Questions 8-10 refer to a steam engine powered by natural gas. 8. A small steam

Question

Questions 8-10 refer to a steam engine powered by natural gas.

8. A small steam engine has a 200 kg water tank. Calculate the heat (q) needed to take 200 kg of water from room temperature, 20.0°C to 100.0°C in kJ. The specific heat capacity of water is 4.184 J/(g*K).

9. Calculate the heat of reaction for the combustion of natural gas based on the following balanced equation and heats of formation CH4(g) + 2 O2(g) CO2(g) + 2 H2O (g) Heats of formation: a. CH4, -74.9 kJ/mol b. CO2, -110.5 kJ/mol c. H2O, -285.8 kJ/mol

10. Calculate the mass of natural gas needed to generate the heat used to boil the water in # 8.

Explanation / Answer

8)

we know that

heat = mass x specific heat x temp change

so

Q = m x s x dT

given

mass = 200 kg = 200 x 1000 g

mass = 2 x 10^5 g

specific heat = 4.184

temp change = 100-20 = 80

so

Q = 2 x 10^5 x 4.184 x 80

Q = 6.6944 x 10^7 J

Q = 66944 kJ

so

the heat required is 66944 kJ

9)

dHof value for C02 should be -393.5 not -110.5

now

CH4 + 202 --> C02 + 2H20

dHrxn = dHof products - dHof reactants

so

dHrxn = dHof C02 + ( 2 x dHof H20) - dHof CH4 - ( 2 x dHof 02)

dHrxn = -393.5 + ( 2 x -285.8) + 74.9 - ( 2 x 0)

dHrxn = -890.2 kJ /mol

so

heat of reaction is -890.2 kJ/mol

10)

now

moles of CH4 required = 66944/ 890.2

moles of CH4 required = 75.2

now

mass = moles x molar mass

so

mass of CH4 = 75.2 x 16

mass of CH4 = 1203.2

so

1203.2 grams of CH4 is needed

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