When baking soda is heated it decomposes

[kuahji]

When baking soda is heated it decomposes according to the following reaction:
2 NaHCO3 (s) -> Na2CO3 (s) + H2) (g) + CO2 (g)

If sufficient baking soda is placed in a container and heated to 90 degrees Celsius, the total pressure of the gases is .5451 atm. What is the value of Kp at that temperature.

So the professor shows the work Kp=[P H2O][P CO2]
this much I agree with.

But then the next step he shows
PH2O=PCO2= .5451/2=.2726
Kp=(.2728)^2=.07428

Is this actually correct. I don't see how you can "assume" the partial pressures are equal to one another. Or can you? I mean why can't the partial pressure of water at that temperature be something like say .3 & CO2 be .2451?

 

[Mapes]

Your professor is assuming that H2O and CO2 are behaving as ideal gases. The pressure of an ideal gas for a given temperature and pressure depends only on the amount of the gas (the number of moles). Since an equal number of moles of H2O and CO2 are produced when NaHCO3 decomposes, their partial pressures are the same. Does this make sense?

 

[Blueshift5]

Your question raises a valid concern about the assumptions made in this calculation. While it is true that the partial pressures of water and CO2 will be equal at equilibrium, it is not necessarily true that they will be equal during the reaction. This is because the reaction is not at equilibrium yet when the total pressure is measured at 90 degrees Celsius. Therefore, assuming equal partial pressures may not be accurate.

In order to accurately calculate the value of Kp at 90 degrees Celsius, we would need to know the equilibrium constant (Kp) at that temperature. This can be determined experimentally or by using thermodynamic data. Once we have the correct value for Kp, we can use the ideal gas law to calculate the partial pressures of water and CO2 at equilibrium.

In summary, while the initial calculation done by the professor may provide an estimate for the value of Kp, it may not be entirely accurate due to the assumptions made about the partial pressures of water and CO2. Further experimentation or use of thermodynamic data would be necessary for a more precise calculation.