The decomposition of \( {N}_2{O}_5(g) \) is a first-order reaction: \[ 2 \, {N}_2{O}_5(g) \rightarrow 4 \, {NO}_2(g) + {O}_2(g) \] Let the initial pressure of \( {N}_2{O}_5 \) be \( a \) atm. After time \( t \), let the pressure of \( {N}_2{O}_5 \) that has decomposed be \( x \) atm.
The total pressure at time \( t \) is given as \( p \) atm. The change in pressure due to the reaction is: \[ {N}_2{O}_5(g) \rightarrow 2 \, {NO}_2(g) + \frac{1}{2} \, {O}_2(g) \] Thus, the total pressure at time \( t \) is: \[ p = (a - x) + 2x + \frac{1}{2}x = a + \frac{3}{2}x \] Solving for \( x \): \[ x = \frac{2(p - a)}{3} \] The pressure of \( {N}_2{O}_5 \) at time \( t \) is: \[ a - x = a - \frac{2(p - a)}{3} = \frac{3a - 2p + 2a}{3} = \frac{5a - 2p}{3} \] For a first-order reaction, the rate constant \( k \) is given by: \[ k = \frac{1}{2} \ln \left( \frac{a}{a - x} \right) = \frac{1}{2} \ln \left( \frac{a}{\frac{5a - 2p}{3}} \right) = \frac{1}{2} \ln \left( \frac{3a}{5a - 2p} \right) \] considering the given options and the context, the correct answer is: \[ k = \frac{1}{2} \ln \left( \frac{3a}{5a - 2p} \right) \] Final Answer:
\( k = \frac{1}{2} \ln \left( \frac{3a}{5a - 2p} \right) \)
The correct statements about the adsorption of gas on solid adsorbent are:
Adsorption is always exothermic. Physisorption may transform into chemisorption at high temperature. Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature. In physisorption enthalpy of adsorption is 100 kJ mol\(^{-1}\).
Two statements are given below:
Statement I: Octet theory accounts for the shape of the molecules.
Statement II: Octet theory does not explain the relative stability of the molecules.
The correct answer is:
Two statements are given below
Statement I: Benzanamine can be prepared from phthalimide.
Statement II: Benzanamine is less basic than phenyl methanamine.
What are X and Z in the following reaction sequence?
What is Y in the following reaction sequence?
Observe the following set of reactions:
Correct statement regarding Y and B is:
What is X in the following reaction?