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  • <img alt="\mathrm{2 \mathrm{SbH}_3 \stackrel{\Delta}{\longrightarrow} \mathrm{Sb}+3 \mathrm{H}_2(\mathrm{~g})}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B2%20%5Cmathrm%7BSbH%

\mathrm{2 \mathrm{SbH}_3 \stackrel{\Delta}{\longrightarrow} \mathrm{Sb}+3 \mathrm{H}_2(\mathrm{~g})}  is a first order reaction. \mathrm{\mathrm{SbH}_3} is allowed to decompose in the presence of inert atmosphere. The change in pressure in the reaction chamber given below. If  \mathrm{x=8 y}, then what is the value of y.

\begin{array}{lllll}\text { Time (min) } & 0 & 10 & x & \infty \\ \text { Total presure(torr) } & 800 & 900 & 950 & 1000\end{array}

 

Option: 1

2.5


Option: 2

5


Option: 3

7.5


Option: 4

4


Answers (1)

best_answer

2 \mathrm{SbH}_3 \stackrel{\Delta}{\longrightarrow} 2 \mathrm{Sb}+3 \mathrm{H}_2(\mathrm{~g})

\begin{array}{cccc} \text { Initial } &\mathrm{ p^0 }& - &\mathrm{ \overline{3 x}} \\ \mathrm{t} & \mathrm{p^0-x} & - & \frac{3}{2} \\ \text { opressure } & - & - & \mathrm{\frac{3 p_0}{2}} \end{array}
\begin{aligned} \text{ Initial }& \mathrm{P^0+P_1=800-10~ \&~ \infty~ time, \frac{3 P^{\circ}}{2}+P_1=1000 }\\ &\mathrm{So, P^{\circ}=400 \& P_1=400 }\end{aligned}\begin{aligned} \text{After 10 min, }&\mathrm{P^0-x+\frac{3 x}{2}+P_1=900 \Rightarrow x=200=\frac{p^0}{2}}\\ &\text{so half life =10 }\mathrm{~min} \end{aligned}\begin{aligned} \text{After x min, }&\mathrm{p^0-a+\frac{3 a}{2}+p_1=950 \Rightarrow a=300}\\ & \mathrm{Thus x=2 t_{1 / 2}=20 \mathrm{~min}}\\ &\mathrm{20=8 y}\\&\mathrm{y=2.5}\end{aligned}

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