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NCERT Exemplar · Q33

Q.Oxygen is available in plenty in air yet fuels do not burn by themselves at room temperature. Explain.

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The Arrhenius equation shows that the rate constant k=Ae−Ea/RTk = A e^{-E_a/RT} is extremely small at room temperature because the thermal energy RTRT is much smaller than the activation energy EaE_a for combustion. So, even though oxygen is abundant, the reaction rate is negligible — fuels do not burn spontaneously.

The key lies not in the availability of oxygen, but in the energy barrier that must be overcome for the reaction to start. Think of it like a boulder at the top of a hill: it has plenty of gravitational potential energy, but it won’t roll down unless you give it a push past the small lip at the top. That push is the activation energy.

  1. The Arrhenius Equation governs reaction rates. For any chemical reaction, the rate constant kk is given by:

k=Ae−Ea/RTk = A e^{-E_a/RT}

where AA is the frequency factor (how often molecules collide in the right orientation), EaE_a is the activation energy (the minimum energy needed for the reaction to occur), RR is the gas constant, and TT is the absolute temperature.

  1. At room temperature, RTRT is small.

    At T≈298 KT \approx 298\ \text{K}, RT≈2.48 kJ/molRT \approx 2.48\ \text{kJ/mol}. For combustion reactions (like burning wood, petrol, or coal), the activation energy EaE_a is typically in the range of 100100–200 kJ/mol200\ \text{kJ/mol}. So the ratio Ea/RTE_a/RT is huge — around 4040 to 8080.

  2. The exponential factor crushes the rate.

    Even a modest Ea/RT=40E_a/RT = 40 gives e−40≈4×10−18e^{-40} \approx 4 \times 10^{-18}. That means the rate constant is astronomically small — effectively zero. Billions of oxygen molecules collide with the fuel every second, but almost none have enough energy to cross the barrier.

  3. Why a spark or flame works. …

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