Question

The mass of methane that occupies 22.7 L of volume at STP if all the methane is produced by
carbon with isotopic abundance of 80% 12C and 20% 14C and hydrogen (only with 1H isotope)
is x . 4.1. Then what is the value of x?​

Answer 1

The mass of methane that occupies 22.7 L of volume at STP if all the methane is produced by carbon with isotopic abundance of 80% 12C and 20% 14C and hydrogen (only with 1H isotope) is x × 4.1

solution : first find molecular weight of methane.

mol wt of methane for ¹²C = 16 u

mol wt of methane for ¹⁴C = 18 u

now average mol wt = (80 × 16 + 20 × 18)/100

= (1280 + 320)/100

= 16 u

now no of moles of methane = given volume/22.4L/mol

= 22.7L/22.4L/mol = 1.0134 mol

now mass of methane = 1.0134 × 16

= 16.2144 g

but given mass of methane is x × 4.1

so, x × 4.1 = 16.2144

⇒x = 3.955

Therefore the value of x is 3.955.