Question

2h₃po₄(aq)→p₂o₅(aq)+3h₂o(aq)
he fills a reaction vessel with h₃po₄ and measures its concentration as the reaction proceeds. heres a graph of his data:
use this graph to answer the following questions:
what is the half - life of the reaction?
round your answer to 2 significant digits.
suppose the rate of the reaction is known to be first order in h₃po₄. calculate the value of the rate constant k.
round your answer to 2 significant digits. also be sure you include the correct unit symbol.

Explanation:

Step1: Determine half - life from graph

The half - life ($t_{1/2}$) of a reaction is the time it takes for the concentration of the reactant to decrease to half of its initial value. From the graph, the initial concentration of $\ce{H3PO4}$ is approximately $0.8\ M$. Half of this value is $0.4\ M$. Reading from the graph, the time at which $[\ce{H3PO4}]=0.4\ M$ is $t = 0.40\ s$. So, $t_{1/2}=0.40\ s$.

Step2: Calculate rate constant for first - order reaction

For a first - order reaction, the relationship between the half - life and the rate constant ($k$) is given by the formula $t_{1/2}=\frac{\ln 2}{k}$. Rearranging for $k$, we get $k=\frac{\ln 2}{t_{1/2}}$. Substituting $t_{1/2}=0.40\ s$ into the formula, $k = \frac{\ln 2}{0.40\ s}\approx1.7\ s^{-1}$.

Answer:

$t_{1/2}=0.40\ s$
$k = 1.7\ s^{-1}$