Respuesta :

Answer:

[tex]24.02gC_{4}H_{10}[/tex]

Explanation:

The balanced equation is the following:

[tex]_{2} C_{4}H_{10}+_{13}O_{2}=_{8}CO_{2}+_{10}H_{2}O[/tex]

The molecular mass of the carbon dioxide is:

Atomic mass of C = 12[tex]\frac{g}{mol}[/tex]

Atomic mass of O = 16[tex]\frac{g}{mol}[/tex]

Molecular mass of [tex]CO_{2}[/tex] = 12 + (16*2) = 44[tex]\frac{g}{mol}[/tex]

The molecular mass of the butano is:

Atomic mass of C = 12[tex]\frac{g}{mol}[/tex]

Atomic mass of H = 1[tex]\frac{g}{mol}[/tex]

Molecular mass of [tex]C_{4}H_{10}[/tex] = (4*12) + (10*1) = 58[tex]\frac{g}{mol}[/tex]

Find the grams of carbon dioxide using the stoichiometry of the reaction:

[tex]72.9gCO_{2}*\frac{1molCO_{2}}{44gCO_{2}}*\frac{2molesC_{4}H_{10}}{8molesCO_{2}}*\frac{58gC_{4}H_{10}}{1molC_{4}H_{10}}=24.02gC_{4}H_{10}[/tex]

Taking into account the stoichiometry of the reaction, the mass of butane needed to produce 72.9 grams of carbon dioxide is 24.02 grams.

The balanced reaction is:

2 C₄H₁₀ + 13 O₂ → 8 CO₂ + 10 H₂O

By reaction stoichiometry (that is, the relationship between the amount of reagents and products in a chemical reaction), the following amounts of moles participate in the reaction:

  • C₄H₁₀: 2 moles
  • O₂: 13 moles
  • CO₂: 8 moles
  • H₂O: 10 moles

The molar mass of the compounds is:

  • C₄H₁₀: 58 g/mole
  • O₂: 32 g/mole
  • CO₂: 44 g/mole
  • H₂O: 18 g/mole

Then, by reaction stoichiometry, the following mass quantities participate in the reaction:

  • C₄H₁₀: 2 moles× 58 g/mole= 116 grams
  • O₂: 13 moles× 32 g/mole= 416 grams
  • CO₂: 8 moles× 44 g/mole= 352 grams
  • H₂O: 10 moles× 18 g/mole= 180 grams

Then you can apply the following rule of three: if by reaction stoichiometry 352 grams of carbon dioxide are produced by 116 grams of butane, 72.9 grams of carbon dioxide are produced from how much mass of butane?

[tex]mass of butane=\frac{72.9 grams of carbon dioxide x116 grams of butane}{352 grams of carbon dioxide}[/tex]

mass of butane= 24.02 grams

Finally, the mass of butane needed to produce 72.9 grams of carbon dioxide is 24.02 grams.

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