How much heat is given off when 24.0 g of methane is burned in air? The equation for the reaction is:
CH4 + 2O2 => CO2 + 2H2O + 890 kJ
What equation or formula should I use to solve this? Thanks!
To solve this problem, you can use the equation that relates the amount of heat released to the amount of substance reacted. The formula for calculating the heat released (q) is:
q = n × ΔH
Where:
q is the heat released (in Joules or kilojoules)
n is the number of moles of the substance reacted
ΔH is the enthalpy change for the reaction (given as 890 kJ in this case)
To solve for the moles of methane reacted (n), you can use the molar mass of methane (CH4):
Molar mass of CH4 = 12.01 g/mol + 4(1.01 g/mol) = 16.04 g/mol
Then, you can calculate the number of moles (n) by dividing the given mass by the molar mass:
n = mass / molar mass = 24.0 g / 16.04 g/mol = 1.494 mol (rounded to 3 decimal places)
Finally, you can substitute the calculated value of n into the equation to find the heat released (q):
q = 1.494 mol × 890 kJ/mol = 1329.06 kJ (rounded to 2 decimal places)
Therefore, when 24.0 g of methane is burned in air, approximately 1329.06 kJ of heat is released.
To solve this problem, you can use the equation for heat of combustion (\(q\)) given by:
\(q = m \times \Delta H\)
Where:
\(q\) is the heat released or absorbed (in Joules),
\(m\) is the mass of the substance being burned (in grams),
\(\Delta H\) is the heat of combustion per mole of the substance (in J/g).
In this case, you are given:
\(m = 24.0 \, \text{g}\)
\(\Delta H = 890 \, \text{kJ}\) (which needs to be converted to Joules)
First, convert the mass given in grams to moles by dividing by the molar mass of methane (CH4):
\(24.0 \, \text{g} \, \text{CH4} \times \left(\frac{1 \, \text{mol} \, \text{CH4}}{16.04 \, \text{g} \, \text{CH4}}\right) \approx 1.497 \, \text{mol} \, \text{CH4}\)
Next, convert the given heat of combustion from kJ to J by multiplying by 1000:
\(890 \, \text{kJ} \times 1000 = 890000 \, \text{J}\)
Now, substitute the values into the equation:
\(q = m \times \Delta H = 1.497 \, \text{mol} \times 890000 \, \text{J/mol} \approx 1.33 \times 10^6 \, \text{J}\)
Therefore, when 24.0 g of methane is burned in air, approximately 1.33 million Joules of heat is given off.