In the fragrance industry, linalool is a commonly used terpene alcohol which gives a floral scent to many consumer products $($soaps$,$ perfumes, lipsticks, etc.$).$ In nature, linalool is biosynthetically produced over by $200$ different flower species as well as certain fruits. The lavender essential oil which contains a high concentration of linalool can be extracted by the distillation process from the Lavender plant. This oil can be used in aromatherapy as well as a disinfectant, antiseptic, or anti$-$inflammatory agent.

Using standard addition method, the concentration of linalool in extracted essential oils was determined using gas chromatographic methods. The isolated data for the analysis was shown below.

a$.$ Complete the table below by solving the average peak area for each calibration standard solution. $(6$ pts$)$

b$.$ Plotting the volume of linalool standard $($column $2)$ against the average peak area $($column $6),$ generate the equation of the line of the calibration curve and the $r^2$ value. $(4$ pts$)$

$y=mx+b$

$1=2\mathrm{.}018x+{1\mathrm{.}8}^{9}6$

$r^2=0\mathrm{.}99604$

c$.$ If the concentration of linalool standard being used is $1m\frac{g}{m}L,$ and $12mL$ of $1\%\frac{v}{v}$ Essential oil was added to the flask. Then, finally diluted to a final volume of $25mL$ using ethanol. Calculate the concentration of linalool in a $1\%(\frac{v}{v})$ Essential oil. $(3$ pts$)$

$c_1,=1mgll,c_1{v}_1,=c_2{v}_2$

$v_1,=12ml,c_2,=c_1{v}_1|v_2|(l|))/(25ml$

d$.$ Calculate the concentration of linalool from the original solution of essential oil $($Hint: dilution occurred when $1\%$ essential oil was used in the preparation of standard addition solution as state in question c$).(2$ pts$)$