To calculate the number of molecules in 0.334g of ethane, we can use the following formula:

Number of molecules = (Mass in grams) / (Molar mass) x Avogadro's number

Number of molecules = 0.334 g / 30.07 g/mol x 6.022 x 10^23 molecules/mol

= 6.88 x 10^21 molecules

Therefore, 0.334 g of ethane contains 6.88 x 10^21 molecules of ethane.