In the case of a 100m Race, displacement equals the distance traveled. If we divide this equation by the time t (assuming t represents the time taken to finish the 100m race), we derive that velocity equals speed. Conversely, in a 400m race where a full lap is completed, the racer’s starting and ending positions overlap, leading to displacement equaling 0, while the distance is not zero (400m). Therefore, it follows that displacement does not equal distance, leading to the conclusion that velocity does not equal speed.
Answer:
The rate law for the decomposition reaction is:
![R=k[D]^2](https://tex.z-dn.net/?f=R%3Dk%5BD%5D%5E2)
The unit for the rate constant will be 
Explanation:
The rate law can be expressed as:
![R=k[D]^x](https://tex.z-dn.net/?f=R%3Dk%5BD%5D%5Ex)
..[1]
When the drug concentration is tripled, the decomposition rate rises by a factor of nine.
![[D]'=3[D]](https://tex.z-dn.net/?f=%5BD%5D%27%3D3%5BD%5D)
![R'=k[D]'^x](https://tex.z-dn.net/?f=R%27%3Dk%5BD%5D%27%5Ex)
...[2]
[1] ÷ [2]
![\frac{R}{R'}=\frac{k[D]^x}{k[D']^x}](https://tex.z-dn.net/?f=%5Cfrac%7BR%7D%7BR%27%7D%3D%5Cfrac%7Bk%5BD%5D%5Ex%7D%7Bk%5BD%27%5D%5Ex%7D)
![\frac{R}{9R}=\frac{k[D]^x}{k[3D]^x}](https://tex.z-dn.net/?f=%5Cfrac%7BR%7D%7B9R%7D%3D%5Cfrac%7Bk%5BD%5D%5Ex%7D%7Bk%5B3D%5D%5Ex%7D)
Solving for x results in:
x = 2.
This indicates a second-order reaction.
The decomposition reaction's rate law is:
The unit for the rate constant will be:
![k=\frac{R}{[D]^2}=\frac{M/s}{(M)^2}=M^{-1}s^{-1}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7BR%7D%7B%5BD%5D%5E2%7D%3D%5Cfrac%7BM%2Fs%7D%7B%28M%29%5E2%7D%3DM%5E%7B-1%7Ds%5E%7B-1%7D)
The unit for the rate constant will be .
To determine the answer, you need to understand the formula for converting grams to moles, which will then lead you to the number of molecules.
The result is 2 moles of N2O5. The process is as follows:
(0.25 g N2O5) (1 mol/ 108 g)=2.31 molecules
Thus, the final answer is 2 molecules.
