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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 C2H6molecules does the sample of gas contain?


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Solution

Step 1: Finding the mass of Methane present:

1mole=6.022×1023 molecules of methane

So, 1.5×1020moleculesofmethaneis:(1.5×1020×1)÷(6.02×1023)moles

Hence, 1.5×1020moleculesofmethane=2.49×10-4 moles

As the Molar mass of Methane: (CH4):12+1×4=16g

Hence, the mass of methane:

Massofmethane=molarmass×Numberofmoles = 16×2.49×10-4:3.984×10-3g(whichissameasthemassofEthane)

Step 2: Finding the number of molecules of C2H6 present in a gas sample:

Molar mass of Ethane = 2×12+1×6=30g.

So, if the 30g of Ethane has 6.02x1023molecules

Then, 3.984×10-3g=(3.984×10-3×6.02×1023)÷30

= 8×109 molecules

Therefore, 8×109 molecules of Ethane (C2H6) gas are present.


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