# Sulfur dioxide is used primarily to make sulfuric acid. One method of producing it is by roasting mineral sulfides, for example...... FeS2(s) + O2(g) --> SO2(g) + Fe2O3(s) [unbalanced] A...

Sulfur dioxide is used primarily to make sulfuric acid. One method of producing it is by roasting mineral sulfides, for example...

...

FeS2(s) + O2(g) --> SO2(g) + Fe2O3(s) [unbalanced]

A production error leads to the sulfide being placed in a 950-L vessel with insufficient oxygen. The partial pressure of O2 is 0.64 atm and the total pressure is initially 1.05 atm, with the balance N2. The reaction is run until 85% of the O2 is consumed, and the vessel is then cooled to its initial temperature. What is the total pressure and partial pressure of each gas in the vessel?

Asked on by spock3

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valentin68 | College Teacher | (Level 3) Associate Educator

Posted on

We know that at normal pressure `P_0 =1 atm` and temperature `T_0 =273 K` one mole of any gas occupies the same volume `V_0 =22.4 Liter` . We suppose that the temperature is standard (`T_0`).

At `P1 =1.05 atm` the volume of one mole of gas is ` `

`V_1 =P_0*V_0/P_1 =1*22.4/1.05 =21.33 ("Liter")/("mole")`

The total number of moles of all gases (`O_2`and `N_2`) initially is

`N1_("tot") = 950/21.33 =44.53 "moles"`

The number of moles of `O_2` initially is

`N1_("O2") =44.53*0.64/1.05 =27.14 "moles"`

Total number of moles of `N_2` initially and finally is

`N1_("N2")=N2_("N2")=44.53-27.14 =17.38 "moles"`

Total number of moles of `O_2` finally is

`N2_("O2") =(1-0.85)*27.14 =4.07 "moles"`

The balanced chemical reaction is

`4*FeS_2 + 11*O_2 = 8*SO_2 + 2*Fe_2O_3`

Molecular masses are

`M(O_2) =32 g`

`M(SO_2) =32+16*2 = 64 g`

Mass of `O_2` gas initial is

`m1(O_2) =27.14*32 =868.48 g`

Mass of `O_2` gas that enters reaction is

`m(O_2) =0.85*m1(O_2)= 0.85*868.48 =738.21 g`

The chemical reaction is as follows

From 11*32g O2 results......8*64 g SO2

from 738.21g O2 results.....x g SO2

Mass of resulting `SO_2` is

`m(SO_2) =8*64*738.21/(11*32) =1073.75 g`

Total number of moles of `SO_2` that results is

`N2_(SO2) =1073.75/64 =16.78 "moles"`

The final gas is composed of the remaining `O_2` , `N_2` and resultant `SO_2` . Final number of gas moles is

`N2_("tot") =4.07 +17.38+16.78 = 38.23 "moles"`

Final volume and temperature are the same

`V =950 L` ,`T =273 K`

Total final pressure is

`P2 = P1*(N2_("tot"))/(N1_("tot")) =1.05*38.23/44.53 =0.9 atm`

Final partial pressures are

`P2_(O2) = 0.9*(N2_(O2))/(N2_("tot")) =0.9*4.07/38.23 =0.096 atm`

`P2_(N2) =0.9*17.38/38.23 =0.409 atm`

`P2_(SO2) =0.9*16.78/38.23 =0.395 atm`

Final check `0.096+0.409+0.395 =0.900 atm`

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