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  • A sample of ethane (C_2H_6)gas has the same mass as 1.5 \times 10^{20}molecules of methane (CH_4)How many C_2H_6 molecules does the sample of gas contain

A sample of ethane (C_2H_6) gas has the same mass as 1.5 \times 10^{20} molecules of methane (CH_4). How many(C_2H_6)  molecules does the sample of gas contain?

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Mass \: of\: 1\: molecule\: of\: CH_4=\frac{16}{N_A}g

Mass \: of\: 1.5 \times 10^{20}\: molecule\: of\: CH_4=\frac{1.5\times 10^{20}\times 16}{N_A}g

Mass \: of\: 1\: molecule\: of\: C_2H_6=\frac{30}{N_A}g

Mass \: of\: C_2H_6\: molecules\: =\frac{1.5 \times 10^{20} \times 16}{N_A}g

Therefore, number of molecules of      C_2H_6 = \frac{1.5 \times 10^{20} \times 16}{N_A}g \times \frac{N_A}{16}

                                                                          =0.8 \times 10^{20}

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