Question

For the first order reaction $A\left(g\right)\to2B\left(g\right)+C\left(g\right),$ the initial pressure is $P_A = 90\, mm\, Hg,$ the pressure after 10 minutes is found to be $180\, mm \,Hg$. The rate constant of the reaction is

• A. $1.15 \times 10^{-3} sec^{-1}$
• B. $2.3 \times 10^{-3} sec^{-1}$
• C. $3.45 \times 10^{-3} sec^{-1}$
• D. $6 \times 10^{-3} sec^{-1}$

Answer 1

Answer: (A)

Total pressure after 10 minutes, $P_T= _PA + P_B + P_c$
or $P_{t}=\left(P_{A}-x\right)+2x+x$
$=p_{A}+2x=180$
$\because P_{A}=90 mm$
$90+2x=180 or X=45mm$
$\therefore P_{A}-x=90-45=45mm$
$kt=2.303 log \frac{P_{A}}{P_{A}-x}$
or $k\times10=2.303 log \frac{90}{90-45}$
$k\times10=0.693$
or $k=\frac{0.693}{10}=0.0693 min^{-1} =\frac{0.693}{10\times60 sec}=1.155\times10^{-1}sec^{-1}$