K_w and auto-ionization of water

[STEMucator]

$K_w$ and auto-ionization of water

Homework Statement

The $K_w$ value decreases as the temperature decreases. Is the auto-ionization of water an exothermic or endothermic reaction in the forward direction?

Homework Equations

The Attempt at a Solution

Water is able to auto-ionize into $H_3O^{+1}$ and $OH^{-1}$ in an equilibrium reaction:

$H_2O_{(L)} + H_2O_{(L)} \leftrightharpoons H_3O^{+1}_{(aq)} + OH^{-1}_{(aq)}$

The equilibrium constant for this reaction is defined as $K_w = [H_3O^{+1}][OH^{-1}]$. It is known that the $K_w$ value increases as the temperature increases and decreases as the temperature decreases.

If $K_w$ is decreasing because temperature is decreasing, it means that the concentration of products is decreasing and so the reaction must move forward to produce more products and restore equilibrium. This means that heat must be a by-product of the reaction and therefore the overall reaction must be exothermic so that the equilibrium will shift right as the temperature decreases.

Is this reasonable?

 

[Keipi]

The autoionization of water is an endothermic reaction.

If we increases the temperature K_w increases and the equilibrium shifts towards the products. Because an increase in temperature favors the endothermic side (the products, in this case) we can conclude that the forward reaction is endothermic and not exothermic.

 

[Borek]

the overall reaction must be exothermic so that the equilibrium will shift right as the temperature decreases.

But it doesn't shift right.

Think in terms of LeChatelier's principle.

 

[STEMucator]

But it doesn't shift right.

Think in terms of LeChatelier's principle.

Ah so I should think of it the other way around.

If $K_w$ is decreasing because temperature is decreasing, it means that the concentration of products is decreasing BECAUSE the reaction is shifting to the left to compensate for the heat loss. While this shift occurs, it is clear that products become reactants.

Since we added heat and the equilibrium shifted left, we can conclude the overall reaction is endothermic.

Thanks guys :)

 

[DeeNos]

Yes, this is a reasonable explanation. As the temperature decreases, the equilibrium between water molecules and ions shifts towards the formation of more ions in order to maintain a constant $K_w$ value. This means that the forward reaction, which produces more ions, is favored and therefore must be exothermic in order to release heat and maintain equilibrium. This is consistent with Le Chatelier's principle, which states that a system will shift in the direction that relieves stress or disturbance. In this case, the decrease in temperature is the stress and the shift towards the forward reaction is the system's way of relieving it.