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Answer : The final temperature would be, 791.1 K
Explanation :
According to the Arrhenius equation,

or,
![\log (\frac{K_2}{K_1})=\frac{Ea}{2.303\times R}[\frac{1}{T_1}-\frac{1}{T_2}]](https://tex.z-dn.net/?f=%5Clog%20%28%5Cfrac%7BK_2%7D%7BK_1%7D%29%3D%5Cfrac%7BEa%7D%7B2.303%5Ctimes%20R%7D%5B%5Cfrac%7B1%7D%7BT_1%7D-%5Cfrac%7B1%7D%7BT_2%7D%5D)
where,
= rate constant at
= 
= rate constant at
= 
= activation energy for the reaction = 265 kJ/mol = 265000 J/mol
R = gas constant = 8.314 J/mole.K
= initial temperature = 
= final temperature = ?
Now put all the given values in this formula, we get:
![\log (\frac{4\times K_1}{K_1})=\frac{265000J/mol}{2.303\times 8.314J/mole.K}[\frac{1}{733K}-\frac{1}{T_2}]](https://tex.z-dn.net/?f=%5Clog%20%28%5Cfrac%7B4%5Ctimes%20K_1%7D%7BK_1%7D%29%3D%5Cfrac%7B265000J%2Fmol%7D%7B2.303%5Ctimes%208.314J%2Fmole.K%7D%5B%5Cfrac%7B1%7D%7B733K%7D-%5Cfrac%7B1%7D%7BT_2%7D%5D)

Therefore, the final temperature would be, 791.1 K
Answer:
1 mole of CO2 and 2 mole H2O will be produced in the reaction.
Explanation:
N:B: I guess it will be 6 moles of O2 not CO2.
Balanced Equation: CH4 + 2O2 --> CO2 + 2H2O
Given,
1 mole CH4
6 moles of O2
According to Stoichiometry,
In the reaction,
2 mole O2 reacts with 1 mole CH4
1 mole O2 reacts with 1/2 mole CH4
∴6 mole O2 reacts with (1/2)*6 mole CH4
= 3 moles of CH4
But, there is only 1 mole CH4 provided. So CH4 is the limiting reagent.
Now,
According to Stoichiometry,
In the reaction,
1 mole CH4 produces 2 moles of H2O
Again,
According to Stoichiometry,
In the reaction,
1 mole CH4 produces 1 mole CO2
So, 1 mole of CO2 and 2 mole H2O will be produced in the reaction.
N:B:[Doing calculation with limiting reagent in problems like these gives you the most accurate answer].