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?