I believe the correct answer is C. The amount of catalyst is the same at the end as at the beginning of the reaction. Catalysts can't be consumed by the reaction thus is not D.
The decomposition time : 7.69 min ≈ 7.7 min
<h3>Further explanation</h3>
Given
rate constant : 0.029/min
a concentration of 0.050 mol L to a concentration of 0.040 mol L
Required
the decomposition time
Solution
The reaction rate (v) shows the change in the concentration of the substance (changes in addition to concentrations for reaction products or changes in concentration reduction for reactants) per unit time
For first-order reaction :
[A]=[Ao]e^(-kt)
or
ln[A]=-kt+ln(A0)
Input the value :
ln(0.040)=-(0.029)t+ln(0.050)
-3.219 = -0.029t -2.996
-0.223 =-0.029t
t=7.69 minutes
Answer: Total pressure inside of a vessel is 0.908 atm
Explanation:
According to Dalton's law, the total pressure is the sum of individual partial pressures. exerted by each gas alone.
= partial pressure of nitrogen = 0.256 atm
= partial pressure of helium = 203 mm Hg = 0.267 atm (760mmHg=1atm)
= partial pressure of hydrogen =39.0 kPa = 0.385 atm (1kPa=0.00987 atm)
Thus 
=0.256atm+0.267atm+0.385atm =0.908atm
Thus total pressure (in atm) inside of a vessel is 0.908
