Calculate the DHof for the following reaction under standard state conditions:
2 Ag2S(s) + 2 H2O(l) ---> 4 Ag(s) + 2 H2S(g) + O2(g)
Given the following information:
Ag2S(s) ÄHof = -32.6 kJ/mol
H2O(l) Ä Hof = -285.83 kJ/mol
H2S(g) ÄHof = -20.6 kJ/mol
To calculate the enthalpy change (ΔHof) for the given reaction, you need to use Hess's Law. Hess's Law states that the total enthalpy change of a reaction is the sum of the enthalpy changes of the individual steps of the reaction.
In this case, you'll need to consider the enthalpy changes for the formation of each reactant and product. Given the enthalpy changes for Ag2S(s), H2O(l), and H2S(g), you can use these values to find the enthalpy change for the formation of Ag(s) and O2(g).
Here's the process to calculate ΔHof for the reaction:
Step 1: Write down the balanced chemical equation:
2 Ag2S(s) + 2 H2O(l) ---> 4 Ag(s) + 2 H2S(g) + O2(g)
Step 2: Calculate the total ΔHof for the reactants:
ΔHof (Ag2S(s)) = -32.6 kJ/mol
ΔHof (H2O(l)) = -285.83 kJ/mol
For Ag2S(s), you don't need any additional steps since it is one of the reactants.
Step 3: Calculate the total ΔHof for the products:
ΔHof (H2S(g)) = -20.6 kJ/mol
You still need to calculate the ΔHof for Ag(s) and O2(g).
Step 4: Use Hess's Law to calculate ΔHof for Ag(s):
Since there are no direct enthalpy values given for Ag(s), you need to consider an intermediate step. In this case, you can use the reaction:
Ag2S(s) + H2O(l) ---> 2 Ag(s) + H2S(g)
The ΔHof for this reaction can be calculated as follows:
ΔHof (Ag(s)) = ΔHof (Ag2S(s)) + ΔHof (H2O(l)) - ΔHof (H2S(g))
So, plug in the given values:
ΔHof (Ag(s)) = -32.6 kJ/mol + (-285.83 kJ/mol) - (-20.6 kJ/mol)
Step 5: Calculate ΔHof for O2(g):
Since there are no direct enthalpy values given for O2(g), you need to consider another intermediate step. In this case, you can use the reaction:
2 H2(g) + O2(g) ---> 2 H2O(l)
The ΔHof for this reaction is known and is equal to -483.6 kJ/mol.
Step 6: Use Hess's Law to calculate ΔHof for O2(g):
Since O2(g) appears on the product side of the balanced equation, you need to reverse the sign of the enthalpy change:
ΔHof (O2(g)) = -(-483.6 kJ/mol)
Step 7: Calculate the total ΔHof for the reaction:
To calculate the total ΔHof for the reaction, sum up the ΔHof values for the products and subtract the sum of the ΔHof values for the reactants:
ΔHof (reaction) = [4 ΔHof (Ag(s))] + [ΔHof (O2(g))] - [2 ΔHof (Ag2S(s))] - [2 ΔHof (H2O(l))] - [2 ΔHof (H2S(g))]
Plug in the calculated values to obtain the final answer.
This step-by-step process allows you to determine the ΔHof for the given reaction using known enthalpy values and applying Hess's Law.