A 6.0g of methane decomposes into 4.5g of Carbon and 1.5g of Heydrogen. Determine the empirical formula of methane.

I would find the percent C and H.

(4.5/6.0)*100 = 75% C
(1.5/6.0)*100 = 25% H

Now take a 100 gram sample which will give you
75g C and 25g H. Now convert to moles.

moles C = 75/12 = 6.25
moles H = 25/1 = 25

Now find the smallest whole-number ratio between the two elements; the easy way to do this is to divide both values for moles by the smaller number, then divide the other value by the same small number. This gives you 1.00 for the first one and usually a whole number for the other. That will be the empirical formula.

To determine the empirical formula of methane, we need to calculate the ratio of the elements present in the compound.

First, we can determine the number of moles of carbon and hydrogen in the given masses.

To calculate the moles of carbon:
Molar mass of carbon (C) = 12.01 g/mol
Moles of carbon = mass of carbon / molar mass of carbon
Moles of carbon = 4.5 g / 12.01 g/mol

To calculate the moles of hydrogen:
Molar mass of hydrogen (H) = 1.01 g/mol
Moles of hydrogen = mass of hydrogen / molar mass of hydrogen
Moles of hydrogen = 1.5 g / 1.01 g/mol

Since methane has one carbon atom and four hydrogen atoms, we can compare the moles of carbon and hydrogen to find the ratio.

Molar ratio of carbon to hydrogen = moles of carbon / moles of hydrogen

Now, calculate the moles of carbon and hydrogen:
Moles of carbon = 4.5 g / 12.01 g/mol = 0.374 mol
Moles of hydrogen = 1.5 g / 1.01 g/mol = 1.48 mol

Molar ratio of carbon to hydrogen = 0.374 mol / 1.48 mol

To simplify the ratio, divide both values by the smallest value in the ratio (0.374):
0.374 mol / 0.374 mol = 1
1.48 mol / 0.374 mol ≈ 3.95

Rounding the ratio to the nearest whole number gives us:
Carbon:Hydrogen = 1:4

Since the ratio of carbon to hydrogen in methane is 1:4, the empirical formula of methane is CH4.