Question

initial - rate data at a certain temperature is given in the table for the reaction c₂h₅cl(g) → c₂h₄(g) + hcl(g)
c₂h₅cl₀(m) initial rate (m/s)
0.100 0.875×10⁻³⁰
0.200 1.75×10⁻³⁰
0.300 2.63×10⁻³⁰
determine the value and units of the rate constant.
k =
tools
×10ʸ
units: s⁻¹

Explanation:

Step1: Determine reaction order

When the concentration of $\ce{C2H5Cl}$ doubles from $0.100\ M$ to $0.200\ M$, the initial - rate doubles from $0.875\times 10^{-30}\ M/s$ to $1.75\times 10^{-30}\ M/s$. Since the rate is directly proportional to the concentration of $\ce{C2H5Cl}$, the reaction is first - order with respect to $\ce{C2H5Cl}$. The rate law is $rate = k[\ce{C2H5Cl}]$.

Step2: Calculate the rate constant

We can use the rate law and any row of the data. Let's use the first row where $rate = 0.875\times 10^{-30}\ M/s$ and $[\ce{C2H5Cl}]=0.100\ M$. Rearranging the rate law $k=\frac{rate}{[\ce{C2H5Cl}]}$. Substituting the values: $k=\frac{0.875\times 10^{-30}\ M/s}{0.100\ M}=8.75\times 10^{-30}\ s^{-1}$.

Answer:

$k = 8.75$, units: $s^{-1}$, $y=-30$