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The enthalpy of combustion of methane, graphite and dihydrogen at 298 K are - 890.3 kJ mol-1, - 393.5 kJ mol-1 and - 285.8 kJ mol-1 respectively. Enthalpy of formation of CH4(g) will be
  • a)
    -74.8 kJ mol-1
  • b)
    -52.57 kJ mol-1
  • c)
    +74.8 kJ mol-1
  • d)
    +52.27 kJ mol-1
Correct answer is option 'A'. Can you explain this answer?
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Enthalpy of Combustion and Enthalpy of Formation

Enthalpy of combustion (ΔHcomb) is the amount of heat released when one mole of a substance undergoes complete combustion in excess oxygen. It is a measure of the energy content of the substance.

Enthalpy of formation (ΔHf) is the amount of heat absorbed or released when one mole of a compound is formed from its constituent elements in their standard states. It is a measure of the stability of the compound.

Given Data:
ΔHcomb of methane (CH4) = -890.3 kJ mol-1
ΔHcomb of graphite (C) = -393.5 kJ mol-1
ΔHcomb of dihydrogen (H2) = -285.8 kJ mol-1

Using these values, we can calculate the enthalpy of formation of methane (CH4).

Equation 1: CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)
Equation 2: C(s) + O2(g) → CO2(g)
Equation 3: H2(g) + 1/2O2(g) → H2O(l)

We can use these equations to manipulate the given enthalpy values and obtain the enthalpy of formation of methane.

Calculations:

1. Write the balanced equation for the combustion of methane:
CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

2. Manipulate the equation to obtain the enthalpy of formation of methane:
ΔHcomb(CH4) = ΔHf(CO2) + 2ΔHf(H2O) - ΔHf(CH4)

3. Substitute the given enthalpy values:
-890.3 kJ mol-1 = ΔHf(CO2) + 2(-285.8 kJ mol-1) - ΔHf(CH4)

4. Substitute the enthalpy of formation of CO2 and H2O:
-890.3 kJ mol-1 = -393.5 kJ mol-1 + 2(-285.8 kJ mol-1) - ΔHf(CH4)

5. Simplify the equation:
-890.3 kJ mol-1 = -965.1 kJ mol-1 - ΔHf(CH4)

6. Solve for ΔHf(CH4):
ΔHf(CH4) = -965.1 kJ mol-1 + 890.3 kJ mol-1
ΔHf(CH4) = -74.8 kJ mol-1

Therefore, the enthalpy of formation of methane (CH4) is -74.8 kJ mol-1.
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The enthalpy of combustion of methane, graphite and dihydrogen at 298 K are - 890.3 kJ mol-1, - 393.5 kJ mol-1 and - 285.8 kJ mol-1 respectively. Enthalpy of formation of CH4(g) will bea)-74.8 kJ mol-1b)-52.57kJ mol-1c)+74.8kJ mol-1d)+52.27kJ mol-1Correct answer is option 'A'. Can you explain this answer?
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