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------------------------------------------------ At some temperature, a 100 L reaction vessel contains a mixture that is initially 4.00 mol CO and 8.00 mol H₂. The vessel also contains a catalyst so that the following equilibrium is attained:

\[ \text{CO} + 2\text{H}_2 \rightleftharpoons \text{CH}_3\text{OH} \]

At equilibrium, the mixture contains 0.400 mol of CH₃OH (methanol).

In a later experiment in the same vessel, you start with 4.00 mol of CH₃OH. How much methanol is there at equilibrium?

Give your answer in moles.

When a chemical reaction involving substances in a gaseous state reaches equilibrium, the quantity of product present at the beginning of the reaction corresponds to the quantity of product at equilibrium, provided that the product is not consumed in the reaction and there are no other reactants available

Explanation:

The subject of this question revolves around chemical equilibrium and stoichiometry, particularly involving gaseous substances. The initial experiment in the problem presents the reaction of CO (carbon monoxide) and Hg (mercury) producing CH3OH (methanol) and reaching equilibrium. In this state, 0.400 mol of methanol was formed.

According to the initial conditions of the reaction and considering the stoichiometry of the reaction, if initially there were 4.00 mol of methanol, then in equilibrium there would be 4.00 mol of methanol. This is because methanol can only come from the equilibrium reaction and is not consumed in it, therefore only changes if CO and Hg are still available to react and to produce more methanol. This is in accordance with the principles of Le Chatelier's Law.

Le Chatelier's Law states that if a system at equilibrium is subjected to a change in concentration, temperature, volume, or pressure, then the system readjusts itself to counteract the effect of the change and a new equilibrium is established. In this case, the quantity of methanol at the start of the reaction is equal to the amount at equilibrium because there is no further production or consumption of methanol after the reaction has reached equilibrium.

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