Combustion of natural gas (primarily methane) occurs in most household heaters. The heat given off in this reaction is used to raise the temperature of the air in the house. Assuming that all the energy given off in the reaction goes to heating up only the air in the house, determine the mass of methane required to heat the air in a house by 10.0 degrees C. Assume each of the following: house dimensions are 30.0 m x 30.0 m x 3.0 m; specific heat capacity of air is 30 J/k•mol; 1.00 mol of air occupies 22.4 L for all temperatures concerned.
My work:
2700 m^3 = 12 mol of air
q= 12 mol x 30 J/k•mol x 283.15 K
q= 1.0 x 10^5 J
Am I on the right track?
I got -890.3 KJ for the change in enthalpy heat for the balanced equation:
CH4 + 2O2 ---> 2H2O + CO2
From then on I would multiply ...
q x 1kJ/1000 J x 1mol/890.3 x 16.05 g CH4/1 mol CH4
However, my answer is incorrect based on the answer key.
the temperature change of the air is 10.0ºk (C)...not 283.15
I will poop in your mouth Scott
Let's go through the problem step-by-step to identify the error:
1. Calculate the volume of the house:
The dimensions of the house are given as 30.0 m x 30.0 m x 3.0 m. Multiplying these values together gives the volume of the house as 2700 m^3.
2. Convert the volume of air in the house to moles of air:
Given that 1.00 mol of air occupies 22.4 L at all temperatures, we can calculate the number of moles of air in the house by dividing the volume by 22.4:
2700 m^3 / (22.4 L/mol) = 120.54 mol
Note: Your calculation of 12 moles of air is incorrect. You should use the volume of the house to find the number of moles.
3. Calculate the heat required to raise the temperature of the air:
The formula q = n * ΔT * Cp can be used to calculate the heat required to raise the temperature, where q is the heat, n is the number of moles, ΔT is the temperature change, and Cp is the specific heat capacity.
For the specific heat capacity of air (Cp), it is given as 30 J/(K*mol).
Substituting the values into the formula, we get:
q = 120.54 mol * 10.0°C * 30 J/(K*mol) = 36,162 J
4. Convert the energy from joules to kilojoules:
To convert from joules (J) to kilojoules (kJ), divide by 1000:
36,162 J / 1000 = 36.162 kJ
Now, let's calculate the mass of methane required:
5. Determine the enthalpy change for the combustion of methane:
The balanced equation for the combustion of methane is:
CH4 + 2O2 → 2H2O + CO2
Using the enthalpy values from the answer key, we can determine the enthalpy change for this reaction to be -890.3 kJ/mol.
6. Calculate the moles of methane required:
We know that the enthalpy change for the reaction is -890.3 kJ/mol and we want to calculate the mass of methane required to produce 36.162 kJ.
We can set up a proportion to find the number of moles of methane required:
-890.3 kJ / 1 mol CH4 = 36.162 kJ / x mol CH4
Cross-multiplying and solving for x, we get:
x = (36.162 kJ * 1 mol CH4) / -890.3 kJ = -0.0405 mol CH4
Note: The negative sign indicates that the reaction is exothermic.
7. Convert moles of methane to mass of methane:
We can convert the moles of methane to grams using the molar mass of methane, which is approximately 16.05 g/mol:
Mass of CH4 = 0.0405 mol CH4 * 16.05 g/mol = 0.65 g
So, the correct answer is approximately 0.65 grams of methane required to heat the air in the house by 10.0 degrees Celsius.
Double-check your calculations to see if you made any errors in the conversion steps or used incorrect values from the answer key.