First, consider the steps to heat the sample from 209 K to 367K.
1) Heating in liquid state from 209 K to 239.82 K
2) Vaporaizing at 239.82 K
3) Heating in gaseous state from 239.82 K to 367 K.
Second, calculate the amount of heat required for each step.
1) Liquid heating
Ammonia = NH3 => molar mass = 14.0 g/mol + 3*1g/mol = 17g/mol
=> number of moles = 12.62 g / 17 g/mol = 0.742 mol
Heat1 = #moles * heat capacity * ΔT
Heat1 = 0.742 mol * 80.8 J/mol*K * (239.82K - 209K) = 1,847.77 J
2) Vaporization
Heat2 = # moles * H vap
Heat2 = 0.742 mol * 23.33 kJ/mol = 17.31 kJ = 17310 J
3) Vapor heating
Heat3 = #moles * heat capacity * ΔT
Heat3 = 0.742 mol * 35.06 J / (mol*K) * (367K - 239.82K) = 3,308.53 J
Third, add up the heats for every steps:
Total heat = 1,847.77 J + 17,310 J + 3,308.53 J = 22,466.3 J
Fourth, divide the total heat by the heat rate:
Time = 22,466.3 J / (6000.0 J/min) = 3.7 min
Answer: 3.7 min
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Answer : (b) The rate law expression for the reaction is:
![\text{Rate}=k[SO_2]^2[O_2]](https://tex.z-dn.net/?f=%5Ctext%7BRate%7D%3Dk%5BSO_2%5D%5E2%5BO_2%5D)
Explanation :
Rate law : It is defined as the expression which expresses the rate of the reaction in terms of molar concentration of the reactants with each term raised to the power their stoichiometric coefficient of that reactant in the balanced chemical equation.
The general reaction is:

The general rate law expression for the reaction is:
![\text{Rate}=k[A]^a[B]^b](https://tex.z-dn.net/?f=%5Ctext%7BRate%7D%3Dk%5BA%5D%5Ea%5BB%5D%5Eb)
where,
a = order with respect to A
b = order with respect to B
R = rate law
k = rate constant
and
= concentration of A and B reactant
Now we have to determine the rate law for the given reaction.
The balanced equations will be:

In this reaction,
and
are the reactants.
The rate law expression for the reaction is:
![\text{Rate}=k[SO_2]^2[O_2]^1](https://tex.z-dn.net/?f=%5Ctext%7BRate%7D%3Dk%5BSO_2%5D%5E2%5BO_2%5D%5E1)
or,
![\text{Rate}=k[SO_2]^2[O_2]](https://tex.z-dn.net/?f=%5Ctext%7BRate%7D%3Dk%5BSO_2%5D%5E2%5BO_2%5D)