91Ó°ÊÓ

The Ideal Gas Law is a critical formula in the study of gases. It allows us to relate the properties of gas, such as pressure, volume, temperature, and the number of moles. It is mathematically expressed as:\[ PV = nRT \]where:

• \( P \) represents the pressure of the gas in atm (atmospheres).
• \( V \) is the volume of the gas in liters.
• \( n \) is the number of moles of gas.
• \( R \) is the universal gas constant, which is \(0.0821 \, \text{L atm/mol K}\).
• \( T \) is the temperature in Kelvin.

In this exercise, you're required to determine the moles of \(\text{CO}_2\) gas produced during a reaction. To do this, you rearrange the formula to solve for \(n\):\[ n = \frac{PV}{RT} \]The pressure, originally given in \(\text{mmHg}\), must be converted to \(\text{atm}\) using the conversion factor \(1 \, \text{atm} = 760 \, \text{mmHg}\). Similarly, convert temperature from Celsius to Kelvin by adding 273.15. These conversions are crucial for any calculations involving the Ideal Gas Law.

Stoichiometry is a branch of chemistry that involves the calculation of reactants and products in chemical reactions. It's a crucial concept when determining the proportions of elements and compounds involved in chemical reactions.In the given problem, stoichiometry helps determine which acid is present through the examination of balanced chemical equations. There are two possibilities:- **Hydrochloric Acid Reaction:** The reaction of \(\text{HCl}\) with \(\text{Na}_2\text{CO}_3\) is: \[ 2\text{HCl} + \text{Na}_2\text{CO}_3 \rightarrow 2\text{NaCl} + \text{H}_2\text{O} + \text{CO}_2 \] This equation indicates that two moles of \(\text{HCl}\) are needed to produce one mole of \(\text{CO}_2\).- **Sulfuric Acid Reaction:** The reaction of \(\text{H}_2\text{SO}_4\) with \(\text{Na}_2\text{CO}_3\) is: \[ \text{H}_2\text{SO}_4 + \text{Na}_2\text{CO}_3 \rightarrow \text{Na}_2\text{SO}_4 + \text{H}_2\text{O} + \text{CO}_2 \] Here, one mole of \(\text{H}_2\text{SO}_4\) produces one mole of \(\text{CO}_2\).By comparing the moles of acid to the moles of \(\text{CO}_2\) produced in the reaction, you can identify the acid. If the ratio is 2:1, it's \(\text{HCl}\), while a 1:1 ratio indicates \(\text{H}_2\text{SO}_4\).

Molarity is a concentration measure indicating the number of moles of solute per liter of solution. It is often used in chemical calculations to find out how much of a substance you have.The formula for molarity \(M\) is:\[ M = \frac{moles \, of \, solute}{volume \, of \, solution \, in \, liters} \]In the problem, you're given the molarity of the acid solution as 0.2040 M and a volume of 48.90 mL. To find the moles of acid, use:1. **Convert the Volume:** Convert mL to L since molarity is moles per liter. \( V = 48.90 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 0.04890 \, \text{L} \)2. **Calculate Moles of Acid:** Multiply molarity by volume in liters: \[ n = 0.2040 \, \text{mol/L} \times 0.04890 \text{L} = 0.0099676 \text{ mol} \]Understanding molarity allows you to calculate how much of the acid is present and helps you evaluate its reaction with other substances in a chemical context.