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Question
. A sample of ethane (C2H6) gas has the same mass as 1.5 ×1020 molecules of methane (CH4). How many C2H6 molecules does the sample of gas contain?
Solution
Molar mass of CH4 = 12 + 4
= 16 g mol−1
1 mole of CH4 = 16g = 6.022 × 1023 molecules
Thus, 6.022 × 1023 molecules of CH4 have mass = 16g
∴ 1.5 × 1020 molecules of CH4 will have mass
= `16/(6.022 xx 10^23) xx 1.5 xx 10^20`
= 4 × 10−3 g
Molar mass of C2H6 = 2 × 12 + 6
= 30 g mol−1
∴ 1 mole of C2H6 = 30g = 6.022 × 1023 molecules
Thus, 30g of C2H6 have molecules = 6.022 × 1023
∴ 4 × 10−3 g of C2H6 will have molecules
= `(6.022 xx 10^23)/30 xx 4 xx 10^-3`
= 0.803 × 1020
= 8.03 × 1019
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