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Grade 11IBChemistry

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Energy sources are classified as renewable (e.g., solar, wind, biofuels) and non-renewable (e.g., fossil fuels, nuclear fission).

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Specific energy is the energy released per unit mass of fuel (kJ⋅kg−1kJ \cdot kg^{-1}), while energy density is the energy released per unit volume (kJ⋅dm−3kJ \cdot dm^{-3}).

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Fossil fuels like coal, oil, and natural gas are formed from fossilized organic matter. Their quality is often measured by the octane number, which indicates resistance to 'knocking' in engines.

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Biofuels such as bioethanol and biodiesel are derived from biomass. Biodiesel is produced via the transesterification of triglycerides with an alcohol (typically CH3OHCH_3OH) using a strong base catalyst.

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Nuclear energy involves changes in the nucleus. Fission is the splitting of heavy nuclei (e.g., 235U^{235}U), while fusion is the combining of light nuclei (e.g., 2H^2H and 3H^3H).

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Mass defect (Δm\Delta m) is the difference between the mass of a nucleus and the sum of the masses of its individual nucleons. This mass is converted into binding energy according to ΔE=Δmc2\Delta E = \Delta m c^2.

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The Greenhouse Effect occurs when greenhouse gases like CO2CO_2, CH4CH_4, and H2OH_2O absorb infrared (IR) radiation due to changes in molecular dipole moments during vibration.

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Photovoltaic cells convert light directly into electricity using semiconductors, while Dye-Sensitized Solar Cells (DSSCs) mimic photosynthesis using a dye to absorb photons.

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Fuel cells convert chemical energy from a fuel (like H2H_2) directly into electrical energy. In an alkaline hydrogen fuel cell, the anode reaction is 2H2(g)+4OH−(aq)→4H2O(l)+4e−2H_2(g) + 4OH^-(aq) \rightarrow 4H_2O(l) + 4e^-.

📐Formulae

Specific Energy=Energy releasedMass of fuel\text{Specific Energy} = \frac{\text{Energy released}}{\text{Mass of fuel}}

Energy Density=Energy releasedVolume of fuel\text{Energy Density} = \frac{\text{Energy released}}{\text{Volume of fuel}}

ΔE=Δmc2\Delta E = \Delta m c^2

Efficiency=Useful energy outputTotal energy input×100%\text{Efficiency} = \frac{\text{Useful energy output}}{\text{Total energy input}} \times 100\%

ln⁡N0Nt=λt\ln \frac{N_0}{N_t} = \lambda t

t1/2=ln⁡2λt_{1/2} = \frac{\ln 2}{\lambda}

💡Examples

Problem 1:

Calculate the specific energy of methane (CH4CH_4) if its standard enthalpy of combustion is −891 kJ⋅mol−1-891\, kJ \cdot mol^{-1}.

Solution:

  1. Molar mass of CH4=12.01+4(1.01)=16.05 g⋅mol−1CH_4 = 12.01 + 4(1.01) = 16.05\, g \cdot mol^{-1}.
  2. Specific energy =∣ΔHc∣Molar Mass=891 kJ⋅mol−116.05 g⋅mol−1=55.51 kJ⋅g−1= \frac{|\Delta H_c|}{\text{Molar Mass}} = \frac{891\, kJ \cdot mol^{-1}}{16.05\, g \cdot mol^{-1}} = 55.51\, kJ \cdot g^{-1}.
  3. Convert to kJ⋅kg−1kJ \cdot kg^{-1}: 55.51×1000=55510 kJ⋅kg−155.51 \times 1000 = 55510\, kJ \cdot kg^{-1}.

Explanation:

Specific energy is calculated by dividing the magnitude of the enthalpy of combustion by the molar mass of the substance.

Problem 2:

Determine the energy released in Joules (JJ) for a nuclear reaction where the mass defect is Δm=2.0×10−29 kg\Delta m = 2.0 \times 10^{-29}\, kg. (Use c=3.00×108 m⋅s−1c = 3.00 \times 10^8\, m \cdot s^{-1})

Solution:

ΔE=Δmc2\Delta E = \Delta m c^2 ΔE=(2.0×10−29 kg)×(3.00×108 m⋅s−1)2\Delta E = (2.0 \times 10^{-29}\, kg) \times (3.00 \times 10^8\, m \cdot s^{-1})^2 ΔE=2.0×10−29×9.00×1016\Delta E = 2.0 \times 10^{-29} \times 9.00 \times 10^{16} ΔE=1.8×10−12 J\Delta E = 1.8 \times 10^{-12}\, J

Explanation:

Einstein's mass-energy equivalence formula is used to calculate the energy released from the mass lost during a nuclear transformation.

Problem 3:

Write the equation for the transesterification of a triglyceride (RCOOCH2−RCOOCH−RCOOCH2RCOOCH_2-RCOOCH-RCOOCH_2) with methanol (CH3OHCH_3OH).

Solution:

C57H110O6+3CH3OH→NaOH/KOH3RCOOCH3+C3H5(OH)3C_{57}H_{110}O_6 + 3CH_3OH \xrightarrow{NaOH/KOH} 3RCOOCH_3 + C_3H_5(OH)_3

Explanation:

Transesterification involves reacting a triglyceride with an alcohol to produce methyl esters (biodiesel) and glycerol (C3H5(OH)3C_3H_5(OH)_3). RR represents long-chain fatty acid groups.