Problem 5

To remove sulfur from fuels, hydrogen-assisted hydrodesulfurization is used at refineries, typically over

\ce{MoS2}

supported on

\ce{SiO2}

. Isotope exchange at the gas–solid interface exchanges only the surface atoms. An experiment studies the exchange between an

\ce{MoS2/SiO2}

catalyst (

m_{\text{cat}} = 1.2350

g, Mo mass fraction

w_{\ce{Mo}} = 4.280\%

, initially containing only

^{32}

S) and gaseous

\ce{H2^{34}S}

in a flow reactor (

p = 1.00

bar, flow

v = 20.0

mL min

^{-1}

T = 23.0

°C,

\varphi(\ce{H2^{34}S}) = 1.00\%

, isotopic purity

\alpha = 99.95

mol%). After

t = 10.0

min, the fraction of

^{34}

S among sulfur atoms in the collected gas was

\gamma = 87.3

mol%. (a) Calculate the amount of exchanged (surface) sulfur atoms

n(\mathrm{S})_{\text{surface}}

in mol. (b) Assuming uniform spherical

\ce{MoS2}

particles of density

\rho = 5.06

g cm

^{-3}

, surface areas per atom

A_S = 3.00\times 10^{-19}

m² (S) and

A_{\ce{Mo}} = 5.00\times 10^{-19}

m² (Mo), and that only half of each

\ce{MoS2}

unit is exposed at the surface, calculate the particle radius

R

in nm (

M(\ce{MoS2}) = 160.07

M(\ce{Mo}) = 95.95

g mol

^{-1}

Step 1 of 4: Sulfur balance in the gas

← Previous Next →

V_{\text{in}} = v\,t\,\varphi\,\alpha = 20\times 10\times 0.01\times 0.9995 = 2.00\ \text{mL};\quad V_{\text{out}}(^{34}\mathrm{S}) = v\,t\,\varphi\,\gamma = 1.75\ \text{mL}

Analysis

The reactor is fed $20\times 10 = 200$ mL of gas, of which 1.00 % is H2S; 99.95 % of it carries $^{34}$ S, so $V_{\text{in}}(^{34}\mathrm{S}) = 2.00$ mL. The collected gas keeps the same total flow, but only $\gamma = 87.3\%$ of its H2S sulfur is $^{34}$ S: $V_{\text{out}} = 200\times 0.01\times 0.873 = 1.75$ mL. The missing 0.25 mL is $^{32}$ S exchanged from the catalyst surface.