Question

Suppose that coal of density 1.5 g/cm^3 is pure carbon. (It is, in fact, much more complicated, but this is a reasonable first approximation.) The combustion of carbon is described by the equation:

C(s) + O2(g) -----> CO2(g) ∆H° = −394 kJ
What is the value of q (heat) when a lump of coal of size 5.6 cm x 5.1 cm x 4.6 cm is burned?
Answer in units of kJ.

Answer 1

To calculate the heat energy released by burning a lump of coal, find the volume, multiply by density to get mass, convert mass to moles, and then multiply by the energy released per mole of carbon. The final calculated heat energy (q) is approximately -6451.75 kJ.

Step-by-step explanation:

The question asks us to calculate the heat energy (q) released when a lump of coal is burned. To find this, we first need to determine the mass of the coal using its volume and density. The volume of the coal lump can be determined by multiplying its dimensions: 5.6 cm × 5.1 cm × 4.6 cm. Once we have the volume, we multiply it by the coal's density to get the mass. The combustion of carbon releases -394 kJ of energy per mole of carbon according to the given chemical equation. Since the molar mass of carbon (C) is 12.01 g/mol, we convert the mass of coal to moles and then multiply by the energy released per mole to find the total energy (q).

Step-by-step calculation:

1. Calculate volume of the coal: Volume = 5.6 cm × 5.1 cm × 4.6 cm = 131.112 cm³.
2. Calculate mass of the coal: Mass = Volume × Density = 131.112 cm³ × 1.5 g/cm³ = 196.668 g.
3. Convert mass to moles: Moles of carbon = Mass / Molar mass of carbon = 196.668 g / 12.01 g/mol ≈ 16.375 moles of C.
4. Calculate the energy released: q = Moles × Energy per mole = 16.375 moles × (-394 kJ/mol) ≈ -6451.75 kJ.

Therefore, the value of q when the lump of coal is burned is approximately -6451.75 kJ.