2 questions from 2024
A sample initially contains only U-\( 238 \) isotope of uranium. With time, some of the U-\( 238 \) radioactively decays into Pb-\( 206 \) while the rest of it remains undisintegrated. When the age of the sample is \( P \times 10^{8} \) years, the ratio of mass of Pb-\( 206 \) to that of U-\( 238 \) in the sample is found to be \( 7 \). The value of \( P \) is _____. [Given: Half-life of U-\( 238 \) is \( 4.5 \times 10^{9} \) years; \( \log_{e} 2 = 0.693 \)]
Consider the following reaction,
\( 2\text{H}_2(\text{g}) + 2\text{NO}(\text{g}) \rightarrow \text{N}_2(\text{g}) + 2\text{H}_2\text{O}(\text{g}) \)
which follows the mechanism given below:
$2\text{NO(g)} \overset{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \text{N}_2\text{O}_2\text{(g)} \qquad \text{(fast equilibrium)}$
\( \text{N}_2\text{O}_2(\text{g}) + \text{H}_2(\text{g}) \xrightarrow{k_{2}} \text{N}_2\text{O}(\text{g}) + \text{H}_2\text{O}(\text{g}) \) (slow reaction)
\( \text{N}_2\text{O}(\text{g}) + \text{H}_2(\text{g}) \xrightarrow{k_{3}} \text{N}_2(\text{g}) + \text{H}_2\text{O}(\text{g}) \) (fast reaction)
The order of the reaction is ______.
