Larger amounts of methane, in the form CH4*6H20 is trapped at the bottom of the ceans in Clatharate compunds (formed when small molecules occupy the empty spaces in cage like structures). Calculate the mass of methane gas trapped with in one Kg of the hydrate
To calculate the mass of methane gas trapped within 1 kg of the hydrate, we need to consider the molecular structure of methane hydrate.
The ratio of methane (CH₄) to water (H₂O) in methane hydrate is 1:6. This means that for every methane molecule, there are 6 water molecules.
The molar mass of methane (CH₄) is approximately 16 g/mol, and the molar mass of water (H₂O) is approximately 18 g/mol.
To calculate the mass of methane gas trapped within 1 kg of the hydrate, we can use the following steps:
Step 1: Calculate the number of moles of methane in 1 kg of the hydrate:
The molar mass of methane is 16 g/mol.
So, the number of moles of methane in 1 kg is:
(1000 g/16 g/mol) = 62.5 moles
Step 2: Calculate the mass of methane gas:
Since the ratio of methane to water is 1:6, for every mole of methane there are 6 moles of water.
So, the moles of water in 1 kg of hydrate is:
(62.5 moles * 6) = 375 moles
Now, we can calculate the mass of methane gas by multiplying the number of moles of methane by its molar mass:
(62.5 moles * 16 g/mol) = 1000 g
Therefore, there is approximately 1000 grams (or 1 kg) of methane gas trapped within one kilogram of the hydrate.
To calculate the mass of methane gas trapped within one kilogram of the hydrate, we need to know the molar mass of methane and the molar mass of the entire hydrate.
1. Molar mass of methane (CH4):
The molar mass of carbon (C) is 12.01 g/mol, and the molar mass of hydrogen (H) is 1.008 g/mol. Since methane has one carbon atom and four hydrogen atoms, the molar mass of methane is:
(12.01 g/mol) + 4(1.008 g/mol) = 16.04 g/mol
2. Molar mass of the hydrate (CH4·6H2O):
The molar mass of water (H2O) is 18.015 g/mol, and since there are six water molecules (6H2O) associated with one methane molecule, the molar mass of the hydrate is:
1(16.04 g/mol) + 6(18.015 g/mol) = 162.09 g/mol
3. Calculate the mass of methane in 1 kg of the hydrate:
We know that 1 kilogram is equal to 1000 grams. To find the mass of methane within 1 kg of the hydrate, we can use the molar mass ratio.
First, calculate the moles of the hydrate in 1 kg:
moles of hydrate = (mass of hydrate) / (molar mass of hydrate)
moles of hydrate = 1000 g / 162.09 g/mol
Next, multiply the moles of the hydrate by the ratio of moles of methane to moles of the hydrate:
moles of methane = (moles of hydrate) × (moles of methane / moles of hydrate)
moles of methane = (1000 g / 162.09 g/mol) × (1 mol methane / 1 mol hydrate)
Finally, calculate the mass of methane gas:
mass of methane = (moles of methane) × (molar mass of methane)
mass of methane = [(1000 g / 162.09 g/mol) × (1 mol methane / 1 mol hydrate)] × (16.04 g/mol)
Simplifying the calculation will give you the mass of methane gas trapped within one kilogram of the hydrate.