Reaction order

Exercise 4

    

At $650\;K$ the reaction $C_2H_5Cl(g)$ $\longrightarrow$ $ C_2H_4(g)$ $+$ $HCl(g)$ is first order with $k$ $=$ $1.60\cdot 10^{-6}\frac{1}{s}$ We begin with $[C_2H_5Cl(g)]_o$ $=$ $0.165\; M$ a) What is the molarity of $C_2H_5Cl(g)$ after $125\; h$? b) After what time the molarity of $C_2H_5Cl(g)$ will it be $0.100\;M $? c) After what time $75\%$ of $C_2H_5Cl(g)$ will it be decomposed? d) Calculate the half-life time $\theta$ !

Let's call $C_2H_5Cl(g)$ $=$ $A $ a) For $t=125\cdot 3600\;s$ we have: $[A]_t=[A]_o\cdot e^{-kt}$ = $0.0803\;M$ b) $t=\frac{ln[A]_o-ln[A]_t}{k}$ =$3.132\cdot 10^5\; s$ c) If $75\%$ are decomposed, $\frac{[A]_t}{[A]_o}$ $=$ $\frac{1}{4}$ $ln\frac{[A]_t}{[A]_o}$ $=$ $ -kt$ $t$ $=$ $-\frac{1}{k}ln\frac{[A]_t}{[A]_o}$ = $8.676\cdot 10^5\; s$ d) $\theta=\frac{ln2}{k}$ = $4.32\cdot 10^5\;s$