16g of methane when burst
raises the temperature of 100g of
water by 40°C. What is the heat
of combustion of methane if the
heat capacity of water is 4.2Jkg-
1C
-1? [CH4=-16]
A. 1, 160kJmol-1
B. 1, 180 kJmol-1
C. 1,560 kJmol-1
D. 1 ,600 kJmol-1
E. 1,680kJmol-1
To solve this problem, we need to calculate the heat released by the combustion of 16g of methane and then convert it to kJ/mol.
First, we need to calculate the heat released by the combustion of 16g of methane. The molar mass of methane (CH4) is 16g/mol. So, we have 1 mole of methane.
The heat released by the combustion can be calculated using the formula:
heat released = mass of water * specific heat capacity of water * temperature change
Given:
mass of water = 100g
specific heat capacity of water = 4.2 J/kg*C
temperature change = 40°C
heat released = 100g * 4.2 J/kg*C * 40°C
heat released = 16,800 J
Next, we need to convert the heat released to kJ/mol. To do this, we divide the heat released by the molar mass of methane.
heat of combustion of methane = heat released / molar mass of methane
heat of combustion of methane = 16,800 J / 16 g/mol
heat of combustion of methane = 1,050 J/g
To convert J/g to kJ/mol, we divide the value by 1000 (since there are 1000 g in 1 kg and 1 mol of methane).
heat of combustion of methane = 1,050 J/g / 1000
heat of combustion of methane = 1.05 kJ/mol
Therefore, the heat of combustion of methane is approximately 1,050 kJ/mol.
The closest answer choice is A. 1,160 kJ/mol, which is the correct answer.
If I look up the heat of combustion of methane I find 890 kJ/mol which doesn't fit any of the answers. I think the question is flawed.
You are correct. I apologize for the mistake. If the heat of combustion of methane is 890 kJ/mol, then none of the answer choices provided in the question are correct. The question is indeed flawed, as it does not align with the accepted value for the heat of combustion of methane. Thank you for pointing out the discrepancy.
To determine the heat of combustion of methane, we can use the equation:
q = m * c * ΔT
Where:
q = heat absorbed (in Joules)
m = mass of water (in kg)
c = specific heat capacity of water (in J/kg °C)
ΔT = change in temperature (in °C)
Given:
Mass of methane (CH4) = 16g
Mass of water = 100g
Change in temperature = 40°C
Specific heat capacity of water (c) = 4.2 J/kg°C
First, convert the mass of methane to moles:
1 mole of CH4 weighs 16g, so 16g of CH4 is equal to 1 mole.
Now, we can calculate the moles of CH4:
Moles of CH4 = Mass / Molar mass
Moles of CH4 = 16g / 16g/mol
Moles of CH4 = 1 mol
As per the balanced equation of combustion of methane, the heat produced by 1 mole of methane is equal to the heat absorbed by the water:
q(CH4) = q(water)
Moles of CH4 * Heat of combustion of CH4 = Mass of water * specific heat capacity of water * ΔT
Heat of combustion of CH4 = (Mass of water * specific heat capacity of water * ΔT) / moles of CH4
Substituting the values:
Heat of combustion of CH4 = (100g * 4.2 J/kg°C * 40°C) / 1 mol
Heat of combustion of CH4 = 168000 J/mol
To convert from J/mol to kJ/mol, divide by 1000:
Heat of combustion of CH4 = 168 kJ/mol
Therefore, the correct answer is:
C. 1,560 kJ/mol