How much methane, in grams, must be burned to release 542 kJ of heat? H=-802kJ
CH4 + 2O2 ==> CO2 + 2H2O
16g CH4 releases 802 kJ so
16 x 542 kJ/802 kJ = ?
Well, it seems like you're trying to set a little fire, huh? Alright, let's do some calculations and get you your answer.
First things first, the heat of combustion for methane is h = -802 kJ/mol. We want to find out how much methane, in grams (g), we need to burn to release 542 kJ of heat.
Step 1: Convert heat released to kJ to mol
542 kJ = 542/(-802) mol
Step 2: Convert mol to grams using molar mass of methane
Now, the molar mass of methane (CH4) is about 16 g/mol. So, multiply the number of moles by the molar mass to get the mass in grams:
(542/(-802)) mol x 16 g/mol = -542*16/802 g
Drumroll, please... and the answer is approximately -10.855 grams of methane!
Now, keep in mind that this answer is a positive value because we used the absolute value of the heat of combustion. But hey, if you're planning on burning that amount of methane, I hope you'll do it in a controlled and safe environment!
To determine the amount of methane that must be burned to release 542 kJ of heat, we need to use the given enthalpy change (∆H) value and the balanced chemical equation for the combustion of methane.
The balanced equation for methane combustion is:
CH₄ + 2O₂ → CO₂ + 2H₂O
From the balanced equation, we can see that the molar ratio between methane (CH₄) and heat released is 1:802 kJ.
To find the amount of methane in grams, we need to calculate the molar mass of methane:
Molecular weight of C = 12.01 g/mol
Molecular weight of H = 1.01 g/mol
Total molar mass of methane (CH₄) = 12.01 g/mol + (1.01 g/mol × 4) = 16.05 g/mol
Now, we can set up and solve a proportion:
1 mol CH₄ / 802 kJ = x mol CH₄ / 542 kJ
Cross-multiplying and solving for x, we get:
x = (1 mol CH₄ × 542 kJ) / 802 kJ
x = 0.675 mol CH₄
Finally, we can calculate the grams of methane:
Grams of CH₄ = 0.675 mol CH₄ × 16.05 g/mol = approximately 10.84 g
Therefore, approximately 10.84 grams of methane must be burned to release 542 kJ of heat.
To determine how much methane needs to be burned to release 542 kJ of heat, we need to use the information provided in the question, specifically the enthalpy change (H) for the combustion of methane.
The enthalpy change for the combustion of methane (CH4) is given as H = -802 kJ, where the negative sign indicates the release of heat during the combustion process.
We can use the following equation to calculate the amount of methane burned:
ΔH = q
where
ΔH = enthalpy change (in kJ)
q = heat released (in kJ)
First, we need to convert the provided heat released from kJ to J since we are looking to find the amount of methane in grams. There are 1000 J in 1 kJ, so:
q = 542 kJ × 1000 J/kJ
q = 542,000 J
Next, we need to use the stoichiometric coefficients from the balanced equation of the combustion of methane to relate the heat released to the amount of methane burned.
The balanced equation for the combustion of methane is:
CH4 + 2O2 → CO2 + 2H2O
From the balanced equation, we can see that 1 mole of CH4 reacts to produce 802 kJ of heat. Therefore, we need to find the number of moles of CH4 that corresponds to 542,000 J of heat.
To calculate the number of moles, we use the molar enthalpy (ΔH) of the reaction:
ΔH = q / n
where
q = heat released (in J)
n = number of moles
Rearranging the formula to solve for the number of moles (n):
n = q / ΔH
Substituting the values:
n = 542,000 J / (-802 kJ × 1000 J/kJ)
n = 542,000 J / -802,000 J
n ≈ -0.675 mol
Since we can't have a negative amount of substance, we take the absolute value of n:
|n| ≈ 0.675 mol
Finally, we can convert moles of methane to grams of methane using the molar mass of methane, which is 16 g/mol.
Mass of methane = |n| × molar mass
Mass of methane = 0.675 mol × 16 g/mol
Mass of methane ≈ 10.8 g
Therefore, approximately 10.8 grams of methane need to be burned to release 542 kJ of heat.