The reaction 2 NOCl(g) ⟶2 NO(g)+Cl2(g) has rate-constant values for the reaction of NOCl of 9.3

The reaction 2 NOCl(g) ⟶2 NO(g)+Cl2(g) has rate-constant...

The reaction $$ 2 \mathrm{NOCl}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) $$ has rate-constant values for the reaction of $\mathrm{NOCl}$ of $9.3 \times 10^{-6} / \mathrm{s}$ at $350 \mathrm{~K}$ and $6.9 \times 10^{-4} / \mathrm{s}$ at $400 \mathrm{~K}$. Calculate the activation energy for the reaction. What is the rate constant at $435 \mathrm{~K} ?$

The reaction
$$
2 \mathrm{NOCl}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)
$$
has rate-constant values for the reaction of $\mathrm{NOCl}$ of $9.3 \times 10^{-6} / \mathrm{s}$ at $350 \mathrm{~K}$ and $6.9 \times 10^{-4} / \mathrm{s}$ at $400 \mathrm{~K}$. Calculate
the activation energy for the reaction. What is the rate constant at $435 \mathrm{~K} ?$

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Key Concepts

Arrhenius Equation

The Arrhenius equation provides a mathematical relationship between the rate constant of a reaction and temperature. It expresses how reaction rates increase exponentially with temperature and includes both the frequency factor and activation energy. This equation is fundamental in chemical kinetics for evaluating how sensitive a reaction is to temperature changes.

Activation Energy

Activation energy is the minimum energy barrier that reacting species must overcome for a chemical reaction to occur. It is a critical parameter that reflects the kinetic stability of reactants and is central to predicting reaction rates. Its determination is achieved through experimental measurements of rate constants at different temperatures and applying the Arrhenius equation.

Temperature Dependence of Reaction Rates

The temperature dependence of reaction rates refers to the fact that the speed of a chemical reaction typically increases with rising temperature. This is explained by the Arrhenius equation, which shows that even small increments in temperature can lead to significant increases in the number of molecules that have enough energy to overcome the activation barrier, resulting in higher reaction rates.

Transcript

00:02 In this problem, we have to calculate the activation energy for the reaction.

00:09 2 moles of nocl gives 2 moles of nitric oxide and cl2 gas.

00:22 And in another subpart, we have to calculate rate constant at 435 kelvin.

00:29 Suppose k1 and k2 are rate constant at temperature.

00:54 T1 and t2 respectively.

01:05 Here, k1 equals to 9 .3 into 10 x to the power minus 6 per second and t1 equals to 350 kelvin.

01:30 When k2 equals to 6 .9 into 10 to the power minus 4 per second, temperature t2 is equal to 400 kelvin.

01:54 Suppose ea indicates activation energy for this reaction.

02:10 From arrhenius equation, we know that a length k2 by k1 is equal to ea divided by gas constant r into t2 minus t1 divided by t1 into t2.

02:41 Now substitute the value of k1, k2, r, t1, t2 in this expression we get ln 6 .9 into 10 -res to the power minus 4 divide by 9 .3 into 10 -3 power minus 6.

03:02 Both have same unit.

03:04 Therefore we did not need to write it is equal to pa divide by.

03:14 Value of r is 8 .31 jule per mole per kelvin into t2 is equal to 400 kelvin and t1 is equal to 350 kelvin.

03:33 Divide by 400 kelvin into 350 kelvin.

03:45 By doing cross multiplication we get e .a equals to 8 .31 into 400 into 350 into ln, 2 ,300 divide by 31, whole divide by 50.

04:21 And here, remaining unit is joule per mole...

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