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The ideal gas law is a fundamental equation in chemistry that describes the relationship between pressure, volume, temperature, and the amount of gas in moles. This law is expressed as \( PV = nRT \), where:

• \( P \) stands for pressure
• \( V \) is the volume
• \( n \) represents the number of moles
• \( R \) is the ideal gas constant
• \( T \) is the temperature in Kelvin

To solve problems using the ideal gas law, you need to ensure all units are converted appropriately. For pressure, you usually convert to atmospheres, volume to liters, and temperature to Kelvin. This helps maintain consistency with the constant \( R \), which is typically 0.0821 L·atm/K·mol. By using the given conditions such as volume, pressure, and temperature, you can determine the number of moles of gas, which is crucial for understanding reactions involving gases.

A balanced chemical equation is essential for understanding the relationships between reactants and products in a reaction. It shows the molecules involved in a reaction with the correct stoichiometric coefficients. These coefficients ensure that the law of conservation of mass is upheld. This means the number of each type of atom is the same on both sides of the equation.
In the reaction \( \mathrm{NaNO}_{2}( ext{aq}) + \mathrm{HSO}_{3} \mathrm{NH}_{2}( ext{aq}) \rightarrow \mathrm{NaHSO}_{4}( ext{aq}) + \mathrm{H}_{2}\mathrm{O}( ext{l}) + \mathrm{N}_{2}( ext{g})\), the equation tells us:

• 1 mole of \( \mathrm{NaNO}_{2} \) reacts with 1 mole of \( \mathrm{HSO}_{3} \mathrm{NH}_{2} \)
• This produces 1 mole of \( \mathrm{N}_{2} \) gas

This balance is crucial for calculating how much product will form from a given amount of reactant. In this context, it helps determine the mass of \( \mathrm{NaNO}_{2} \) needed based on the moles of \( \mathrm{N}_{2} \) gas produced.

Chemical reactions involve the transformation of reactants into products. They can be complex, but they all follow the basic principle of rearranging atoms to form new substances. The specific reaction in this exercise involves sodium nitrite (\( \text{NaNO}_{2} \)) and sulfamic acid (\( \text{HSO}_{3} \text{NH}_{2} \)).

• This reaction produces nitrogen gas (\( \text{N}_2 \)), water (\( \text{H}_2\text{O} \)), and sodium bisulfate (\( \text{NaHSO}_{4} \))
• The generation of \( \text{N}_2 \) gas is significant because it allows the use of the ideal gas law to find the amount of \( \text{NaNO}_{2} \)

Understanding these transformations is fundamental. It allows chemists to predict the outcomes of a reaction and calculate how much of each substance is involved or produced. Reactions are often used in industry and laboratory settings to produce desired products efficiently.

Calculating moles is a central skill in chemistry. Moles allow chemists to quantify the amount of a substance, akin to counting atoms or molecules considering Avogadro's number (approximately \(6.022 \times 10^{23}\)). In the context of the given problem, we can determine the moles of \( \text{N}_2 \) gas produced by using the ideal gas law.
Once the moles of \( \text{N}_2 \) are known, you can infer the moles of \( \text{NaNO}_2 \) used. Given the balanced equation states a 1:1 ratio of \( \text{NaNO}_2 \) to \( \text{N}_2 \), the same number of moles applies to both compounds, facilitating further calculations.

• To convert moles to grams, simply multiply the moles by the molar mass of the compound (e.g., \( \text{NaNO}_2 = 69.00 \text{ g/mol} \))
• This conversion is vital for finding the mass composition of the mixture

These calculations help identify the mass percentage of substances in mixtures, providing crucial information for analyses and formulations.