6. Methane gas, CH₄, can be captured from the breakdown of waste in landfills - VCE - SSCE Chemistry - Question 6 - 2020 - Paper 1

First, we need to convert the temperature from Celsius to Kelvin:

$T = 25 °C + 273.15 = 298.15 K$

Next, we can calculate the number of moles of CH₄:

$n(CH₄) = \frac{20.0\, g}{16.0\, g/mol} = 1.25\, mol$

Now, we can use the Ideal Gas Law to find the pressure (P):

$PV = nRT$

Rearranging for P gives us:

$P = \frac{nRT}{V}$

Substituting the known values:

$P = \frac{(1.25\, mol)(8.31\, kPa\cdot L/(mol\cdot K))(298.15\, K)}{5.0\, L}$

Calculating this gives:

$P ≈ 62.01\, kPa$

To calculate the percentage of energy lost, we first need to determine the energy provided by the combustion of CH₄ and the energy absorbed by the water.

1. Calculate the energy required to heat the water:

   • Mass of water, m = 350.0 g
   • Specific heat capacity of water, c = 4.18 J/g°C
   • Temperature change, ΔT = 32.3 °C - 20 °C = 12.3 °C

   Energy absorbed by the water, Q = mcΔT:

   $Q = 350.0\, g \times 4.18\, J/g°C \times 12.3\, °C = 18,363\, J$

2. Calculate the energy released by the combustion of 0.485 g of CH₄:

   • Molar mass of CH₄ = 16.0 g/mol
   • The energy released during the combustion of CH₄ (approximately 890 kJ/mol):

   $Q_{combustion} = \left( \frac{0.485\, g}{16.0\, g/mol} \right) \times 890\, kJ/mol \times 1000\, J/kJ \\ Q_{combustion} ≈ 28,413.75\, J$

3. Calculate the percentage of energy lost:

   $\text{Percentage lost} = \left( \frac{Q_{combustion} - Q}{Q_{combustion}} \right) \times 100$

   $\text{Percentage lost} = \left( \frac{28413.75\, J - 18363\, J}{28413.75\, J} \right) \times 100 \approx 35.2\%$

The environmental impact of methane (CH₄) derived from landfill versus natural gas can be compared by looking at both similarities and differences:

Similarity: Both sources of methane produce atmospheric carbon dioxide (CO₂) when burned. This contributes to greenhouse gas emissions and impacts climate change.

Difference: Methane from landfills is often considered more environmentally friendly due to its renewable nature. In comparison, methane from natural gas extraction contributes to additional environmental damage due to its extraction process, which can release other harmful gases, such as sulfur oxides (SOₓ) and nitrogen oxides (NOₓ).

Furthermore, methane from landfills is often a byproduct of waste decomposition, which poses fewer risks compared to the drilling and fracking associated with conventional natural gas extraction. The latter can lead to land degradation and increased atmospheric CO₂ levels.