How would decreasing the volume of the reaction vessel affect each of the following equilibria?

$2 N O B r \left(g\right) r i g h t \le f t h a r p \infty n s 2 N O \left(g\right) + B {r}_{2} \left(g\right)$

Jul 19, 2016

It will cause the equilibrium to shift to the left.

Explanation:

Start by taking a look at the equilibrium given to you

$\textcolor{red}{2} {\text{NOBr"_ ((g)) " "rightleftharpoons" " 2"NO"_ ((g)) + "Br}}_{2 \left(g\right)}$

Notice that you have $\textcolor{red}{2}$ moles of nytrosyl bromide on the reactants' side and a total of

$\text{2 moles NO " + " 1 mole Br"_2 = "3 moles gas}$

on the products' side. Keep this in mind.

Now, decreasing the volume of the reaction vessel, provided that the temperature of the reaction is kept constant, will affect the pressure inside the reaction vessel.

As you know, volume and pressure have an inverse relationship when temperature is kept constant $\to$ this is known as Boyle's Law.

Simply put, when you decrease the volume of the reaction vessel, you proceed to increase the pressure inside the vessel.

As you know, equilibrium reactions are governed by Le Chatelier's Principle, which states that a system at equilibrium will react in such a way as to counteract any stress placed on the position of the equilibrium.

Increasing the pressure inside the reaction vessel will cause the equilibrium to shift in such a way as to reduce this increase in pressure.

Since gas pressure is caused by the collisions that take place between the molecules of gas and the walls of the container, you can decrease pressure when temperature is kept constant by decreasing the number of moles of gas.

As a result, the equilibrium will shift to the left, i.e. it will favor the reverse reaction, since that's the side that contains the fewer moles of gas.

overbrace(color(red)(2)"NOBr"_ ((g)))^(color(blue)("2 moles gas")) " "rightleftharpoons" " overbrace(2"NO"_ ((g)) + "Br"_ (2(g)))^(color(purple)("3 moles gas"))

color(white)(aaaaa)stackrel(larr)(color(white)(aaacolor(darkgreen)("shift to the left")aaaaa)

Therefore, decreasing the volume of the reaction vessel would cause the equilibrium to shift to the left, meaning that more nitrosyl bromide will be produced and nitric oxide and bromine gas will be consumed.