Question

The following data is obtained during the first order thermal decomposition of $2A_{(g)} \rightarrow B_{(g)} + C_{(s)}$,
at constant volume and temperature

Sr. No.	Time	Total pressure in pascal
1.	At the end of 10 minutes	300
2.	After completion	200

The rate constant in $min^{-1}$ is

• A. $0.0693$
• B. $69.3$
• C. $6.93$
• D. $0.00693$

Answer 1

Answer: (A)

$\underset{2-2x}{2A(g)} \to B \underset{x}{(g)}+C(s)$

At the end of reaction, only 1 mole of gas is present whose pressure is 200 pascal. $\therefore $ At the beginning of the reaction 2 moles of gas should have a pressure of 400 pascal.

After time 10 min

No. of moles present,

$2-2 x+x=2-x$

The pressure of 2 moles $=400$

$400-x=300$

$\therefore \,x=100$

$\therefore $ Pressure due to $2-2 x$ moles of $A$

$=400-200=200$

$ \therefore k =\frac{2.303}{t} \log \left(\frac{a}{a-x}\right)=\frac{2.303}{10} \log \left(\frac{400}{200}\right) $

$=\frac{2.303}{10} \log 2=\frac{0.693}{10} $

$=0.0693\, min ^{-1} $