A reaction has a rate constant of 0.264 𝐌^-1 sec^-1 at 45.6^∘ C and 0.833 𝐌^-1 sec^-1 at 58.8^∘

A reaction has a rate constant of 0.264 𝐌^-1 sec^-1 at...

Key Concepts

Arrhenius Equation

The Arrhenius Equation, expressed as k = A exp(-Ea/(RT)), is fundamental in chemical kinetics. It quantitatively relates the rate constant (k) of a reaction to the temperature (T) and activation energy (Ea), with A being the pre-exponential factor. This equation explains how even small increases in temperature can lead to significant increases in the reaction rate, highlighting the exponential dependency on the ratio Ea/(RT).

Activation Energy

Activation Energy is the minimum amount of energy required for reactants to undergo a transformation to products. It represents the energy barrier that must be overcome for a reaction to proceed. In practical applications, activation energy is often derived from the slope of a plot of ln(k) versus 1/T based on the Arrhenius Equation.

Temperature Dependence of Reaction Rates

The dependence of reaction rates on temperature arises because molecular collisions occur more frequently and with greater energy at higher temperatures. This results in a higher probability that the collisions will overcome the activation energy barrier necessary for the reaction, thereby increasing the rate constant as described by the Arrhenius Equation.

Transcript

00:02 According to question, a second -order reaction has a rate constant k1 equals to 8 .7 into 10 -res -to -the -power minus 4 per mole per second at temperature t1 equals to 30 degrees c, which is equal to 30 -degree kelvin, and rate constant k2 equals to 30 degrees c, which is equal to 30 -3 kelvin, and rate constant k2 equals to, 1 .8 into 10 -res to the power minus 4 per molar per second at temperature t2 equals to 40 degrees c, which is equal to 40 plus 273 kelvin, which is equal to 313 kelvin.

01:12 Suppose ea indicates activation energy, a indicates frequency factor, k3 indicates rate constant at 45 degrees c and t3 is equal to 45 degrees c which is equal to 45 plus 273 kelvin which is equal to 300 18 kelvin.

02:32 From arrhenius equation, ln k2 by k1 is equal to ea upon r into t2 minus t1 divided by t1t2.

03:09 Now substitute the value of k1, k2 r t1 t2 in this expression, ln 1.

03:21 1 .8 into 10 to the power minus 3 divide by 8 .7 into 10 to the power minus 4.

03:31 Both have same in it.

03:34 Therefore, we did not need to write e upon value of r is equal to 8 .31 joule per mole per kelvin into t2 is equal to 313 kelvin, t1 is equal to 303 kelvin, divide by 303 kelvin into 313 kelvin.

04:14 From this we get ln 180 divide by 87 is equal to ea divide by 8 .3 1 joule per mole per kelvin into 10 kelvin divide by 303 kelvin into 313 kelvin.

04:45 Now doing cross multiplication we get ea equals to 8 .31 into 303 into 313 into ln 180 divide by 87, whole divide by 10 and the unit is joule per 1 .5.

05:08 With the help of calculator we get ea equals to 5 .7 into 10 -res to the power 4 joules per mode.

05:27 Thus activation energy is equal to 5 .7 into 10 raise to the power 4 joule per mole.

06:08 Now we have to calculate frequency factor from arrhenius equation we know that rate constant k is equal to a into e to the power minus ea by rt so we can write k2 is equal to a into the power minus ea by r into t2 we can use this expression to evaluate the value of frequency factor a.

07:13 Frequency factor, denoted by a is equal to k2 into e raised to the power ea by rt2...

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