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Class 10 Class 12

Chemical Kinetics

The rate of the chemical reaction doubles for an increase of 10 k in absolute temperature from 298 K. Calculate E_a.

Given that initial temperature, T₁ = 298 K
Final temperature, T₂ = 298 + 10 = 308 K
Rate of chemical reaction will increase with raise of rate constant so that take
Initial value of rate constant k₁ = k
find rate constant, k₂ = 2k
Also, R = 8.314 J K⁻¹ mol⁻¹
Use Arrhenius equation

According to Arrchenium equation,

\log \frac{k_{2}}{k_{1}} = \frac{Ea}{2.303 R} [\frac{1}{T_{1}} - \frac{1}{T_{2}}]

\frac{k_{2}}{k_{1}} = 2, T_{1} = 298 K, T_{2} = 298 + 10 = 308 k R = 8.314 J k^{- 1} {mol}^{- 1}

\log 2 = \frac{Ea}{2.303 \times (8.314 J K^{- 1} {mol}^{- 1})} [\frac{1}{298 k} - \frac{1}{308 k}]

0.3010 = \frac{Ea}{2.303 \times 8.314} \times \frac{10}{298 \times 308}

Ea = \frac{0.3010 \times 2.303 \times 8.314 \times 298 \times 308}{10} J {mol}^{- 1}

Ea = \frac{0.3010 \times 2.303 \times 8.314 \times 298 \times 308}{10 \times 100} kJ {mol}^{- 1} = 52.89 kJ {mol}^{- 1}

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Time required to decompose SO₂ Cl₂ to half its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.

Given that
half life, t_1/2 = 60 min = 60 x 60 = 3600 sec (1 min = 60 sec)
The formula of half life for the a 1^st order

reaction,For a first order reaction.

t = \frac{2.303}{k} \log \frac{1}{a - x} t_{1 / 2} = 60 minutes = 60 \times 60 \sec . = 360 \sec . k = \frac{0.693}{3600 \sec .} = 1.925 \times 10^{- 4} s^{- 1}

227 Views

The activation energy for the reaction
2HI (g) → H₂ + I₂(g)
is 209.5 kJ mol^–1 at 581 k. Calculate the fraction of molecules of reactants having energy equal to or greater than activation energy?

2HI (g) → H + I₂(g)
Activation energy, E_a = 209.5 kJ mol⁻¹
Multiply by 1000 to convert in j
E_a= 209500 J mol⁻¹
Temperature, T = 581 K
Gas constant, R = 8.314 JK⁻¹ mol⁻¹
According to Arhenious equation
K = A e^–Ea/RT
In this formula term e^–Ea/RTrepresent the number of molecules which have energy equal or more than activation energy
Number of molecules = e^–Ea/RT
Plug the values we get
Number of molecules
$= e^{- \frac{209500}{8.314 \times 581}} = e^{- 43.4} = \frac{1}{e^{43.4}}$

taking antilog of we get

1.47 x 10^-19

249 Views

The decomposition of dimethyl ether leads to the formation of CH₄, H₂ and CO and the rate is given by
Rate = k[CH₃OCH₃]^3/2
The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e.,
Rate = k pCH₃O CH₃^3/2.
If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?

The reaction for decomposition of dimethyl ether can be written as

{CH}_{3} - O - {CH}_{3} \to {CH}_{4} + H_{2} + CO

The rate of reaction,

(\frac{dx}{dt}) = \frac{d ({CH}_{3} {OCH}_{3})}{dt} = \frac{d [{CH}_{4}]}{dt} = \frac{d [H_{2}]}{dt} \frac{d [CO]}{dt}

= k ({pCH}_{3} {OCH}_{3})^{3 / 2}

The unit of rate is: bar min^–1 or bar s^–1.
The unit of rate constant, k is bar s^–1 bar^–3/2

[∵ k = rate (pCH₃OCH₃)^–3/2∴ bar^–1/2 s^–1.

163 Views

What will be the effect of temperature on rate constant?

Rate constant of the chemical reaction increase with the raise of temperature. It is observed that the rate constant of a reaction is nearly doubled when the temperature increased by 10°C.

177 Views

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Chemical Kinetics

Time required to decompose SO₂ Cl₂ to half its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.

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Chemical Kinetics

Time required to decompose SO2 Cl2 to half its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.

Time required to decompose SO₂ Cl₂ to half its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.