High quality coal (anthracite) is almost pure carbon. The combustion of carbon to carbon dioxide
releases 393 kJ per mol of carbon burnt. If 1.000 kg of anthracite is burnt:
(i) How much heat is released?
(ii) How much ice (in kg) at 273 K could be melted to give water at 273 K using the heat in (i)? (iii)How much ice at 273 K could be melted to give water at 100 °C using the heat in (i)?
(iv) How much ice at 273 K could be melted to give steam at 373 K using the heat in (i)?
C + O2 ==> CO2 +393 kJ/mol = 393 kJ/12 g C.
1. So 393 kJ x (1,000 g/12 g) = ? = approx 33,000 kJ but that's just an estimate.
2. How much heat is required to melt 1 g ice. That's approx 334 J/g ice but you need to use the value in your text/tables. You have about 33,000 kJ. How much ice can you melt with that.
3 & 4. Same thing as 2 but the ice, after metling must raise the T from the melted ice at zero C to 100 C. In 4 you must add enough to raise change the phase from liquid to steam.
Post your work if you need more help.
To solve this problem, we need to use the concept of heat released during combustion and heat required for phase changes.
(i) To calculate the heat released when 1.000 kg of anthracite is burnt, we need to determine the number of moles of carbon in 1.000 kg. We know that the molar mass of carbon (C) is 12.01 g/mol. Therefore, the number of moles of carbon is given by:
moles = mass / molar mass
moles = 1000 g / 12.01 g/mol
Now, we can calculate the heat released using the given information:
Heat released = moles of carbon * heat of combustion
Heat released = moles * 393 kJ/mol
(ii) To determine how much ice at 273 K could be melted using the heat released, we need to consider the heat required to melt ice at that temperature. The heat required to melt ice is 333.55 J/g.
First, we need to convert the heat released into joules:
Heat released in joules = Heat released in kJ * 1000
Now, we can calculate the amount of ice that can be melted:
Mass of ice melted = Heat released in joules / Heat required to melt ice
(iii) To calculate how much ice at 273 K could be melted to give water at 100 °C using the heat released, we need to consider two phase changes: melting ice at 273 K and heating the water from 273 K to 100 °C.
The heat required to raise the temperature of water from 0 °C to 100 °C is 4186 J/g.
First, we need to calculate the amount of ice that can be melted at 273 K:
Mass of ice melted = Heat released in joules / Heat required to melt ice
Next, we need to calculate the amount of water that can be heated from 273 K to 100 °C:
Mass of water heated = Mass of ice melted * (100 - 273) °C / Heat required to raise the temperature of water
(iv) To calculate how much ice at 273 K could be melted to give steam at 373 K using the heat released, we need to consider three phase changes: melting ice at 273 K, heating the water from 273 K to 100 °C, and converting the water into steam at 100 °C.
The heat required to convert water into steam at 100 °C is 2260 J/g.
First, we calculate how much ice can be melted at 273 K:
Mass of ice melted = Heat released in joules / Heat required to melt ice
Next, we calculate how much water can be heated from 273 K to 100 °C:
Mass of water heated = Mass of ice melted * (100-273) °C / Heat required to raise the temperature of water
Finally, we calculate how much steam can be obtained from the heated water:
Mass of steam = Mass of water heated * Heat required to convert water to steam / Heat required to raise the temperature of water
Keep in mind that all the answers should be in kilograms (kg).