Acidic oxides such as carbon dioxide react with basic oxides like calcium oxide (CaO) and barium oxide \((\mathrm{BaO})\) to form salts (metal carbonates). (a) Write equations representing these two reactions. (b) A student placed a mixture of \(\mathrm{BaO}\) and \(\mathrm{CaO}\) of combined mass \(4.88 \mathrm{~g}\) in a 1.46 - \(\mathrm{L}\) flask containing carbon dioxide gas at \(35^{\circ} \mathrm{C}\) and \(746 \mathrm{mmHg}\). After the reactions were complete, she found that the \(\mathrm{CO}_{2}\) pressure had dropped to \(252 \mathrm{mmHg}\). Calculate the percent composition by mass of the mixture. Assume volumes of the solids are negligible.

The reactions of carbon dioxide with calcium oxide and barium oxide can be represented as follows: \n1. \(\mathrm{CaO} + \mathrm{CO}_{2} \rightarrow \mathrm{CaCO}_{3}\) \n2. \(\mathrm{BaO} + \mathrm{CO}_{2} \rightarrow \mathrm{BaCO}_{3}\)

First, it has to be acknowledged that the Pressure in the flask is not totally due to CO2 but also air. The pressure of air at sea level and at room temperature is 760mmHg. So, to find the actual pressure exerted by the CO2, subtract the reported pressure from the standard atmospheric pressure: \[\mathrm{Initial \, CO2 \, pressure}= \mathrm{Atmospheric \, pressure} - \mathrm{Given \, pressure} = 760 \, mmHg - 746 \, mmHg = 14mmHg.\]

To find the final pressure of CO2, we subtract the final pressure value from standard atmospheric pressure thus : \[\mathrm{Final \, CO2 \, pressure}= \mathrm{Atmospheric \, pressure} - \mathrm{Final \, pressure} = 760 \, mmHg - 252 \, mmHg = 508mmHg.\]

To find out how much CO2 reacted, subtract the final pressure from the initial pressure of CO2. \[\mathrm{Pressure \, of \, CO2 \, consumed} = \mathrm{Initial \, CO2 \, pressure} - \mathrm{Final \, CO2 \, pressure} = 14 \, mmHg - 508 \, mmHg = -494 \, mmHg = 494 \, mmHg. \] Note that , we usually don't have negative pressures but the data suggests that some pressure was consumed hence indicating a negative pressure. This value is absolute.

We can use the Ideal Gas Law to convert this pressure to moles of CO2. The Ideal Gas Law is PV = nRT, where P is pressure, V is volume, n is number of moles, R is the Ideal Gas constant, and T is temperature. Solving for n (the number of moles) gives: \[\mathrm{n} = \frac{PV}{RT}.\] Plugging in the values (and converting to the appropriate units), we get \[\mathrm{n} = \frac{494 \, mmHg × 1.46 \, L}{62.4 \, L \, mmHg/mol \, K × (35 °C + 273)} = 0.0315 \, mol.\] Note that we used the value 62.4 L mmHg/mol K for R and added 273 to the temperature in Celsius to convert it to Kelvin.

From the equations, both BaO and CaO react with CO2 in a 1:1 ratio. Therefore, the total moles of BaO and CaO that reacted is the same as the moles of CO2 that reacted. The molar mass of BaO is 153.3 g/mol, and the molar mass of CaO is 56.08 g/mol. Using the formula, Mass = moles × molar mass, we find that \[\mathrm{Mass \, of \, BaO} = 0.0315 \, mol × 153.3 \, g/mol = 4.83 \, g \] and \[\mathrm{Mass \, of \, CaO} = 0.0315 \, mol × 56.08 \, g/mol = 1.77 \, g.\] Note that the combined mass of BaO and CaO is more than 4.88 g. Therefore, all of the BaO and CaO could not have reacted. Since BaO is heavier than CaO, we can assume that less of it will be present in the mixture. Assuming the entire 4.88 g is BaO gives a percentage by mass of 100%. A value of less than 100% will be obtained only if we assume the entire 4.88 g to be CaO. Therefore, this assumption gives a minimum percentage.

The percent composition by mass of an element in a compound is given by (mass of element/total mass) × 100. Using the maximum possible mass of BaO (4.88 g) and the total mass of BaO and CaO (4.88 g), the percent composition by mass of BaO in the mixture is (4.88 g / 4.88 g) × 100 = 100%. Similarly, using the minimum possible mass of CaO (0 g) and the total mass of BaO and CaO (4.88 g), the percent composition by mass of CaO in the mixture is (0 g / 4.88 g) × 100 = 0%. Therefore, the mixture is composed of 100% BaO and 0% CaO.