Respuesta :
The time required by [tex]\rm N_2O_5[/tex] to reach the total pressure of 176 kPa has been 113 minutes. Thus, option A is correct.
For the decomposition of Nitrogen pentaoxide, the ICE table for the balanced chemical equation will be:
2 [tex]\rm N_2O_5[/tex] [tex]\rightarrow[/tex] 4 [tex]\rm NO_2[/tex] + [tex]\rm O_2[/tex]
I   2x      0     0
C   -2x    +4x    +x
E   -2x    +4x    +x
Total pressure has been the partial pressure of each gas.
Final pressure = Initial pressure -2x + 4x + x
176 kPa = 125 kPa -3x
3x = 51
x = 17
The pressure of [tex]\rm N_2O_5[/tex] = 125 kPa.
After the completion of reaction the pressure has been reduced by 2x.
Final pressure of [tex]\rm N_2O_5[/tex] = 125 - 2x
= 125 - 2(17)
= 125 - 34
= 91 kPa.
The initial pressure [tex]\rm N_2O_5[/tex] = 125 kPa
The time can be given by:
t = [tex]\rm \dfrac{2.303}{Rate\;constant}\;\times\;log\;\dfrac{Initial\;pressure}{Final\;pressure}[/tex]
t = [tex]\rm \dfrac{2.303}{2.8\;\times\;10^-^3}\;\times\;log\;\dfrac{125}{91}[/tex]
t = 113.3963 minutes
t = 113.4 minutes.
The time required by [tex]\rm N_2O_5[/tex] to reach the total pressure of 176 kPa has been 113 minutes. Thus, option A is correct.
For more information about the decomposition reaction, refer to the link:
https://brainly.com/question/24936069
