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Gas laws are essential in understanding how gases behave under various conditions. Three key gas laws are Boyle's Law, Charles's Law, and Avogadro's Law, which describe relationships between volume, pressure, and temperature of gases.
Boyle's Law explains that the pressure of a gas is inversely proportional to its volume, provided the temperature and number of moles remain constant.

• This means as the volume increases, the pressure decreases and vice versa.
• The equation used is: \(P_1V_1 = P_2V_2\).

Charles's Law states that the volume of a gas is directly proportional to its Kelvin temperature when the pressure is constant.

• This implies as the temperature increases, so does the volume.
• The formula is: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\).

Finally, Avogadro's Law shows that the volume of a gas is directly proportional to the number of moles, given constant pressure and temperature.

• This can be represented as \(V_1/n_1 = V_2/n_2\).

Together, these laws can be combined in the ideal gas law: \(PV = nRT\), where \(R\) is the gas constant. Understanding these relationships helps in predicting the behavior of gases during chemical reactions under different conditions.

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows us to predict how much of a substance is needed or produced in a reaction. One fundamental aspect of stoichiometry is understanding and using the balanced chemical equation. This indicates the mole ratio of reactants and products.
In the given reaction, \(2 \ ext{NO}(g) + \text{O}_2(g) \rightarrow 2 \ ext{NO}_2(g)\), stoichiometry tells us:

• 2 moles of \(NO\) react with 1 mole of \(O_2\).
• If 1 mole of \(O_2\) is used, it will completely react with 2 moles of \(NO\) to produce 2 moles of \(NO_2\).

This process can also be used to calculate the necessary amounts of reactants needed for a reaction to proceed. For example, if we start with a certain pressure of \(NO\), we can use stoichiometry to find the required pressure of \(O_2\). This ensures the reactants are in the correct proportions, leading to a complete reaction and accurate product amounts. Understanding stoichiometry is crucial for efficiency and cost-effectiveness in chemical reactions.

Root Mean Square (RMS) speed is the measure of the speed of particles in a gas. It is related to the average kinetic energy of gas particles. RMS speed can be calculated using the formula: \[ \text{RMS speed} = \sqrt{\frac{3RT}{M}} \]where:

• \(R\) is the universal gas constant, \(8.314 \ J/(mol\cdot K)\).
• \(T\) is the absolute temperature in Kelvin.
• \(M\) is the molar mass of the gas in kilograms per mole.

This equation shows that the speed of gas molecules increases with temperature and decreases with increased molar mass.
For instance, in the given exercise:

• \(NO\) has the lowest molar mass (30 g/mol) and hence the highest RMS speed.
• \(O_2\) follows with a slighter greater molar mass.
• \(NO_2\) has the highest molar mass (46 g/mol) and thus the lowest RMS speed.

Understanding RMS speed is crucial in calculating and predicting the behavior of gases in reactions by analyzing their molecular speeds at different temperatures.

Partial pressure is a concept that helps us understand the contribution of each gas in a mixture to the total pressure. According to Dalton's Law, in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of individual gases.

• This can be mathematically represented as \(P_{total} = P_1 + P_2 + \ldots + P_n\).

To find the partial pressure of a gas, you need its mole fraction and the total pressure. The formula is: \[ P_i = \chi_i \times P_{total} \]where \(P_i\) is the partial pressure, \(\chi_i\) is the mole fraction, and \(P_{total}\) is the total pressure.
In the exercise, stoichiometry helps determine that since 2 moles of \(NO\) react with 1 mole of \(O_2\), if \(NO\) has a partial pressure of 150 mm Hg, \(O_2\)'s partial pressure must be half, 75 mm Hg. Understanding partial pressures is significant in predicting how gases will behave when mixed, ensuring proper conditions for reactions.