Isoprene (methylbuta-1,3-diene) is dimerized following:
$2 C_5H_8$ $\longrightarrow$ $C_{10}H_{16}$
Here the experimental results for the dimer formation rate (in $\frac{mol}{L\cdot s})$ depending on the initial concentration of isoprene (in $\frac{mol}{L})$:
$[C_5H_8]$
$v_{C_{10}H_{16}}$
$0.50$
$1.98$
$1.50$
$17.8$
Find the reaction law! Compare order and molecularity!
- As the coefficient of $C_{10}H_{16}$ is $1$ we have:
$v_r$ $=$ $\frac{\Delta [C_{10}H_{16}]}{1\cdot \Delta t}$ $=$ $\frac{\Delta [C_{10}H_{16}]}{\Delta t}$ $=$ $v_{C_{10}H_{16}}$
- The rate law
$v_r=k[ C_5H_8]^{\alpha}$
becomes:
(1) $1.98$ $=$ $k\cdot 0.50^{\alpha}$
(2) $17.8$ $=$ $k\cdot 1.50^{\alpha}$
Dividing (2) by (1):
$9 = 3^{\alpha}$
$\alpha=2$
Order equals (here) molecularity!
