The graph of log x/m vs log p for an adsorption process is a straight line inclined at an angle of 45° with intercept equal to 0.6020. The mass of gas adsorbed per unit mass of adsorbent at the pressure of 0.4 atm is _________ × 10⁻¹ (Nearest integer).
Given: log 2=0.3010

Solution

Chemistry ma’am · 4 steps

Read the Freundlich line: the 45° slope gives 1/n, and the intercept is log k, not k itself.

1. Freundlich isotherm. The Freundlich isotherm is x/m = k p^(1/n). Taking logs turns it into a straight line, with slope 1/n and intercept log k.

   log x/m = log k + 1/n log p

2. Slope and intercept. The line is at 45°, so the slope is 1/n = tan 45° = 1. The intercept is log k = 0.6020 = 2 × 0.3010 = 2 log 2 = log 4, so k = 4.
3. Put in pressure. With 1/n = 1, the isotherm becomes x/m = k p = 4 × 0.4 = 1.6.
4. So. x/m = 1.6 = 16 × 10⁻¹, so the answer is 16.

The common slip: 2. Using the intercept 0.6020 directly as k gives 0.602 × 0.4 ≈ 2.4 × 10⁻¹, which rounds to 2, not 16. The intercept is log k, so k = 4.

The idea to keep. In a log x/m vs log p plot, slope is 1/n and intercept is log k. Always take the antilog of the intercept before using k.

Answer from the NTA final answer key. Solution by PrepWiser.