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Chapter 3: Problem 26

How many molecules of ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) are present in \(0.334 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{6} ?\)

Short Answer

Expert verified
The number of molecules present in 0.334 g of \(\mathrm{C}_{2} \mathrm{H}_{6}\) is approximately \(\6.63 x 10^22\) molecules.

Step by step solution

01

Determine the Molar Mass of Ethane

The molar mass of Ethane (`\(\mathrm{C}_{2} \mathrm{H}_{6}\)`) is `30.07 \mathrm{~g/mol}`. It's calculated by adding the molar masses of Carbon (C) and Hydrogen (H) in the atomic units. Ethane has 2 Carbon atoms (12.01 g/mol each) and 6 Hydrogen atoms (1.01 g/mol each) so the calculation becomes `(2*12.01) + (6*1.01) = 30.07 g/mol`.
02

Calculate the number of Moles

Moles of a substance is calculated by dividing the given mass of the substance by the molar mass of that substance. Ergo, the moles of Ethane can be calculated as `0.334 g ÷ 30.07 g/mol = 0.011 moles`.
03

Calculate the Number of Molecules

Using Avogadro’s number (`6.023 x 10^23 molecules/mol`), the number of molecules of Ethane can be calculated as `0.011 moles x 6.023 x 10^23 molecules/mol = 6.63 x 10^22 molecules`.

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