When 1 mol of CH4 is burned, 490 kJ of energy are released as heat.
CH4 + O2 -> 2H2 + CO2
If 3.2g of CH4 are burned, what is the value of the heat of the reaction?
The answer worked in class was -180 kJ, but while I was redoing problems, I got the answer 98 kJ (both approximations according to sfs). When I was working the
stoichiometry, I wrote that each mole of CH4 burned produced 490 kJ, like the question said, so my equation was:
(3.2gCH4 * 1molCH4 * 490kJ)/
(16.05gCH4 * 1molCH4)
= 98 kJ (app.)
However, in the class working, we multiplied the kJ by -2 for some reason:
(3.2gCH4 * 1molCH4 * -890kJ)/
(16.05gCH4 * 1molCH4)
= 108 kJ (app.)
Is there a reason to change the number of kJ per mole of CH4 to -890, or was there a mistake?
To determine the correct value for the heat of the reaction when 3.2g of CH4 is burned, we need to understand the stoichiometry of the reaction and the concept of enthalpy change.
The balanced chemical equation you provided is:
CH4 + O2 → 2H2 + CO2
The given information states that when 1 mol of CH4 is burned, 490 kJ of energy are released as heat. This means that the enthalpy change, ΔH, for the combustion of 1 mol of CH4 is -490 kJ.
To find the enthalpy change for the combustion of 3.2g of CH4, we can use stoichiometry and the molar mass of CH4.
Step 1: Calculate the number of moles of CH4:
n(CH4) = mass(CH4) / molar mass(CH4)
= 3.2g / 16.05g/mol
≈ 0.1998 mol
Step 2: Use the stoichiometry of the balanced equation to calculate the moles of H2 produced:
From the balanced equation, we see that 1 mol of CH4 reacts to form 2 mol of H2. Therefore, moles of H2 = 2 * n(CH4) = 2 * 0.1998 mol = 0.3996 mol.
Now, we can determine the heat of the reaction for 3.2g of CH4.
Option 1: Calculation using the given value of 490 kJ/mol:
ΔH = -490 kJ/mol * 0.1998 mol
≈ -98 kJ
Option 2: Calculation using the opposite sign for the coefficient of the equation:
ΔH = 490 kJ/mol * 0.3996 mol * (-1) (multiplying by -1 reflects the change in sign due to reversing the equation)
≈ -196 kJ
Both options should result in a negative value for ΔH since the reaction is exothermic (heat is released).
Based on your calculations, it seems like you mistakenly used a different value for the heat released per mole of CH4 (-890 kJ) instead of the given value of -490 kJ/mol. This could be the reason for the discrepancy in the result.
Therefore, the correct answer for the value of the heat of the reaction when 3.2g of CH4 is burned should be approximately -98 kJ, reflecting option 1 above.