$(40$ P$)$ In a constant volume batch reactor, acetaldehyde decomposes to methane and carbon monoxide at an elevated temperature. During the reaction, the increase in pressure $(P)$ is recorded with time. The initial pressure is $0\mathrm{.}478$atm in the reactor.

a$)$ Calculate the partial pressures of the reactant and the products based on the data given in the table below.

b$)$ Propose a rate law for the reaction, and calculate the reaction rate constant in the units of pressure $($atm$)$ and concentration.

$C{H}_3$CHO$C{H}_4+CO$

$\backslash$table$[[t(s),42,105,242,480,840,1440],[P(atm),0\mathrm{.}044,0\mathrm{.}097,0\mathrm{.}176,0\mathrm{.}255,0\mathrm{.}320,0\mathrm{.}374]]$