Question

Carbon disulfide, a poisonous, flammable liquid, is an excellent solvent for phosphorus, sulfur, and some other nonmetals. A kinetic study of its gaseous decomposition reveals these data: Experiment Initial [CS2] (mol/L) Initial Rate (mol/L·s) 1 0.100 2.7 × 10−7 2 0.080 2.2 × 10−7 3 0.055 1.5 × 10−7 4 0.044 1.2 × 10−7 (a) Choose the rate law for the decomposition of CS2

Answer 1

`r=-3.73x10^(5)s^(-1) [CS_2]`

Step-by-step explanation:

Hello,

In this case, a linealization helps to choose the rate law for the decomposition of CS₂ as it is generalized via:

`r=-k[CS_2]^(n)`

Whereas
`n` accounts for the order of reaction, which could be computed by linealizing the given data using the following procedure:

`-ln(r)=ln(k[CS_2]^(n))\\-ln(r)=ln(k)+ln([CS_2]^(n))\\-ln(r)=ln(k)+n*ln([CS_2])`

Therefore, on the attached picture you will find the graph and the lineal equation wherein the slope is the order of the reaction and the y-axis intercept the natural logarithm of the rate constant. In such a way, the order of reaction is 1 and the rate constant is:

`ln(k)=12.83\\k=exp(12.83)\\k=3.73x10^(5)s^(-1)`

Best regards.

Answer 2

Rate law: =
`k[CS_2]^1`

Step-by-step explanation:

Given:

t
`[CS_2]`

0.100
`2.7 * 10^(-7)`

0.080
`2.2 * 10^(-7)`

0.055
`1.5* 10^(-7)`

0.044
`1.2* 10^(-7)`

Rate law for the given reaction:
`k[CS_2]^n`

Where, n is the order of the reaction.

Divide rate 1 with rate 3

`(0.100)/(0.055) =(k[CS_2 (1)]^n)/(k[CS_2 (3)]^n) \\(0.100)/(0.055) =(k[2.7 * 10^(-7)]^n)/(k[1.5* 10^(-7)]^n)\\1.81=[1.8]^n\\ n=1`

So, rate law =
`k[CS_2]^1`