The reaction for the complete combustion of acetylene is shown below.
C2H2(g) + 5/2 O2(g) -----------> 2 CO2(g) + H2O(l) ΔH = -1299 kJ
Use this reaction and the data below to calculate the heat of formation for acetylene.
ΔHf[H2O(l)] = -285.8 kJ/mol
ΔHf[CO2(g)] = -393.5 kJ/mol
To find the heat of formation for acetylene (C2H2), we can use the equation:
ΔHrxn = ΣΔHf[products] - ΣΔHf[reactants]
Where ΔHrxn is the heat of reaction, ΣΔHf[products] is the sum of the heats of formation of the products, and ΣΔHf[reactants] is the sum of the heats of formation of the reactants.
Given:
ΔHrxn = -1299 kJ/mol
ΔHf[H2O(l)] = -285.8 kJ/mol
ΔHf[CO2(g)] = -393.5 kJ/mol
We can substitute these values into the equation:
-1299 kJ/mol = 2(-393.5 kJ/mol) + (-285.8 kJ/mol) - ΣΔHf[C2H2]
Simplifying the equation, we have:
-1299 kJ/mol = -787 kJ/mol - ΣΔHf[C2H2]
To isolate ΣΔHf[C2H2], we move the known values to the other side of the equation:
ΣΔHf[C2H2] = -787 kJ/mol - (-1299 kJ/mol)
ΣΔHf[C2H2] = -787 kJ/mol + 1299 kJ/mol
ΣΔHf[C2H2] = 512 kJ/mol
Therefore, the heat of formation for acetylene is 512 kJ/mol.
To calculate the heat of formation for acetylene (C2H2), we need to use the given data and Hess's law. Hess's law states that the enthalpy change of a reaction is independent of the pathway taken, as long as the initial and final conditions are the same.
First, let's write the equation for the combustion of acetylene, as given:
C2H2(g) + 5/2 O2(g) -> 2 CO2(g) + H2O(l), ΔH = -1299 kJ
We know the heat of formation for CO2 and H2O, and we want to find the heat of formation for acetylene (C2H2). The heat of formation is defined as the enthalpy change when one mole of a compound is formed from its elements in their standard states.
Using Hess's law, we can break down the given reaction into a series of reactions with known enthalpy changes:
1) C(s) + O2(g) -> CO2(g), ΔH = -393.5 kJ (this is the heat of formation for CO2)
2) H2(g) + 1/2 O2(g) -> H2O(l), ΔH = -285.8 kJ (this is the heat of formation for H2O)
3) 2C(s) + H2(g) -> C2H2(g) (unknown heat of formation)
We can reverse reaction 1) and multiply it by 2 to match the coefficients in reaction 3):
2CO2(g) -> 2C(s) + 2O2(g), ΔH = 2*(-393.5) kJ = -787 kJ
We can reverse reaction 2) and multiply it by 2 to match the coefficients in reaction 3):
2H2O(l) -> 2H2(g) + O2(g), ΔH = 2*(-285.8) kJ = -571.6 kJ
Now we can add the two reversed reactions and reaction 3) to cancel out the common species and obtain the complete balanced equation:
2CO2(g) + 2H2O(l) -> 2C2H2(g) + O2(g)
Finally, we sum up the enthalpy changes of each reaction:
ΔHf[C2H2(g)] = (-1299 kJ) - (-787 kJ) - (-571.6 kJ)
ΔHf[C2H2(g)] = -1299 + 787 - 571.6
ΔHf[C2H2(g)] = -1083.6 kJ/mol
Therefore, the heat of formation for acetylene (C2H2) is -1083.6 kJ/mol.