Question

The initial rates listed below were measure for the thermal decomposition of azomethane (CH3NMCH3)

Answer 1

from unit of rate constant you can derive that reaction is a first order reaction.
Its rate law is given by the rate equation:
d[CH₃NNCH₃]/dt = -k∙[CH₃NNCH₃]
where k = 40.8min⁻¹

The integrated rate law is
ln[CH₃NNCH₃] = -k∙t + ln[CH₃NNCH₃]₀
<=>
[CH₃NNCH₃] = [CH₃NNCH₃]₀ ∙ e^( -k∙t)
[CH₃NNCH₃]₀ is the initial concentration.

If you multiply this by the volume of the flask you get a integrated rate law in terms of amount of substance;
n(CH₃NNCH₃) = n₀(CH₃NNCH₃) ∙ e^( -k∙t)

The initial amount is
n₀(CH₃NNCH₃) = 2.00g / 58.0825g/mol = 0.0344mol

after 0.05min
n(CH₃NNCH₃) = 0.0344mol ∙ e^( -40.8min⁻¹ ∙ 0.05min) = 0.045mol

the amount of azomethane, which has reacted away is:
∆n(CH₃NNCH₃) = 0.0344mol - 0.0045mol = 0.0299 mol

According to reaction equation one mole of nitrogen and ethane are formed per mole azomethane decomposed., hence:
n(N₂) = n(C₃H₆) = ∆n(CH₃NNCH₃) = 0.0299 mol