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Thermodynamicsintermediate

Enthalpy Calculation Using Hess's Law

Use Hess's Law to calculate the enthalpy change of a reaction from known thermochemical equations. Master energy calculations in chemistry.

Problem Scenario

Calculate the standard enthalpy of formation of methane (CH4) using the following data: C(graphite) + O2(g) -> CO2(g), deltaH = -393.5 kJ; H2(g) + 1/2 O2(g) -> H2O(l), deltaH = -285.8 kJ; CH4(g) + 2O2(g) -> CO2(g) + 2H2O(l), deltaH = -890.3 kJ

Given Data

Equation 1C(s) + O2(g) -> CO2(g), deltaH1 = -393.5 kJ

Equation 2H2(g) + 1/2 O2(g) -> H2O(l), deltaH2 = -285.8 kJ

Equation 3CH4(g) + 2O2(g) -> CO2(g) + 2H2O(l), deltaH3 = -890.3 kJ

TargetC(s) + 2H2(g) -> CH4(g)

Requirements

Write the target equation
Manipulate given equations to match target
Apply Hess's Law
Calculate the final deltaH

Solution

Step 1:

Write the target equation for formation of methane: C(s) + 2H2(g) -> CH4(g)

Step 2:

Keep Equation 1 as is (we need C on the left): C(s) + O2(g) -> CO2(g), deltaH = -393.5 kJ

Step 3:

Multiply Equation 2 by 2 (we need 2H2 on the left): 2H2(g) + O2(g) -> 2H2O(l), deltaH = 2(-285.8) = -571.6 kJ

Step 4:

Reverse Equation 3 (we need CH4 on the right): CO2(g) + 2H2O(l) -> CH4(g) + 2O2(g), deltaH = +890.3 kJ

Step 5:

Add the modified equations: C(s) + O2(g) + 2H2(g) + O2(g) + CO2(g) + 2H2O(l) -> CO2(g) + 2H2O(l) + CH4(g) + 2O2(g). Cancel species appearing on both sides: C(s) + 2H2(g) -> CH4(g)

Step 6:

Sum the enthalpy values: deltaH = (-393.5) + (-571.6) + (+890.3) = -74.8 kJ

Final Answer

The standard enthalpy of formation of methane is deltaHf = -74.8 kJ/mol. This negative value indicates that the formation of methane from its elements is exothermic.

Key Takeaways

✓Enthalpy is a state function - the path doesn't matter
✓When reversing a reaction, change the sign of deltaH
✓When multiplying a reaction, multiply deltaH by the same factor
✓Species on both sides cancel out when adding equations

Common Errors to Avoid

✗Forgetting to change the sign when reversing a reaction
✗Forgetting to multiply deltaH when multiplying the equation
✗Not canceling species properly when adding equations
✗Incorrect target equation setup

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FAQs

Common questions about this problem type

Look at your target equation. Find where each species appears and manipulate equations so those species end up on the correct side. Then adjust coefficients to match the target.

Check your manipulations. If done correctly, all intermediate species should cancel. If they don't, you may have an error in reversing or multiplying equations.