in a study of ammonia production, an industrial chemist discovers that the compound decomposes to its…

in a study of ammonia production, an industrial chemist discovers that the compound decomposes to its elements n₂ and h₂ in a first - order process. she collects the following data: time (s) nh₃(mol/l) 0.0 4.000 1.0 3.986 3.0 3.974 part 1 of 3 graph a line that can be used to determine the rate constant. to do this, convert the nh₃ values to lnnh₃ values with 4 decimal places. precisely plot the 3 points and graph a line through the first and third point. graph of lnnh₃ over time

in a study of ammonia production, an industrial chemist discovers that the compound decomposes to its elements n₂ and h₂ in a first - order process. she collects the following data: time (s) nh₃(mol/l) 0.0 4.000 1.0 3.986 3.0 3.974 part 1 of 3 graph a line that can be used to determine the rate constant. to do this, convert the nh₃ values to lnnh₃ values with 4 decimal places. precisely plot the 3 points and graph a line through the first and third point. graph of lnnh₃ over time

Answer

Answer:

First, convert the $[\text{NH}_3]$ values to $\ln[\text{NH}_3]$ values:

  • When $t = 0.0\ s$, $[\text{NH}_3]=4.000\ mol/L$, $\ln[\text{NH}_3]=\ln(4.000)\approx1.3863$
  • When $t = 1.0\ s$, $[\text{NH}_3]=3.986\ mol/L$, $\ln[\text{NH}_3]=\ln(3.986)\approx1.3828$
  • When $t = 3.0\ s$, $[\text{NH}_3]=3.974\ mol/L$, $\ln[\text{NH}_3]=\ln(3.974)\approx1.3804$

The three - point coordinates for plotting are $(0.0,1.3863)$, $(1.0,1.3828)$ and $(3.0,1.3804)$. Plot these points on a graph with time on the x - axis and $\ln[\text{NH}_3]$ on the y - axis and draw a line through the first and third point.

Explanation:

Step1: Recall the conversion formula

For a value $x$, $\ln(x)$ is calculated.

Step2: Calculate $\ln[\text{NH}_3]$ for $t = 0.0\ s$

$\ln(4.000)\approx1.3863$

Step3: Calculate $\ln[\text{NH}_3]$ for $t = 1.0\ s$

$\ln(3.986)\approx1.3828$

Step4: Calculate $\ln[\text{NH}_3]$ for $t = 3.0\ s$

$\ln(3.974)\approx1.3804$

Step5: Prepare for plotting

Identify the points $(0.0,1.3863)$, $(1.0,1.3828)$ and $(3.0,1.3804)$ for the graph.