<u>Answer:</u>
<u>For a:</u> The amount of heat transferred for the given amount of methanol is 94.6736 kJ.
<u>For b:</u> The mass of methane gas produced will be 10.384 g.
<u>Explanation:</u>
For the given chemical reaction:
![2CH_3OH(g)\rightarrow 2CH_4(g)+O_2(g);\Delta H=+252.8kJ](https://tex.z-dn.net/?f=2CH_3OH%28g%29%5Crightarrow%202CH_4%28g%29%2BO_2%28g%29%3B%5CDelta%20H%3D%2B252.8kJ)
To calculate the number of moles, we use the equation:
......(1)
Given mass of methanol = 24.0 g
Molar mass of methanol = 32.04 g/mol
Putting values in above equation, we get:
![\text{Moles of methanol}=\frac{24.0g}{32.04g/mol}=0.749mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20methanol%7D%3D%5Cfrac%7B24.0g%7D%7B32.04g%2Fmol%7D%3D0.749mol)
By Stoichiometry of the reaction:
For every 2 moles of methanol, the amount of heat transferred is +252.8 kJ.
So, for every 0.749 moles of methanol, the amount of heat transferred will be = ![\frac{252.8}{2}\times 0.749=94.6736kJ](https://tex.z-dn.net/?f=%5Cfrac%7B252.8%7D%7B2%7D%5Ctimes%200.749%3D94.6736kJ)
Hence, the amount of heat transferred for the given amount of methanol is 94.6736 kJ.
By Stoichiometry of the reaction:
252.8 kJ of energy is absorbed when 2 moles of methane gas is produced.
So, 82.1 kJ of energy will be absorbed when =
of methane gas is produced.
Now, calculating the mass of methane gas from equation 1, we get:
Molar mass of methane gas = 16 g/mol
Moles of methane gas = 0.649 moles
Putting values in equation 1, we get:
![0.649mol=\frac{\text{Mass of methane gas}}{16g/mol}\\\\\text{Mass of methane}=10.384g](https://tex.z-dn.net/?f=0.649mol%3D%5Cfrac%7B%5Ctext%7BMass%20of%20methane%20gas%7D%7D%7B16g%2Fmol%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20methane%7D%3D10.384g)
Hence, the mass of methane gas produced will be 10.384 g.