Answer :
Final answer:
The volume of methane released from each kg of methane hydrate, under Standard Temperature and Pressure (STP), is 1.12 cubic decimeters (dm³). This calculation is made by converting the mass of the hydrate to moles and then using the molar volume.
Explanation:
To calculate the volume of methane, we will use the ideal gas law PV = nRT, assuming conditions of Standard Temperature and Pressure (STP). Methane hydrate is a solid that consists of methane gas molecules trapped in a crystal lattice of water molecules. Each mole of the hydrate releases 1 mole of methane upon melting.
Since the molecular weight of methane hydrate is about 20 g/mole, each kg (1000 g) of hydrate contains about 1000/20 = 50 moles of methane. At STP, 1 mole of a gas occupies 22.4 L. Therefore, the 50 moles of methane occupy a volume of 50 moles x 22.4 L/mole = 1120 L or 1.12 dm³.
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