Q. 435.0( 2 Votes )

# A sample of ethane (C_{2}H_{6}) gas has the same mass as 1.5 ×10^{20} molecules of methane (CH_{4}). How many C_{2}H_{6} molecules does the sample of gas contain?

Answer :

Number of molecules of methane (CH_{4}) = 1.5 ×10^{20}

Mass of 1 mole of CH_{4} = 16 g

Mass of 1 mole of ethane (C_{2}H_{6}) = 30g

1 mole of substances contains 6.022 X 10^{23} molecules.

Thus, the mass of 6.022 X 10^{23} molecules of CH_{4} = 16 g

Thus, the mass of 1.5 ×10^{20} molecules of methane = 1.5 ×10^{20} × 16/ 6.022 X 10^{23}

= 3.98 x 10^{-3}g

Mass of molecules of C_{2}H_{6} is = Mass of CH_{4}(given)

Mass of 6.022 X 10^{23} molecules of C_{2}H_{6} = 30g

Therefore, 3.98 x 10^{-3}g of ethane will contain = 6.022 x 10^{23} x 3.98 x 10^{-3} / 30

= 0.8 × 10^{20} molecules

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