Problem $6.(2$ points$)$ Recall for a given species, the acentric factor is defined as

$=-lo{g}_{10}{p}_r^{\text{s}\text{a}\text{t}}{|}_{T_r}=0\mathrm{.}7-1,$ where $p_r^{\text{s}\text{a}\text{t}}$ is the reduced saturation pressure. Derive

the following formula for the calculation of the acentric factor:

$=\frac{3}{7}(\frac{lo{g}_{10}(\frac{p_c}{14\mathrm{.}695})}{\frac{T_c}{T_b}-1})-1,$

where $P_c$ is in psia. $[$Hint: Use the assumption that the vapor$-$pressure data is

represented by $lo{g}_{10}{p}^{\text{s}\text{a}\text{t}}=+\frac{}{T}.]$