Nitrogen adsorbs on a catalyst following the Langmuir isotherm. The volumes adsorbed (STP) per gram are 4.0 cm^3 at 8.0 kPa and 6.0 cm^3 at 24.0 kPa. Each N2 molecule covers 0.162 nm^2; use 22400 cm^3 mol^-1 at STP and N_A=6.022x10^23 mol^-1. Find the surface area of the catalyst in m^2 g^-1 (one decimal).

JEE Advanced levelNumerical answerDifficulty 3 of 3sc045

Nitrogen adsorbs on a catalyst following the Langmuir isotherm. The volumes adsorbed (STP) per gram are $4.0 c m^{3}$ at $8.0 kPa$ and $6.0 c m^{3}$ at $24.0 kPa$ . Each $N X_{2}$ molecule covers $0.162 n m^{2}$ ; use $22400 c m^{3} mo l^{- 1}$ at STP and $N_{A} = 6.022 \times 1 0^{23} mo l^{- 1}$ . Find the surface area of the catalyst in $m^{2} g^{- 1}$ (one decimal).

Numerical answer type, answer in m^2/g, tolerance 0.2.

p / V = 2.00

and

4.00

8

and

24 kPa

, so slope

= 2.00/16 = 0.125

and

V_{m} = 1/0.125 = 8.0 c m^{3} g^{- 1}

. Moles

= 8.0/22400 = 3.571 \times 1 0^{- 4}

; molecules

= 2.151 e + 20

. Area

= 2.151 e + 20 \times 0.162 \times 1 0^{- 18} = 34.8 m^{2} g^{- 1}