Atmospheric stoichiochemistry: what mass of oxygen gas is produced?

[Fifty]

Homework Statement

Oxgyen gas generated in the thermal decomposition of potassium chlorate is collected over water. At 24 C and an atmospheric pressure of 762 mm Hg ((101.6 kPa), the volume of gas collected is 0.128 L. The vapor pressure of water is 22.4 torr (2.98 kPa). What mass of oxygen is created.

Homework Equations

2KClO₃ → 2KCl + 3O₂
P₁V₁ = P₂V₂

The Attempt at a Solution

I can't explain it mathematically, but I figured that if the water vapour accounted for 2.937 percent of the pressure, it must also account for 2.937 percent of the volume, which leaves 1.242 L of the oxygen gas.

Of course, that could be the problem right there (my assumption) but let's move on for the sake of this post.

The volume of just oxygen gas is 0.1242 L, pressure is 98.61 kPa (found by subtracting pressure of water vapor from total pressure), and the temperature is 298 K. I used those values to find the moles of oxygen produced (0.004963 mol) and mulitplied it by molar mass to get 0.1587 g.

I didn't have enough time to complete this question on my test, but I still want to answer it, particularly because I have an exam in three days (though I doubt there will be any calculation question this difficult --my teacher told me so).

Thanks in advance for all the help! :)

 

[mfb]

To account for water, you can reduce the volume ("separating" water and oxygen) or the pressure, but not both at the same time.

Apart from that, the approach looks good.

which leaves 1.242 L of the oxygen gas.

I guess that is a typo.

 

[Fifty]

To account for water, you can reduce the volume ("separating" water and oxygen) or the pressure, but not both at the same time.

Apart from that, the approach looks good.

I guess that is a typo.

Yeah, that was a typo. How do I correct this approach then?

 

[mfb]

How do I correct this approach then?

As I posted: reduce volume OR pressure for your calculation, but not both.

 

[Fifty]

As I posted: reduce volume OR pressure for your calculation, but not both.

Well, I suppose I couldn't reduce volume and I understand why we do this, mathematically, but isn't only a certain percentage of the mixture water vapour, and thus exerts the same amount of pressure.

 

[Borek]

Two ways of seeing that.

1. Starting with Avogadro's hypothesis - you have two gases, each occupies part of the volume.

2. Using Dalton's law - you have two gases, each has a partial pressure.

In the first case, it is partial volume, but same pressure in each time, in the second case, it is different pressure, but same volume in each case. In neither case it is partial volume AND partial pressure at the same time.