Partial Pressure - Which solution is right?

Question: Carbon dioxide (1.100 g) was introduced into a 1.00 L flask which contained some pure oxygen gas. The flask was warmed to 373 K and the pressure was then found to be 608 mmHg. If CO2 and O2 were the only gases present, what was the mass of oxygen in the flask?

Solution: Moles of CO2 = mass/molar mass $= 1.100/44.01 = 0.02499$ mol.

The partial pressure of carbon dioxide can then be calculated from the Ideal Gas Equation. $$V = 1.00\,\text{L}$$ $$T = 373\,\mathrm K$$

Pcarbon dioxide $$\frac{nRT}{V}= 0.02499 \cdot 8.314 \cdot 373/1.00= 77.5\,\mathrm{kPa}$$

The total pressure Ptotal = Poxygen + Pcarbon dioxide

$$P_{\text{total}} = 608\cdot \text{mmHg} = (608/760) \cdot 101.3\,\mathrm{kPa} = 81.0\,\mathrm{kPa}$$

Therefore 81.0 = Poxygen $+ 77.5$ Poxygen $= 3.5\,\mathrm{kPa}$

From the ideal gas equation, the moles of O2 can be deduced.

$$n=\frac{PV}{RT} = 3.5 \cdot \frac{1.00}{8.314 \cdot 373} = 1.13 \cdot 10^{-3}\,\text{mol}$$

Mass of oxygen = moles x molar mass $$= 1.13 \cdot 10^{-3} \cdot 32.00\,\text{g} = 0.0361\,\text{g}$$

Ambiguity: While calculating Pcarbon dioxide via $\frac{nRT}{V}$ why don't the author utilised dalton's law of partial pressures & multiplied?

(moles of CO2[0.02499] x Total pressure[81kPa]) to get the Pcarbon dioxide. Of coarse this is applicable while system is heated or cooled

• Welcome to Physics SE! I edited your post to add the nice layout of the equations. MathJax on this website makes math more readable. Check it out! To learn it, just hit the edit button on your post and see, that the math simply is marked up using a dollar. SI units are separated by a small blank with "\,". – Stefan Bischof Aug 24 '14 at 7:21

Ahh, I spent quite some time reading this problem, the problem with applying Dalton's Law of Partial Pressures is that we shouldn't be multiplying moles of $CO2$ with the total Pressure, rather we should multiply the mole fraction of $CO2$ with the total Pressure, in this case however, since the initial quantity/moles of oxygen is not known, it is not possible to find the mole fraction of $CO2$ directly and thus simplify the problem. Thus the solution you provided first is the correct way to go about the problem.