Question

Most of the sulfur used in the United States is chemically synthesized from hydrogen sulfide gas recovered from natural gas wells. In the first step of this synthesis, called Claus process, hydrogen sulfide gas is reacted with dioxygen gas to produce gaseous sulfur dioxide and water. Suppose a chemical engineer studying a new catalyst for the Claus reaction finds that 450 liters per second of dioxygen are consumed when the reaction is run at 264 degrees Celsius and 0.48 atm.
Required:
Calculate the rate at which sulfur dioxide is being produced. Give the answer in kg per second.

Answer 1

Answer:

$0.21\ \text{kg/s}$

Explanation:

P = Pressure = $0.48\ \text{atm}=0.48\times 101325\ \text{Pa}$

V = Volume = $450\ \text{L/s}=450\times 10^{-3}\ \text{m}^3/\text{s}$

R = Gas constant = $8.314\ \text{J/mol K}$

T = Temperature = $(264+273.15)\ \text{K}$

The reaction is

$2H_2S+3O_2\rightarrow 2SO_2+2H_2O$

From ideal gas equation we have

$PV=nRT\\\Rightarrow n=\dfrac{PV}{RT}\\\Rightarrow n=\dfrac{0.48\times101325\times 450\times 10^{-3}}{8.314\times (264+273.15)}\\\Rightarrow n=4.9\ \text{mol}$

Moles of $SO_2$ produced is

$\dfrac{2}{3}\times 4.9=3.267\ \text{moles}$

Molar mass of $SO_2$ = 64.066 g/mol

Production rate is

$3.267\times 64.066=209.3\ \text{g/s}=0.21\ \text{kg/s}$

The rate at which sulfur dioxide is being produced $0.21\ \text{kg/s}$.