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JEE Advanced levelSingle correct optionDifficulty 3 of 3sc040

For a Langmuir adsorption, a plot of $p / V$ (in $kPa g c m^{- 3}$ ) against $p$ (in kPa) gives a straight line of slope $0.0500 g c m^{- 3}$ and intercept $0.400 kPa g c m^{- 3}$ on the $p / V$ axis. The Langmuir constant $K$ in $kP a^{- 1}$ is:

A $8.0$
B $0.125$
C $2.5$
D $0.40$

Answer: B

Langmuir gives

p / V = p / V_{m} + 1/ (K V_{m})

. Slope

= 1/ V_{m} = 0.0500

, so

V_{m} = 20 c m^{3} g^{- 1}

. Intercept

= 1/ (K V_{m}) = 0.400

, so

K = 1/ (0.400 \times 20) = 0.125 kP a^{- 1}

, i.e. slope/intercept.

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