# Calculate the value of the equilibrium constant

• fk378
In summary, the conversation discusses finding the equilibrium constant for the reaction between solid sodium hydrogen carbonate and gaseous water and carbon dioxide at 110.0 degrees C. The equation is provided and it is mentioned that solids are usually treated as constants when calculating equilibrium constants.
fk378

## Homework Statement

The total pressure of gases in equilibrium with solid sodium hydrogen carbonate at 110.0 degrees C is 1.648 atm, corresponding to the reaction

2NaHCO3(s) <--> Na2CO3(s) + H2O(g) + CO2(g)

a) Calculate the value of the equilibrium constant at 110.0 degrees C.

## The Attempt at a Solution

I don't know how to begin this because I don't know how to find the initial partial pressure of sodium hydrogen carbonate. How am I supposed to use P total at equilibrium in this problem?

The solid sodium bicarbonate has negligible vapor pressure at 110 degrees C. We usually treat solids as constants, which we then divide out of the equilibrium constant; the only terms you should be left with in your expression for K are from gaseous water and gaseous carbon dioxide.

This approach for dealing with solids holds true in general, unless the equilibrium being studied occurs in a solid solution (e.g., molten rock.)

the first step in finding the value of the equilibrium constant is to understand the given reaction and its equilibrium conditions. In this case, we have a reaction involving solid sodium hydrogen carbonate, which means it is in its solid state at the given temperature of 110.0 degrees C. We also have gases, H2O and CO2, which are in their gaseous state at the given temperature. The total pressure of these gases at equilibrium is given as 1.648 atm.

The equilibrium constant, K, is defined as the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of their respective coefficients in the balanced chemical equation. In this case, the concentrations of the solids do not change and therefore do not affect the equilibrium constant.

To calculate the equilibrium constant, we need to find the partial pressure of each gas at equilibrium. We can use the ideal gas law, PV = nRT, to calculate the moles of each gas present at equilibrium. Since the volume and temperature are constant, we can simplify the equation to P = nRT/V. Since we know the total pressure (P total) and the temperature (T), we can calculate the number of moles of each gas (n) present at equilibrium.

For H2O, n = P total x V / RT = (1.648 atm) x (V) / (0.08206 L atm/mol K) x (383.15 K) = 0.0642 mol

For CO2, n = P total x V / RT = (1.648 atm) x (V) / (0.08206 L atm/mol K) x (383.15 K) = 0.0642 mol

Since both gases have the same number of moles, their partial pressures will be equal.

Now, we can use the equilibrium constant expression, K = [H2O] x [CO2] / [NaHCO3]^2, to calculate the value of K. We know that the concentration of a solid is constant and does not affect the equilibrium constant, so we can simplify the expression to K = [H2O] x [CO2]. Substituting the values we calculated above, we get K = (0.0642 mol) x (0.0642 mol) = 0.00412 mol^2.

Therefore,

## What is the equilibrium constant?

The equilibrium constant, denoted as K, is a value that represents the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium for a chemical reaction. It is a measure of the extent to which a reaction will proceed towards products or reactants at equilibrium.

## How is the equilibrium constant calculated?

The equilibrium constant is calculated by dividing the concentration of the products by the concentration of the reactants, with each concentration raised to the power of its coefficient in the balanced chemical equation. The resulting expression is known as the equilibrium constant expression and is represented as Kc.

## What factors affect the value of the equilibrium constant?

The value of the equilibrium constant is affected by changes in temperature, pressure, and concentration. For example, an increase in temperature will cause the equilibrium constant to shift in the direction of the endothermic reaction, while an increase in pressure will favor the reaction that produces fewer moles of gas.

## What does the value of the equilibrium constant indicate?

The value of the equilibrium constant indicates the relative concentrations of the products and reactants at equilibrium. A value of K greater than 1 indicates that the products are favored at equilibrium, while a value less than 1 indicates that the reactants are favored. A value close to 1 indicates that the reactants and products are present in similar concentrations at equilibrium.

## Can the value of the equilibrium constant be changed?

Yes, the value of the equilibrium constant can be changed by altering the conditions of the reaction. As mentioned before, changes in temperature, pressure, and concentration can impact the value of K. However, the equilibrium constant is a characteristic of a specific reaction at a given temperature, and it cannot be changed by adding a catalyst or changing the initial concentrations of the reactants.

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