Question

Assume that water boils at 100.0°C in Houston (near sea level), and at 90.0°C in Cripple Creek, Colorado (near 9500 ft). If it takes 4.8 min to cook an egg in Cripple Creek and 4.5 min in Houston, what is Ea for this process?

Answer 1

The $E_{a}$ for the process is 7265.2 Joules/mol.

Calculation of $E_{a}$ :

Instead of providing us with the rate constants at two distinct temperatures, the information in the issue provides us with the time needed at two different temperatures.

For a specific process, the ratio of rate constants will match the ratio of rates.

A ratio of rates will have an inverse relationship with a ratio of times since rates are inversely related to time (greater time equals smaller rate). Below is a summary of this.

Using Arrhenius equation:

ln$\frac{k_{1} }{k_{2} } =\frac{-Ea [1/T_{2} -1/T_{1}] }{R}$

$k_{1} =1/4.5$

$k_{2} =1/4.8$

$T_{1}$ = 273 +100

= 373 K

$T_{2}$ = 273 + 90

= 363 K

Gas constant R = 8.314 Joules/Kelvin.mol

ln4.8/4.5 = -Ea/8.314 [1/373 - 1/363]

0.064539 x 8.314 = Ea x 0.000073856

$E_{a}$ = 7265.2 Joules/mol

Hence, The $E_{a}$ for the process is 7265.2 Joules/mol.

Learn more about rate constant here:

brainly.com/question/14977272

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