$ **Step 4: Calculate log p at 4 atm** $$\log(4) = \log(2^2) = 2\log(2) = 2(0.301) = 0.602$$ **Step 5: Calculate x/m** $$\log\frac{x}{m} = 0.4771 + 2(0.602)$$ $$\log\frac{x}{m} = 0.4771 + 1.204 = 1.6811$$ $$\frac{x}{m} = 10^{1.6811} = 10^{0.4771} \times 10^{1.204} = 3 \times 16 = 48$$ Therefore, the answer is 48.00.