Question

A certain chemical reaction rate is given as $\text{Rate}=k\left[C{]}^2\right[H{]}^2$, where $C\to$ carbon, $H\to$ hydorgen and $k\to$ rate constant. It was found that at certian concentrations of $C=4\frac{moles}{m^3}$ and $H=5\frac{moles}{m^3}$,the rate was $30\frac{moles}{m^3\times sec}$. What is the value of $k$?

Note: Ignore the units; only report the magnitudes.

• A. $\frac{3}{40}$
• B. $\frac{3}{4}$
• C. $\frac{3}{400}$
• D. $\frac{3}{50}$

Answer 1

The correct option is A $\frac{3}{40}$

$\text{Rate}=k\left[C{]}^2\right[H{]}^2$

Puttimg $\text{Rate}=30,C=4,H=5$ into the given equation we get,
$30=k\left[4{]}^2\right[5{]}^2$
$\Rightarrow 30=k(4\times 5{)}^2=k(20{)}^2$

$\underset{–}{\text{Note:}}$ the rule for bases with the same exponent $a^m\times b^m=(a\times b{)}^m$

$\Rightarrow 30=k\times 400$
Dividing both the sides by $400$, we get,
$\Rightarrow k=\frac{30}{400}$
$\Rightarrow k=\frac{3}{40}$