Question
In a reaction, $$2X \to Y,$$ the concentration of $$X$$ decreases from $$3.0\,moles{\text{/litre}}$$ to $${\text{2}}{\text{.0}}\,moles{\text{/litre}}$$ in 5 minutes. The rate of reaction is
A.
\[0.1\,mol\,{{L}^{-1}}\,{{\min }^{-1}}\]
B.
\[5\,mol\,{{L}^{-1}}\,{{\min }^{-1}}\]
C.
\[1\,mol\,{{L}^{-1}}\,{{\min }^{-1}}\]
D.
\[0.5\,mol\,{{L}^{-1}}\,{{\min }^{-1}}\]
Answer :
\[0.1\,mol\,{{L}^{-1}}\,{{\min }^{-1}}\]
Solution :
\[\begin{align}
& \text{Rate}=-\frac{1}{2}\frac{\Delta \left[ X \right]}{\Delta t} \\
& \,\,\,\,\,\,\,\,\,\,\,=-\frac{1}{2}\frac{\left( 2-3 \right)}{5} \\
& \,\,\,\,\,\,\,\,\,\,\,=0.1\,mol\,{{L}^{-1}}\,{{\min }^{-1}} \\
\end{align}\]