A sample of liquefied natural gas, LNG, from Alaska has the following molar composition: \(93.5 \% \mathrm{CH}_{4}, 4.6 \% \mathrm{C}_{2} \mathrm{H}_{6}, 1.2 \% \mathrm{C}_{3} \mathrm{H}_{8}\), and \(0.7 \% \mathrm{CO}_{2}\). Calculate:

(a) Average molecular weight of the LNG mixture.

(b) Weight fraction of \(\mathrm{CH}_{4}\) in the mixture.

(c) The LNG is heated to \(320 \mathrm{~K}\) and \(140 \mathrm{kPa}\) and vaporizes completely. Estimate the density of the gas mixture under these conditions.