A sample of ethane (C_2H_6) gas has the same | vedclass

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(C) The molar mass of methane $(CH_4)$ is $16 	ext{ g/mol}$ and ethane $(C_2H_6)$ is $30 	ext{ g/mol}$.The mass of $1.5 	imes 10^{20}$ molecules of

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$0.8 	imes 10^{20}$

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(C) The molar mass of methane $(CH_4)$ is $16 	ext{ g/mol}$ and ethane $(C_2H_6)$ is $30 	ext{ g/mol}$.The mass of $1.5 	imes 10^{20}$ molecules of $CH_4$ is given by: $	ext{Mass} = \frac{1.5 	imes 10^{20}}{N_A} 	imes 16 	ext{ g}$.Let $x$ be the number of molecules of $C_2H_6$. The mass of $x$ molecules of $C_2H_6$ is: $	ext{Mass} = \frac{x}{N_A} 	imes 30 	ext{ g}$.Since the masses are equal:$\frac{1.5 	imes 10^{20} 	imes 16}{N_A} = \frac{x 	imes 30}{N_A}$.Solving for $x$:$x = \frac{1.5 	imes 10^{20} 	imes 16}{30} = \frac{24 	imes 10^{20}}{30} = 0.8 	imes 10^{20}$ molecules.

$A$ 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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