A mixture of gases $X_{2}, Y_{2}$, and $X_{2} Y$ are confined in a cylinder under a piston. A chemical reaction $2 X_{2}+Y_{2} \leftrightarrow 2 X_{2} Y$ proceeds in the cylinder. In equilibrium (when the reaction proceeds at the same rate in both directions) the system occupied a volume $V$ under a pressure $p$ while the amount of substances $X_{2}, Y_{2}$, and $X_{2} Y$, was $\nu_{1}, \nu_{2}$, and $\nu_{3}$, respectively. Then the pressure was changed by, a small amount $\Delta p$.

Determine the volume increment $\Delta V$ and the increments $\Delta \nu_{1}, \Delta \nu_{2}$, and $\Delta \nu_{3}$ when new equilibrium had been reached.

S

The temperature was maintained constant during the process.

Note. It is known that a chemical reaction rate is proportional to the product of concentrations $\nu_{i} / V$ of participating substances. Therefore, the rates of the forward and reverse reactions are proportional to

$$\left(\frac{\nu_{1}}{V}\right)^{2}\left(\frac{\nu_{2}}{V}\right) \quad \text { and } \quad\left(\frac{\nu_{3}}{V}\right)^{2}$$ The proportionality factors can be different but depend on temperature only. A gas is considered to be ideal.