Amixture of methane gas, ch4(g) , and pentane gas, c5h12(g) , has a pressure of 0.5239 atm when placed in a sealed container. the complete combustion of the mixture to carbon dioxide gas, co2(g) , and water vapor, h2o(g) , was achieved by adding exactly enough oxygen gas, o2(g) , to the container. the pressure of the product mixture in the sealed container is 2.429 atm . calculate the mole fraction of methane in the initial mixture, assuming the temperature and volume remain constant.

Let the partial pressure of methane, CH₄ be u

Let the partial pressure of pentane, C₅H₁₂ be v

The total pressure of the mixture is 0.5239 atm i.e

Partial pressure of methane + partial pressure of pentane = 0.5239 atm

Combustion reaction of the mixture.

CH₄ + 2O₂ —> CO₂ + 2H₂O

From the balanced equation above,

u atm of CH₄ produced u atm of CO₂ and 2u atm of H₂O.

Thus, the partial pressure of CH₄ produces = u + 2u = 3u atm of the products.

C₅H₁₂ + 8O₂ —> 5CO₂ + 6H₂O

From the balanced equation above,

v atm of C₅H₁₂ produced v atm of CO₂ and 6v atm of H₂O.

Thus, the partial pressure of C₅H₁₂ produces = 5v + 6v = 11v atm of the products.

CH₄ produced 3u atm

C₅H₁₂ produced 11v atm

But the total pressure of the products is 2.429 atm.

Thus,

Next, we shall determine the partial pressure of methane, CH₄ i.e u.

u + v = 0.5239 1

3u + 11v = 2.429 2

From equation 1,

v = 0.5239 – u

Substitute v into equation 2

3u + 11v = 2.429

3u + 11(0.5239 – u) = 2.429

3u + 5.7629 – 11u = 2.429

Collect like terms

3u – 11u = 2.429 – 5.7629

–8u = –3.3339

Divide both side by –8

u = –3.3339 / –8

Therefore, the partial pressure of methane, CH₄ in the initial mixture is 0.4167 atm.

Finally, we shall determine the mole fraction of methane CH₄ in the initial mixture.

Partial pressure of methane, CH₄ = 0.4167 atm.

Total pressure = 0.5239 atm

Mole fraction = partial pressure / Total pressure

Mole fraction of methane CH₄ = 0.4167 / 0.5239

Therefore, the mole fraction of methane CH₄ in the initial mixture is 0.795

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each  column  of the  table  is called a group. elements in a group share similar properties. groups are  read  from  top  to  bottom. metal. metalloid. nonmetal. solid. liquid. gas. fe. hg. o.  2. 3. 4. 5. 6. 7. 8. 9.  2. beryllium. 9.012. 4.  sodium. 22.990.  11. 3.  magnesium. 24.305.  12.  potassium. 39.098.  19. 4.  calcium. 40.078.  20. i guess  i