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MARCH 2024 — Chemistry STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceChemistryMARCH 20244 Marks
Question
Derive the relation between half life period and rate constant for first order reaction.
Write the net cell reaction during discharging of lead accumulator.
Draw the structure of peroxymonosulphuric acid.
✓

Answer

The relation between half-life and rate constant for first-order reaction:
The integrated rate law for the first-order reaction is $k =\frac{2.303}{ t } \log _{10} \frac{[A]_0}{[A]_{ t }}$where,$[ A ]_0$
is the initial concentration of reactant at t = 0. It falls to $[ A ]_t$ at time t after the start of the reaction.The time required for $[ A ]_0$ to become $\frac{[ A ]_0}{2}$ is denoted as $t_{1 / 2}$ or $[ A ]_{ t }=\frac{[ A ]_0}{2}$ at $t=t_{1 / 2}$
Putting this condition in the integrated rate law we write
$k=\frac{2.303}{t_{1 / 2}} \log _{10} \frac{[A]_t}{[A]_0 / 2}=\frac{2.303}{t_{1 / 2}} \log _{10} 2$
Substituting value of $\log _{10} 2$
$k=\frac{2.303}{ t _{1 / 2}} \times 0.3010$
$\therefore k =\frac{0.693}{ t _{1 / 2}}$
$\therefore t _{1 / 2}=\frac{0.693}{ k }$

The net cell reaction during the discharging of a lead accumulator is represented by the equation:
$Pb ( s )+ PbO _2(s)+4 H ^{\oplus}( aq )+2 SO _4^{2 \Theta}( aq ) \longrightarrow 2 PbSO _4(s)+2 H _2 O ( l )$
This reaction summarizes the overall process occurring within the lead acid battery during discharge, where lead and lead dioxide undergo a chemical reaction in the presence of sulfuric acid to produce lead sulfate and water.
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