I am to do an equilibrium constant lab and I am supposed to only find the Kc value. i have to find the equilibrium constant for NaHCO3 (s) <--> NaOH (s) + CO2 (g) at 800K. The partial pressure in the bulb reads 420 kPa on the manometer, 1 gram of NaHCO3 was added to the bulb and the bulb's volume is 500 mL.
I'm not sure if I did this correct but I used the PV=nRT formula and solved for n and I got 0.00316 mols. Then I used the c=n/v formula to find the concentration, and i got 6.3x10^-6. I don't know where to go from here to find the Kc value.
I think you've made two errors in calculation. If I use 420 kPa and 0.5 L volume with T 800K I solve for n = PV/RT and I obtained your value x 10. Then if I use c = n/v that's n/0.5L = Your value divided by 1000. I think your data are good; I think your calculations need work. If I didn't goof I found n = 0.03157; then
c = n/0.5 = 0.063148 which I would round to 0.0632.
Kc = (CO2)
Then for the fun of it convert Kc = 0.0632 to Kp and see if you get 420 kPa.
To find the equilibrium constant (Kc) for the given reaction, NaHCO3 (s) <--> NaOH (s) + CO2 (g), you need to determine the concentrations of each species at equilibrium and then plug these values into the equation for Kc. Here's how you can proceed:
Step 1: Convert the mass of NaHCO3 to moles
Given that you added 1 gram of NaHCO3, you can determine the number of moles using its molar mass. The molar mass of NaHCO3 is approximately 84 g/mol. Therefore:
moles of NaHCO3 = mass of NaHCO3 / molar mass of NaHCO3
moles of NaHCO3 = 1 g / 84 g/mol ≈ 0.0119 mol (rounded to four decimal places)
Step 2: Calculate the volume of the bulb in liters
Given that the volume of the bulb is 500 mL, you need to convert it to liters to be consistent with the units in the ideal gas law equation. Since 1 L = 1000 mL:
volume of the bulb = 500 mL / 1000 mL/L = 0.5 L
Step 3: Calculate the concentration of NaHCO3
The concentration can be calculated using the formula c = n / V, where c is the concentration, n is the number of moles, and V is the volume. Therefore:
concentration of NaHCO3 = moles of NaHCO3 / volume of the bulb
concentration of NaHCO3 = 0.0119 mol / 0.5 L = 0.0238 M (rounded to four decimal places)
Step 4: Determine the concentration of NaOH and CO2 at equilibrium
Since the reaction has a 1:1 stoichiometric ratio between NaHCO3 and NaOH, the concentration of NaOH would be the same as NaHCO3 at equilibrium, which is 0.0238 M.
Step 5: Obtain the partial pressure of CO2
Given that the partial pressure in the bulb reads 420 kPa, you can directly use this value for the partial pressure of CO2 at equilibrium.
Step 6: Calculate the equilibrium constant (Kc)
The equilibrium constant (Kc) can be expressed as the ratio of the product concentrations to the reactant concentrations, each raised to their respective stoichiometric coefficients. In this case:
Kc = ([NaOH] * [CO2]) / [NaHCO3]
Kc = (0.0238 M * 420 kPa) / 0.0238 M
Note: The units of concentration and partial pressure must match. Therefore, either convert the partial pressure to concentration or the concentration to partial pressure. For this example, we'll keep the concentration units. If you choose to convert partial pressure to concentration, you will need the ideal gas law equation.
Finally, simplify and evaluate the expression above using the values obtained:
Kc ≈ (0.0238 M * 420) / 0.0238 M
Kc ≈ 420
Therefore, the equilibrium constant (Kc) for the given reaction at 800K is approximately 420.