Calcium carbide (CaC2) reacts with water to form acetylene (C2H2) gas and calcium hydroxide (Ca(OH)2). If the ΔH for:
CaC2(s) + 2H2O(l) = Ca(OH)2(s) + C2H2(g)
is -127 kJ, then what is the enthalpy of formation for calcium carbide? The ΔH of formation for H2O(l), Ca(OH)2(s) and C2H2(g) are -286, -986, 227 kJ/mol respectively. The units are kJ.
dHrxn = (n*dHf products) - (n*dHf products)
dHrxn = -127 = (n*dHf .....etc)
Substitute and solve for dHf CaC2 which is the only unknown in the equation.
To find the enthalpy of formation of calcium carbide (CaC2), we need to use the concept of Hess's Law and the known enthalpies of formation of other substances involved in the reaction.
Hess's Law states that the overall enthalpy change of a reaction is independent of the pathway taken and is equal to the sum of the enthalpy changes of its individual steps.
In this case, we can break down the reaction into the following steps:
1. CaC2(s) + 2H2O(l) → Ca(OH)2(s) + C2H2(g) (given)
2. Ca(OH)2(s) → CaO(s) + H2O(l) (unknown)
3. C(s) + O2(g) → CO2(g) (unknown)
4. H2(g) + 1/2O2(g) → H2O(l) (known: ΔH = -286 kJ/mol)
5. H2O(l) → H2(g) + 1/2O2(g) (known: ΔH = +286 kJ/mol)
Now, we'll use the known enthalpies of formation to calculate the unknown enthalpies of formation for steps 2 and 3.
Step 2:
Ca(OH)2(s) → CaO(s) + H2O(l)
Since we know the ΔH value for the overall reaction (step 1) and the ΔH value for H2O(l), we can use Hess's Law to find the enthalpy change for step 2:
ΔH2 = ΔH1 - ΔH5
ΔH2 = (-127 kJ/mol) - (-286 kJ/mol)
ΔH2 = 159 kJ/mol
Step 3:
C(s) + O2(g) → CO2(g)
To calculate the enthalpy change for step 3, we can again use Hess's Law and the known enthalpies of formation:
ΔH3 = ΔH4 - ΔH5
ΔH3 = 0 - (-286 kJ/mol)
ΔH3 = 286 kJ/mol
Now, with the values obtained for ΔH2 and ΔH3, we can calculate the enthalpy of formation of calcium carbide (CaC2) using the equation:
ΔHf(CaC2) = ΔH1 - ΔH2 - ΔH3
ΔHf(CaC2) = -127 kJ/mol - 159 kJ/mol - 286 kJ/mol
ΔHf(CaC2) = -572 kJ/mol
Therefore, the enthalpy of formation for calcium carbide (CaC2) is -572 kJ/mol.
To find the enthalpy of formation for calcium carbide (CaC2), we can use the concept of Hess's Law. Hess's Law states that the overall enthalpy change of a reaction is independent of the pathway taken.
We can use the given equation:
CaC2(s) + 2H2O(l) = Ca(OH)2(s) + C2H2(g) (ΔH = -127 kJ)
We need to rearrange this equation to solve for the enthalpy of formation of CaC2:
CaC2(s) = Ca(OH)2(s) + C2H2(g) - 2H2O(l)
The enthalpy of formation for CaC2 can be calculated using the enthalpy of formation values for the other compounds involved in the reaction.
The enthalpy change for the reaction is given as -127 kJ. This is the overall change in enthalpy for the reaction.
The enthalpy change for the reaction can be calculated using the enthalpy of formation values as follows:
ΔH = [ΔHf(Ca(OH)2) + ΔHf(C2H2)] - [2 × ΔHf(H2O)]
Substituting the given enthalpy of formation values:
-127 kJ = [-986 kJ + 227 kJ] - [2 × -286 kJ]
Simplifying:
-127 kJ = -986 kJ + 227 kJ + 572 kJ
-127 kJ = -187 kJ + 572 kJ
-127 kJ = 385 kJ
Therefore, the enthalpy of formation for calcium carbide (CaC2) is 385 kJ.