Freundlich Adsorption Isotherm Linear Form

The graph of logx/m vs logp 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 0.4atm is × 10^(-1) (Nearest integer) Given: log 2 = 0.3010

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Question type: Numerical
Exam relevance: JEE Main · Chemistry
Academic status: Answer verified against the official NTA key
Source: Previous-year question
Editorial review: 19 September 2026

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How do we find k from log k = 0.6020 without an antilog table?

Notice that 0.6020 is exactly 2 * 0.3010, which equals 2 log 2 = log(2^2) = log 4. Thus k = 4.

Answer

Accepted answer: 16

Using the Freundlich adsorption equation, the calculated value of $\frac{x}{m}$ at $0.4 atm$ is $1.6$ , which is $16 \times 10^{- 1}$ .

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Step-by-step solution

Given: Graph of $\log (x / m)$ vs $\log p$ is a straight line inclined at an angle of $45^{\circ}$ with intercept equal to $0.6020$ . Pressure $p = 0.4 atm$ . Given $\log 2 = 0.3010$ .
Find: The mass of gas adsorbed per unit mass of adsorbent, $\frac{x}{m}$ , expressed in the form $N \times 10^{- 1}$ to find integer $N$ .
Strategise: Freundlich adsorption isotherm is given by $\frac{x}{m} = k p^{1 / n}$ . In logarithmic form: $\log (\frac{x}{m}) = \log k + \frac{1}{n} \log p$ Here, slope $m_{line} = \frac{1}{n} = \tan 45^{\circ} = 1$ and intercept $c = \log k = 0.6020$ . Find $k$ using $\log 2 = 0.3010$ , then compute $\frac{x}{m} = k p^{1 / n}$ .
Execute: Slope $= \frac{1}{n} = \tan 45^{\circ} = 1$ . $\log k = 0.6020 = 2 \times 0.3010 = 2 \log 2 = \log (2^{2}) = \log 4 ⟹ k = 4$ . Now calculate $\frac{x}{m}$ at $p = 0.4 atm$ : $\frac{x}{m} = 4 \times (0.4)^{1} = 1.6 = 16 \times 10^{- 1}$ Thus, the integer value is 16.
Verify: Check: $\log (1.6) = \log (16 / 10) = 4 \log 2 - 1 = 4 (0.3010) - 1 = 1.2040 - 1 = 0.2040$ . From the equation: $\log (x / m) = 0.6020 + 1 \times \log (0.4) = 0.6020 + (2 (0.3010) - 1) = 0.6020 - 0.3980 = 0.2040$ . Matches perfectly.

Freundlich Adsorption Isotherm Linear Form

What feels right?

Using the Freundlich adsorption equation, the calculated value of $\frac{x}{m}$ at $0.4 atm$ is $1.6$ , which is $16 \times 10^{- 1}$ .

Why each option works or fails

Solution

01Given

02Find

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