please help with my chemistry homework

Question

Suppose a boil water notice is sent out advising all residents in the area to boil their water before drinking it or using it for cooking. You need to boil  of water using your natural gas (primarily methane) stove. What volume of natural gas is needed to boil the water if only  of the heat generated goes towards heating the water. Assume the density of methane is , the density of water is , and that the water has an initial temperature of . Enthalpy of formation values can be found in this . Assume that gaseous water is formed in the combustion of methane.

Answer 1

For this question, you will have to calculate the amount of heat required to bring 18.5 L of H₂O to boil and determine how much methane gas would be required to produce that much energy in a stove with 19.4% efficiency.

Equations required:

Heat energy (q) = mass (m) * specific heat (c) * change in temperature (ΔT)

Heat of reaction (ΔH_rº) = Sum of heat of formation of products (ΣΔH_fº_products)*stoichiometric coefficients (v) - sum of heat of formation of reactants (ΣΔH_fº_reactants)* stoichiometric coefficients (v)  

Density (ρ) * volume (V) = mass (m)

Mass (m) /molar mass (mm) = moles (n)

Total heat produced * efficiency = total heat used

Givens from this question:

Volume H₂O: 18.5 L

Efficiency of stove: 19.4%

Density of methane: 0.668 g/L

Density of H₂O: 1.00 g/mL

Initial temperature of H2O: 20.0 °C

Volume of methane needed:??

Knowns/standards:

The balanced equation for the combustion of methane:

CH₄ (g) + 2O₂ (g) -> CO₂ (g) + 2H₂O (g)

Boiling point of H₂O: 100 °C

Specific heat of H₂O: 4.186 J/g

Molar mass CH₄: 16.04 g/mol

Molar mass of H₂O: 18.02 g/mol

Heat of formation of:

CH₄: -74.5 kJ/mol (USE SOURCE PROVIDED BY YOUR TEACHER)

O₂: 0 kJ/mol

CO₂: -394 kJ/mol (USE SOURCE PROVIDED BY YOUR TEACHER)

H₂O: -293 kJ/mol (USE SOURCE PROVIDED BY YOUR TEACHER)

To determine amount of heat required to raise the temperature of 18.5 L H₂O from 20 °C to 100 °C, use the equation q=mcΔT:

Mass of H2O:

18.5 L x 1000 mL /1L x 1.00 g/mL = 18500 g H20

Change in Temperature:

100 ºC -20 ºC = 80 ºC

q = 18500g * 4.186 J/gC  *80ºC

   =6195280 J

    =6195 kJ

To determine the amount of energy methane produces per mole, use ΔH_rº = vΣΔH_fº_products - vΣΔH_fº_reactants for CH₄ (g) + 2O₂ (g) -> CO₂ (g) + 2H₂O (g)

ΔH_cº_CH4 = (1*ΔH_fº_CO2 + 2*ΔH_fº_H2O) -(1*ΔH_fº_CH4 + 2*ΔH_fº_O2)

                                = (1*-394 kJ/mol + 2*-293 kJ/mol) – (1*-74.5 kJ/mol + 2*0kJ/mol)

                               =-905.5 kJ/mol

 (NOTE: heat of combustion can be used instead of calculating the heat of reaction.)  

Determine TOTAL energy needed with a 19.4% efficiency stove:

Total energy* .194 = 6195 kJ

Total energy = 31934 kJ

Determine number of moles of methane required to produce this much energy:

31934 kJ x 1mol/905.5 kJ =   35.27 moles CH₄

              (Note the negative turns into a positive, because the heat released by methane is taken up by H₂O and the surroundings)

 

Determine the volume of methane:

35.27 mol CH₄ x 16.07 g/mol x 1L/0.668 g = 848.4 L

Answer 2

There is a lot of extraneous information here. Also, how much heat is released when natural gas is burned?