Apply Energy from Fuels - IB Chemistry

1. What is the correct classification of hydrogen fuel and its justification?
   Answer: It is a secondary energy carrier because it must be produced using energy from another source, which may be renewable or non-renewable. Hydrogen gas (H₂) is not found in large quantities naturally on Earth; it must be manufactured. Therefore, it is not a primary energy source. It is an energy carrier, meaning it is a way to store and transport energy that has been generated from a primary source (like natural gas, solar, or nuclear). Its classification as renewable or non-renewable depends entirely on the primary energy source used to produce it.
2. What is the primary reason that a hydrogen-oxygen fuel cell is theoretically more efficient at producing useful work than an internal combustion engine?
   Answer: A fuel cell converts chemical potential energy directly into electrical energy, bypassing the production of thermal energy as an intermediate step. The high efficiency of a fuel cell stems from its direct conversion of chemical energy to electrical energy. An internal combustion engine follows the path: chemical energy → thermal energy → mechanical energy. Each conversion step, particularly the thermal to mechanical step, is subject to significant energy loss as waste heat, as described by the laws of thermodynamics (e.g., Carnot efficiency limits).
3. In the operation of a direct methanol fuel cell (DMFC) with an acidic electrolyte, which statement correctly describes the process at the cathode?
   Answer: Oxygen from the air is reduced to form water, and its oxidation state changes from 0 to -2. The cathode is the site of reduction. In a DMFC (and most fuel cells), the oxidant is oxygen, typically from the air. In an acidic medium, oxygen is reduced to water according to the half-equation: O₂(g) + 4H⁺(aq) + 4e⁻ → 2H₂O(l). In this process, the oxidation state of oxygen changes from 0 in O₂ to -2 in H₂O. Methanol is oxidized at the anode, not the cathode.
4. Which fuel produces a smaller mass of CO₂ per MJ of energy released?
   Answer: Methane, because the ratio of mass of CO₂ produced to energy released is lower than that for octane. We need to calculate the mass of CO₂ (M = 44.01 g mol⁻¹) per unit of energy. For Methane (CH₄): 1 mole produces 1 mole CO₂ (44.01 g) and 890 kJ of energy. Mass/Energy = 44.01 g / 0.890 MJ ≈ 49.4 g CO₂/MJ. For Octane (C₈H₁₈): 1 mole produces 8 moles CO₂ (8 * 44.01 g = 352.08 g) and 5470 kJ of energy. Mass/Energy = 352.08 g / 5.470 MJ ≈ 64.4 g CO₂/MJ. Methane produces a smaller mass of CO₂ per MJ of energy.
5. The claim that bioethanol is a 'carbon-neutral' fuel is often considered an oversimplification. What is the main reason for this?
   Answer: The energy required for farming, distillation, and transportation of bioethanol is often derived from fossil fuels. While it is true that the CO₂ released during combustion is theoretically balanced by the CO₂ absorbed during the plant's growth, the entire life cycle is not carbon-neutral. Significant energy input from fossil fuels is required for planting, harvesting, fermentation, distillation, and transportation, which adds a net amount of CO₂ to the atmosphere.
6. Based on the provided data, which statement correctly compares the energy produced by these two fuels?
   Answer: Octane produces more energy per mole, and also produces more energy per gram, than ethanol. To compare energy per gram, we must calculate the specific energy. M(C₂H₅OH) ≈ 46.07 g mol⁻¹. Specific energy = 1367 kJ / 46.07 g ≈ 29.7 kJ g⁻¹. M(C₈H₁₈) ≈ 114.26 g mol⁻¹. Specific energy = 5470 kJ / 114.26 g ≈ 47.9 kJ g⁻¹. Therefore, octane produces more energy per mole (-5470 vs -1367 kJ mol⁻¹) and also more energy per gram (47.9 vs 29.7 kJ g⁻¹).
7. What is the primary reason carbon monoxide (CO) is considered a more immediate health hazard than carbon dioxide (CO₂) when produced by indoor fuel combustion?
   Answer: CO binds strongly and preferentially to hemoglobin in the blood, preventing the transport of oxygen to tissues. The acute toxicity of carbon monoxide stems from its effect on the circulatory system. The CO molecule has a similar size and shape to O₂ and can fit into the same binding site on hemoglobin in red blood cells. However, its affinity for hemoglobin is over 200 times greater than that of oxygen. It binds effectively irreversibly, forming carboxyhemoglobin and preventing the blood from carrying oxygen from the lungs to the body's tissues, leading to asphyxiation.
8. A fuel cell uses hydrogen gas with an energy density of 120 MJ/kg, but the overall system efficiency is only 45% due to conversion losses. A gasoline engine has fuel with energy density of 44 MJ/kg and operates at 25% efficiency. If both systems must provide 500 MJ of useful energy output, what is the difference in fuel mass required, and which factor most significantly affects this comparison?
   Answer: Fuel cell requires 9.26 kg, gasoline requires 45.45 kg; difference = 36.19 kg; energy density is the most significant factor For fuel cell: Energy input needed = 500 MJ ÷ 0.45 = 1111.1 MJ. Mass = 1111.1 ÷ 120 = 9.26 kg. For gasoline: Energy input needed = 500 MJ ÷ 0.25 = 2000 MJ. Mass = 2000 ÷ 44 = 45.45 kg. Difference = 36.19 kg. To determine the most significant factor: If only energy density differed (120 vs 44 MJ/kg at same efficiency), mass ratio would be 44/120 = 0.37. If only efficiency differed (45% vs 25% with same energy density), mass ratio would be 25/45 = 0.56. Since 0.37 < 0.56, energy density has the larger effect on fuel mass requirements.
9. Which statement correctly distinguishes a key feature of a hydrogen fuel cell compared to a typical rechargeable battery for powering a device?
   Answer: A fuel cell is an open system that continuously converts the chemical energy of externally supplied fuel into electricity. The fundamental difference is that a battery is a closed system that stores energy; its reactants are contained within its casing and are depleted during discharge (and regenerated during charging). A fuel cell is an open system; it does not store energy but rather converts it. It requires a continuous external supply of fuel (like hydrogen) and an oxidant (like oxygen) to operate, much like an engine.
10. Which statement best describes the molecular mechanism by which gases like CO₂ contribute to the enhanced greenhouse effect?
    Answer: The bonds within these molecules vibrate upon absorbing outgoing low-frequency infrared radiation, which is then re-radiated in all directions. Greenhouse gases do not absorb incoming UV radiation (that's ozone's role) or form a simple reflective layer. The mechanism involves the absorption of specific frequencies of outgoing infrared (IR) radiation from the Earth's surface. This absorbed energy causes the covalent bonds in the gas molecules (like the C=O bonds in CO₂) to vibrate. The excited molecules then re-radiate this energy as IR radiation in all directions, including back towards the Earth's surface, thus trapping heat in the lower atmosphere.
11. What is the ultimate origin of the chemical energy released when fossil fuels are burned?
    Answer: Solar energy captured via photosynthesis by ancient plants and microorganisms. Fossil fuels are formed from the remains of ancient living organisms (plants, algae, plankton). These organisms originally captured energy from the sun through photosynthesis, converting light energy into chemical energy stored in complex organic molecules (biomass). Over millions of years, heat and pressure transformed this stored chemical energy into the forms we know as coal, oil, and natural gas. The geothermal energy provided the conditions for transformation but was not the original source of the stored chemical energy.
12. In a direct methanol fuel cell (DMFC) with an acidic electrolyte, what is the correct half-equation for the reaction at the anode?
    Answer: CH₃OH(l) + H₂O(l) → CO₂(g) + 6H⁺(aq) + 6e⁻ The anode is the site of oxidation. Methanol (CH₃OH) is the fuel and is oxidized to carbon dioxide (CO₂). Balancing the atoms and charge in an acidic medium gives the half-equation: CH₃OH(l) + H₂O(l) → CO₂(g) + 6H⁺(aq) + 6e⁻. Choice A is the cathode reaction. Choice C is the reverse of the anode reaction (reduction). Choice D is an unbalanced overall combustion equation, not a half-equation.
13. Which statement correctly compares the complete combustion of 1.0 mole of methane (CH₄) and the incomplete combustion of 1.0 mole of methane to produce carbon monoxide and water?
    Answer: Complete combustion is a more exothermic process and produces carbon dioxide, a greenhouse gas, while incomplete combustion produces toxic carbon monoxide. Complete combustion (CH₄ + 2O₂ → CO₂ + 2H₂O) releases more energy (is more exothermic) than incomplete combustion (CH₄ + 1.5O₂ → CO + 2H₂O) because the formation of C=O bonds in CO₂ is energetically more favorable than the formation of the C≡O bond in CO. Complete combustion produces CO₂, a greenhouse gas. Incomplete combustion produces CO, which is toxic as it binds irreversibly to hemoglobin.
14. A student compares the energy density of three fuels by measuring the temperature change when 2.50 g of each fuel is completely combusted in a calorimeter containing 150.0 g of water. Fuel A increases the water temperature by 18.2°C, Fuel B by 24.6°C, and Fuel C by 21.8°C. If the specific heat capacity of water is $4.18 \text{ J g}^{-1} \text{°C}^{-1}$ and heat losses are negligible, which statement correctly ranks the fuels by energy density and identifies the most suitable fuel for a portable camping stove where weight is the primary concern?
    Answer: Energy density: B > C > A; Fuel B is most suitable because it has the highest energy density and will provide the longest burning time per gram First, calculate energy released: Fuel A: $q = 150.0 \times 4.18 \times 18.2 = 11,400 \text{ J}$; Fuel B: $q = 150.0 \times 4.18 \times 24.6 = 15,400 \text{ J}$; Fuel C: $q = 150.0 \times 4.18 \times 21.8 = 13,700 \text{ J}$. Energy density per gram: A = 4,560 J/g, B = 6,160 J/g, C = 5,480 J/g. Therefore B > C > A. For portable use where weight matters, highest energy density (B) provides most energy per unit mass. Choice B incorrectly ranks energy density. Choice C correctly ranks but incorrectly suggests lower energy density is better for portability. Choice D incorrectly ranks the fuels.
15. Which of these energy sources is correctly described as a renewable fuel?
    Answer: Hydrogen produced from the electrolysis of water using geothermal power. A renewable fuel is derived from a source that is not depleted with use or can be replenished within a human lifespan. Natural gas and uranium are non-renewable. Hydrogen is an energy carrier, and its renewability depends on its production method. Hydrogen from steam reforming of methane (a fossil fuel) is non-renewable. Hydrogen produced via electrolysis is only renewable if the electricity for the process comes from a renewable source, such as geothermal, solar, or wind power.
16. Incomplete combustion of propane (C₃H₈) produces carbon monoxide and water as the only products. What is the sum of all integer coefficients when the equation for this reaction is balanced?
    Answer: 23 The unbalanced equation is C₃H₈ + O₂ → CO + H₂O. Balancing C and H gives C₃H₈ + O₂ → 3CO + 4H₂O. The right side has 3 + 4 = 7 oxygen atoms. So, 3.5 O₂ molecules are needed: C₃H₈ + 3.5O₂ → 3CO + 4H₂O. To get integer coefficients, multiply the entire equation by 2: 2C₃H₈ + 7O₂ → 6CO + 8H₂O. The sum of the coefficients is 2 + 7 + 6 + 8 = 23.
17. Hydrogen is often cited as a clean fuel. What is a primary reason why its widespread use is currently limited by challenges in production?
    Answer: The vast majority of commercial hydrogen is produced from the steam reforming of methane, a process that consumes fossil fuels and releases carbon dioxide. Although 'green' hydrogen can be produced by electrolysis of water using renewable energy, this is currently expensive and not widespread. The most common and cheapest method for producing H₂ is the steam reforming of natural gas (methane): CH₄(g) + H₂O(g) → CO(g) + 3H₂(g). This process uses a fossil fuel as a feedstock and also releases CO₂, undermining the 'clean' aspect of the hydrogen fuel cycle.
18. What distinguishes coal from natural gas in terms of chemical composition and environmental impact upon combustion?
    Answer: Coal is a complex solid mixture containing sulfur impurities, leading to SO₂ emissions and acid rain; natural gas is primarily CH₄ with fewer impurities. Coal is not pure carbon but a complex solid containing various elements, notably sulfur. Burning coal releases sulfur dioxide (SO₂), a primary precursor to acid rain. Natural gas is mostly methane (CH₄) and is typically processed to remove most sulfur compounds. Therefore, burning natural gas is significantly cleaner in terms of SO₂ emissions. Also, methane's high hydrogen-to-carbon ratio means it produces less CO₂ per unit of energy than coal.
19. How would the standard enthalpy of combustion of propan-1-ol (C₃H₇OH) be expected to compare with that of ethanol (C₂H₅OH)?
    Answer: Propan-1-ol would be more exothermic because more moles of energy-releasing C=O and O-H bonds are formed per mole of fuel. Combustion involves breaking bonds in reactants (endothermic) and forming bonds in products (exothermic). Propan-1-ol (C₃H₇OH) has more C-C and C-H bonds to break than ethanol (C₂H₅OH). Upon combustion, it produces more moles of products (3 moles of CO₂ and 4 moles of H₂O, vs. 2 moles of CO₂ and 3 moles of H₂O for ethanol). The formation of these additional, very stable C=O and O-H bonds releases a large amount of energy, far outweighing the extra energy needed to break the bonds in the larger fuel molecule. Therefore, the overall enthalpy change is more exothermic (more negative) for propan-1-ol.
20. An automotive engineer compares two fuel injection strategies for ethanol ($\text{C}_2\text{H}_5\text{OH}$). Strategy A injects fuel at stoichiometric air-fuel ratio, while Strategy B uses 10% excess air. The standard enthalpy of combustion of ethanol is -1367 kJ/mol. If the engine operates at 30% thermal efficiency under both conditions, but Strategy B reduces combustion temperature by 80°C, which strategy provides better fuel economy and why?
    Answer: Both strategies provide identical fuel economy because thermal efficiency and enthalpy of combustion remain constant regardless of air-fuel ratio The enthalpy of combustion (-1367 kJ/mol) is a thermodynamic property that depends only on the initial and final states, not the combustion conditions. Both strategies completely combust ethanol to CO₂ and H₂O, so the energy released per mole of fuel is identical. The thermal efficiency (30%) is stated to be the same for both conditions. Therefore, the useful work output per mole of fuel is identical (0.30 × 1367 = 410 kJ/mol). Excess air affects combustion temperature and emissions, but not the fundamental energy conversion. Choice A incorrectly suggests energy release changes with air ratio. Choice B incorrectly relates air dilution to energy density. Choice C incorrectly assumes lower temperature improves efficiency when thermal efficiency is given as constant.

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