Write the equilibrium expression, and calculate Kp for the reaction under the conditions described:
2NaHCO3 (s) --> <--- Na2CO3 (s) + H2O (g) + CO2 (g)
100 g of solid NaHCO3 was placed in a previously evacuated rigid 5.00 L container and heated to 160 degrees C. Some of the original solid remained and the total pressure in the container was 7.76 atm when equilibrium was reached.
The answer is 15.1, I need to find how to get it, and how to write the expression.
Answer is posted below at an earlier post.
To write the equilibrium expression for the given reaction, you need to take into account the coefficients of the balanced equation. The expression is written as:
Kp = ([CO2] * [H2O]) / ([Na2CO3])
Now let's calculate Kp using the given information:
First, convert the mass of NaHCO3 to moles:
Molar mass of NaHCO3 = (23.0 * 2) + 12.0 + (16.0 * 3) = 84.0 g/mol
Moles of NaHCO3 = mass / molar mass = 100 g / 84.0 g/mol = 1.190 moles
Next, consider the stoichiometry of the reaction:
From the balanced equation, you can see that 2 moles of NaHCO3 react to produce 1 mole each of Na2CO3, H2O, and CO2.
At equilibrium, some of the original solid NaHCO3 remains. Let's say x moles remain. Therefore, the moles of Na2CO3, H2O, and CO2 formed are also equal to x.
The total pressure at equilibrium is given as 7.76 atm.
Since the reaction is occurring in a closed system (rigid container), the total pressure is equal to the pressure of CO2 and H2O.
Since x moles of CO2 and x moles of H2O are formed, their partial pressure can be calculated as follows:
Partial pressure of CO2 = x moles * (7.76 atm / Total moles)
Partial pressure of H2O = x moles * (7.76 atm / Total moles)
The partial pressure of CO2 is equal to its concentration in moles per liter (mol/L) since the volume is constant at 5.00 L.
So, we can write the expression for Kp as follows:
Kp = ([CO2] * [H2O]) / ([Na2CO3])
= (x/V) * (x/V) / (1.190 / 5.00)
Simplifying further,
Kp = (x^2 / V^2) / (1.190 / 5.00)
Now, plug in the given values: V = 5.00 L, x = remaining moles = 1.190 moles - x.
Substituting these values:
Kp = (1.190 - x)^2 / (5.00^2 * 1.190 / 5.00)
= (1.190 - x)^2 / (1.190 * 5.00)
Lastly, use the given total pressure of 7.76 atm to solve for x:
Total pressure = sum of partial pressures of CO2 and H2O at equilibrium.
7.76 atm = (x/V) * (7.76 atm / Total moles) + (x/V) * (7.76 atm / Total moles)
Now, solve this equation for x.
Once you find the value of x, substitute it back into the Kp expression and simplify to find the final value of Kp, which is 15.1, as given in the answer.