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The equilibrium constant, denoted as \(K\), provides a snapshot of a chemical reaction at equilibrium. It is a numerical value that connects the concentrations of products and reactants in a balanced reaction. For the reaction in question, the equilibrium constant is expressed as:

• \[K = \frac{[\mathrm{H}_2]^2[\mathrm{O}_2]}{[\mathrm{H}_2\mathrm{O}]^2}\]

The values in the numerator and denominator represent the concentrations of products and reactants raised to the power corresponding to their coefficients in the balanced equation. Here, we see the equilibrium constant incorporates the concentrations of hydrogen and oxygen gas over the concentration of water vapor squared.
This ratio remains constant at equilibrium at a given temperature, encapsulating the idea that reactions move toward equilibrium regardless of starting conditions.

Stoichiometry is the calculation method in chemistry adjusting amounts based on balanced equations. For our reaction:

• \(2\, \mathrm{H}_2\mathrm{O}(g) \rightleftharpoons 2\, \mathrm{H}_2(g) + \mathrm{O}_2(g)\)

The stoichiometry tells us the relative amounts of reactants and products. Given that two moles of water decompose to form two moles of hydrogen and one mole of oxygen, the stoichiometric coefficients (2, 2, 1) are essential in forming the equilibrium expression for \(K\) and understanding the transformation of matter.
Through stoichiometry, we can predict the relationship among amounts of different substances and use this relationship to calculate various properties, such as how changes in one substance might affect another.

Concentration is a measure of how much of a substance is present in a given volume of solution or gas. For gases, concentrations are typically expressed in molarity (M), defined as moles of gas per liter of volume (mol/L). In chemical equilibrium, it is crucial to calculate the concentration of reactants and products accurately:

• For water vapour, \([\mathrm{H}_2\mathrm{O}] = 1.1 \times 10^{-1} \: \mathrm{M}\)
• For hydrogen gas, \([\mathrm{H}_2] = 1.9 \times 10^{-2} \: \mathrm{M}\)

These concentrations are used to plug into the equilibrium expression to help us find unknown concentrations, like that of oxygen. Understanding gas concentrations is critical in predicting how the reaction components interact and establish equilibrium state.

To find how many moles of a gas are present in a container at equilibrium, we use the concentration (in M) and the volume (in L) of the container. The formula is straightforward:

• Moles = Concentration \( \times \) Volume

For example, after finding the concentration of \(\mathrm{O}_2\) to be approximately \(7.8 \times 10^{-3} \: \mathrm{M}\), we multiply by the container volume, 2 L, to calculate moles:

• \(1.6 \times 10^{-2}\) moles of \(\mathrm{O}_2\)

This simple multiplication shows the power of stoichiometry and equilibrium calculations to inform us about not just ratios, but actual physical entities in a closed system. Performing mole calculations is foundational in understanding material balances in chemical reactions.