A gas mixture of $0\mathrm{.}51$ mole fraction n$-$pentane and the rest n$-$hexane at $17\mathrm{.}0\backslash$deg C is in equilibrium with a liquid mixture of the two components. Determine the mole fraction of n$-$pentane in the liquid.

Your answer must have three decimal figures and should be accurate to $\backslash$pm $0\mathrm{.}002.$ Do not truncate intermediate results, but only the final answer. Use the following Raoult's Law equations to solve for the unknown:

x$1$P$1*=$ y$1$PT

x$2$P$2*=$ y$2$PT