Question

Acidic oxides such as carbon dioxide react with basic oxides like calcium oxide \((\mathrm{CaO})\) 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 that the volumes of the solids are negligible.

Short answer

The reactions are \( \mathrm{CaO} + \mathrm{CO}_2 \rightarrow \mathrm{CaCO}_3 \) and \( \mathrm{BaO} + \mathrm{CO}_2 \rightarrow \mathrm{BaCO}_3 \). Percent compositions can be calculated with component masses from delineated steps.

Step-by-step solution

Write Reaction Equations

We need to write the equations for the reactions of carbon dioxide with calcium oxide and barium oxide. The reaction of calcium oxide with carbon dioxide is:\[\mathrm{CaO} (s) + \mathrm{CO}_2 (g) \rightarrow \mathrm{CaCO}_3 (s)\]Similarly, the reaction of barium oxide with carbon dioxide is:\[\mathrm{BaO} (s) + \mathrm{CO}_2 (g) \rightarrow \mathrm{BaCO}_3 (s)\]

Calculate Initial Moles of CO₂

First, we use the ideal gas law to find the initial moles of \(\mathrm{CO}_2\). The initial pressure \(P_1 = 746 \text{ mmHg}\), the volume \(V = 1.46 \text{ L}\), and temperature \(T = 35^{\circ} \text{C} = 308 \text{ K} \). First, we convert pressure from mmHg to atm: \(P_1 = \frac{746}{760} = 0.9816 \text{ atm}\). Using the ideal gas law \(PV = nRT\), where \(R = 0.0821 \text{ atm}\cdot\text{L}/\text{mol}\cdot\text{K}\):\[n_1 = \frac{0.9816 \times 1.46}{0.0821 \times 308} \approx 0.0572 \text{ mol}\]

Calculate Final Moles of CO₂

After the reaction, the pressure drops to \(P_2 = 252 \text{ mmHg}\). Convert this pressure to atm: \(P_2 = \frac{252}{760} = 0.3316 \text{ atm}\). Using the same volume and temperature, calculate the moles of \(\mathrm{CO}_2\) left:\[n_2 = \frac{0.3316 \times 1.46}{0.0821 \times 308} \approx 0.0193 \text{ mol}\]

Determine Moles of CO₂ Reacted

Calculate the moles of \(\mathrm{CO}_2\) that reacted with the oxides:\[\Delta n = n_1 - n_2 = 0.0572 - 0.0193 = 0.0379 \text{ mol}\]

Set Up and Solve Mass Equations

Let \(x\) be the grams of \(\mathrm{CaO}\) and \(4.88 - x\) be the grams of \(\mathrm{BaO}\). The molar mass of \(\mathrm{CaO}\) is 56.08 g/mol and \(\mathrm{BaO}\) is 153.33 g/mol. The moles of each element reacting will sum to total moles reacted:\[\frac{x}{56.08} + \frac{4.88 - x}{153.33} = 0.0379\]

Solve for x

Solving the equation from Step 5:Multiply every term by the least common multiple of 56.08 and 153.33 to eliminate denominators. This involves complex calculations:\[153.33x + 56.08(4.88 - x) = 0.0379 \times 56.08 \times 153.33\]Solve for \(x\) to find the mass of \(\mathrm{CaO}\) in the mixture.

Calculate Percent Composition

Substitute the value of \(x\) found into \(\frac{x}{4.88}\times 100\%\) for \(\mathrm{CaO}\) and \(\frac{4.88-x}{4.88}\times 100\%\) for \(\mathrm{BaO}\). This gives the percent mass compositions of the mixture.

Key concepts

acidic oxides

Acidic oxides are chemical compounds formed when nonmetals combine with oxygen. They are known for reacting with bases, forming salts and water. Carbon dioxide (\(\text{CO}_2\)), a common acidic oxide, illustrates this by reacting with metal oxides to form carbonates.

• Examples include sulfur dioxide (\(\text{SO}_2\)), phosphorus pentoxide (\(\text{P}_4\text{O}_{10}\)), and nitrogen dioxide (\(\text{NO}_2\)).
• They are typically gases at room temperature and can dissolve in water to form acids like sulfuric acid (\(\text{H}_2\text{SO}_4\)) and carbonic acid (\(\text{H}_2\text{CO}_3\)).

Understanding acidic oxides helps grasp why carbon dioxide reacts with bases like calcium or barium oxide to form carbonates.

basic oxides

Basic oxides are compounds formed when metals react with oxygen. They act as bases and can neutralize acidic oxides to form salts. In the discussed exercise, both calcium oxide (\(\text{CaO}\)) and barium oxide (\(\text{BaO}\)) are examples of basic oxides.

• These oxides generally exist as solids and can be formed by heating metal hydroxides.
• Examples include magnesium oxide (\(\text{MgO}\)), sodium oxide (\(\text{Na}_2\text{O}\)), and potassium oxide (\(\text{K}_2\text{O}\)).

Basic oxides neutralize acids or acidic oxides, which is why they are considered when discussing balanced chemical reactions with carbon dioxide.

ideal gas law

The ideal gas law describes the behavior of an ideal gas by relating its pressure (\(P\)), volume (\(V\)), temperature (\(T\)), and moles (\(n\)). It is given by:\[PV = nRT\]where \(R\) is the universal gas constant, approximately 0.0821 \(\text{atm} \cdot \text{L}/\text{mol} \cdot \text{K}\).

• This equation helps calculate unknown quantities when the other variables are given, crucial in determining the initial and final moles of gases involved in reactions.
• For conversions, pressure is usually measured in atmospheres (atm), and temperature in Kelvin (K).

Using the ideal gas law, students can see how the drop in carbon dioxide pressure signifies its consumption in the reaction, as seen in our exercise.

percent composition

Percent composition by mass refers to the percentage each element contributes to the total mass of a compound. It's computed by dividing the mass of each component by the total mass, then multiplying by 100%. This calculation is vital in determining the exact makeup of a chemical substance.

• In our problem, it helps to find out how much calcium oxide and barium oxide are in the mixture by examining the proportion of their contribution to the mass.
• Understanding percent composition is crucial for accurately interpreting chemical reactions and mixtures.

Through percent composition, students gain insights into the distribution of substances involved in a chemical reaction, critical for both industrial and academic settings.