Calculate the value of the equilibrium constant

[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?

 

[Kalirren]

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.)

 

[Blueshift5]

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,