The rate constant of a reaction is 4.7x10⁻³ s⁻¹ at 25°C, and the activation energy is 33.6 kJ/mol. then value of K at 75°C is 4.7x10⁻³ s⁻¹ .
Calculation ,
The relation between rate constant and activation energy ( which is denoted by Ea ) is given as ,
㏑[tex]K_{1}/K_{2}[/tex] = Ea/R[1/[tex]T_{1}[/tex] - 1/[tex]T_{2}[/tex] ]
㏑4.7x10⁻³ s⁻¹ [tex]/K_{2}[/tex] = 33.6 kJ/mol/8.3 [ 1/298 - 1/348]
㏑4.7x10⁻³ s⁻¹ [tex]/K_{2}[/tex] = 33.6 × [tex]10^{3}[/tex] × 50 /298 × 348× 8.3 = 1.68/860743.2
㏑4.7x10⁻³ s⁻¹ [tex]/K_{2}[/tex] = 1.95 × [tex]10^{-6}[/tex]
4.7x10⁻³ s⁻¹ [tex]/K_{2}[/tex] = [tex]e^{ 0.00000195 }[/tex] = 1
[tex]K_{2}[/tex] = 4.7x10⁻³ s⁻¹/1 = 4.7x10⁻³ s⁻¹
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