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Natural gas is a source of methane - Scottish Highers Chemistry - Question 7 - 2022

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Natural gas is a source of methane. (a) Methane, CH₄, can be used as a fuel. In an experiment, methane was burned to raise the temperature of 100 cm³ of water by 27... show full transcript

Worked Solution & Example Answer:Natural gas is a source of methane - Scottish Highers Chemistry - Question 7 - 2022

Step 1

Methane Mass Calculation

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Answer

To find the mass of methane burned, use the formula:

q=mcΔTq = mcΔT

Where:

  • qq is the heat absorbed (in joules)
  • mm is the mass of water (in grams, which for 100 cm³ of water is 100 g)
  • cc is the specific heat capacity of water (approximately 4.18 J g⁻¹ °C⁻¹)
  • ΔTΔT is the temperature change (27 °C).

Calculating qq:
q=100imes4.18imes27=11286J=11.286kJq = 100 imes 4.18 imes 27 = 11286 J = 11.286 kJ

Next, since combustion of 1 mole of methane releases 891 kJ, we set up the proportion:

ext{moles of methane} = rac{11.286 ext{ kJ}}{891 ext{ kJ mol}^{-1}} ext{ moles}

This gives approximately 0.01270.0127 moles. Since the molar mass of methane (CH₄) is approximately 16 g/mol:

extmassofmethane=0.0127extmolesimes16extg/mol=0.203g ext{mass of methane} = 0.0127 ext{ moles} imes 16 ext{ g/mol} = 0.203 g

Step 2

Enthalpy Change for Combustion

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The bond enthalpy method involves breaking and forming bonds. First, we calculate the total bond enthalpies of the reactants and products:

  • Reactants: 1 C–H bond broken (4 bonds total), and 2 O=O bonds (2 bonds)
  • Products: 2 C=O bonds and 4 H–O bonds Using the bond enthalpies from the data booklet, compute the enthalpy change:

extΔH=extBondenergiesofreactantsextBondenergiesofproducts ext{ΔH} = ext{Bond energies of reactants} - ext{Bond energies of products}

If calculated correctly, should yield approximately -816 kJ mol⁻¹.

Step 3

Atom Economy Calculation

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The formula for atom economy is given by:

ext{Atom Economy} = rac{ ext{Molar mass of desired product}}{ ext{Total molar mass of all products}} imes 100

In this case, the desired product is hydrogen (3 H₂) with a mass of 6 g. The total mass of products (1 CO + 3 H₂) is:

GFM: CO = 28 g and 3 H₂ = 6 g → Total = 34 g.

Thus, the atom economy is:

ext{Atom Economy} = rac{6}{34} imes 100 = 17.65 ext{%}

Step 4

Conditions for Nitrogen Dioxide Yield

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To maximize the yield of nitrogen dioxide (NO₂):

  • Temperature: low (to favor the exothermic forward reaction)
  • Pressure: high (since there are fewer moles of gas on the right side of the reaction).

Step 5

Enthalpy Calculation for the Reaction

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Answer

To calculate the enthalpy of the reaction, we use:

extΔHreaction=extΔHproductsextΔHreactants ext{ΔH}_{reaction} = ext{ΔH}_{products} - ext{ΔH}_{reactants} Inserting the respective enthalpy values:

  • For products: 4imesextΔHforCO+12imesextΔHforH2O+9imesextΔHforN24 imes ext{ΔH for } CO + 12 imes ext{ΔH for } H_2O + 9 imes ext{ΔH for } N_2.
  • For reactants: 4imesextΔHforCH4NH3+5imesextΔHforN2O44 imes ext{ΔH for } CH₄NH₃ + 5 imes ext{ΔH for } N_2O₄. Calculating yields approximately -4632 kJ.

Step 6

Structural Formula for Methylhydrazine

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Answer

The full structural formula for methylhydrazine, CH₄N₂H₈, is as follows:

  H  H
   |  |
H--N--N--H
   |  |
   H  H

This depicts two nitrogen atoms bonded together, each bonded to two hydrogen atoms and one carbon atom.

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