Respuesta :
Answer:
For a: The amount of heat transferred for the given amount of methanol is 94.6736 kJ.
For b: The mass of methane gas produced will be 10.384 g.
Explanation:
For the given chemical reaction:
[tex]2CH_3OH(g)\rightarrow 2CH_4(g)+O_2(g);\Delta H=+252.8kJ[/tex]
- For a:
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex] ......(1)
Given mass of methanol = 24.0 g
Molar mass of methanol = 32.04 g/mol
Putting values in above equation, we get:
[tex]\text{Moles of methanol}=\frac{24.0g}{32.04g/mol}=0.749mol[/tex]
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 = [tex]\frac{252.8}{2}\times 0.749=94.6736kJ[/tex]
Hence, the amount of heat transferred for the given amount of methanol is 94.6736 kJ.
- For b:
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 = [tex]\frac{2}{252.8}\times 82.1=0.649mol[/tex] 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:
[tex]0.649mol=\frac{\text{Mass of methane gas}}{16g/mol}\\\\\text{Mass of methane}=10.384g[/tex]
Hence, the mass of methane gas produced will be 10.384 g.
