# 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?

valentin68 | College Teacher | (Level 3) Associate Educator

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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`