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In the context of chemical reactions, a balanced chemical equation is essential. It shows the relationship between the reactants and products in a chemical process. When balancing chemical equations, you ensure that the number of atoms of each element is the same on both sides of the equation. This is important because of the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a closed system.

For example, when hydrochloric acid (HCl) reacts with either magnesium carbonate (MgCO_3) or calcium carbonate (CaCO_3), it produces magnesium chloride (MgCl_2) or calcium chloride (CaCl_2), along with carbon dioxide (CO_2) and water (H_2O).

• For the reaction between HCl and MgCO_3: \[ MgCO_3(s) + 2HCl(aq) \rightarrow MgCl_2(aq) + CO_2(g) + H_2O(l) \]


• For the reaction between HCl and CaCO_3: \[ CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + CO_2(g) + H_2O(l) \]

Balancing these equations involves ensuring that there are equal numbers of each type of atom on both sides of the equation. This way, the calculated results reflect the true chemical behavior in the reaction.

The Ideal Gas Law is a crucial tool in chemistry for relating the physical properties of gases. It combines several gas laws into a single equation to describe the state of an ideal gas:

\[ PV = nRT \]

Where:

• P is the pressure of the gas (in atmospheres).
• V is the volume of the gas (in liters).
• n is the number of moles of gas.
• R is the ideal gas constant (0.0821 Lâ‹…atm/molâ‹…K).
• T is the temperature of the gas (in Kelvin).

To apply the Ideal Gas Law, one needs to ensure that all quantities are in the appropriate units. For instance, temperature must be converted to Kelvin by adding 273.15 to the Celsius measurement. Pressure must often be converted from units like Torr to atmospheres (using a conversion factor of 1 atm = 760 Torr).

By using the Ideal Gas Law, the number of moles of carbon dioxide produced can be calculated accurately from volume, temperature, and pressure data. In the given exercise, the calculation involves converting 1.72 L of CO_2 at 28°C and 743 torr into the number of moles of CO_2, providing vital information needed for further stoichiometric calculations.

Percentage composition by mass is a way of expressing the concentration of an element or compound in a mixture. It is calculated by taking the mass of the individual component, divided by the total mass of the mixture, and then multiplying by 100% to get the percentage.

In the context of the given problem, the percentage composition by mass of magnesium carbonate in the sample is determined after establishing the number of moles of CO_2 produced. For each component (MgCO_3 and CaCO_3), the number of moles of CO_2 they produce can be calculated using their respective balanced reactions and molar masses.

Once the moles are known, you can calculate the mass of each carbonate, and hence, use the formula:

\[ \text{Percentage by mass of component} = \left( \frac{\text{mass of component}}{\text{total mass of mixture}} \right) \times 100 \% \]

This calculation is crucial, as it gives insight into the composition of the sample, which is particularly useful in analytical chemistry for understanding the make-up of complex mixtures. In this case, solving the relevant equation for the mass of MgCO_3 provides its percentage in the original sample, resulting in a calculated percentage of 56.2%.