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The ideal gas law is a fundamental equation in chemistry. It assists us in understanding the relationship between the pressure, volume, temperature, and number of moles of a gas. The equation is expressed as:
\[ PV = nRT \]
Here's what each term means:

• P stands for pressure in atm (atmospheres).
• V stands for volume in liters (L).
• n stands for the number of moles of the gas.
• R is the ideal gas constant, which is 0.0821 L·atm/K·mol.
• T stands for the temperature in Kelvin (K).

To use this equation, we must ensure all units match up. For instance, temperature must be in Kelvin, not Celsius. Conversion from Celsius to Kelvin is simple: add 273.15.
For example, a temperature of 307°C becomes
307 + 273.15 = 580.15 K.
When you have values for P, n, R, and T, you can find the volume V by rearranging the equation: \[ V = \frac{nRT}{P} \].
We use this rearranged equation to determine the volume of gas formed in the ammonium nitrate decomposition: \[ V = \frac{656.25 * 0.0821 * 580}{1.00} = 31,327 \text{ L} \].

Stoichiometry is the part of chemistry that deals with the calculation of reactants and products in chemical reactions. It is key to understand quantities in balanced chemical equations.
Take the decomposition of ammonium nitrate as an example: \[ 2 \text{NH}_4\text{NO}_3(s) \rightarrow 2 \text{N}_2(g) + O_2(g) + 4 \text{H}_2\text{O}(g) \].
This equation tells us that 2 moles of \( \text{NH}_4\text{NO}_3 \) produce 7 moles of gas (2 moles \( \text{N}_2 \), 1 mole \( \text{O}_2 \), and 4 moles \( \text{H}_2\text{O} \)). This mole ratio is key for stoichiometric calculations.
For instance, given 15.0 kg of \( \text{NH}_4\text{NO}_3 \), we convert the mass to moles: \[ 15,000 \text{ g} * \frac{1 \text{ mol}}{80 \text{ g}} = 187.5 \text{ mol} \].
From our balanced equation, we know that 2 moles of \( \text{NH}_4\text{NO}_3 \) produce 7 moles of gas. Thus, \[ 187.5 \text{ mol NH}_4\text{NO}_3 * \frac{7 \text{ mol gas}}{2 \text{ mol NH}_4\text{NO}_3} = 656.25 \text{ mol gas} \].
Using this ratio, we calculate the volume of gas produced.

Mole calculations are fundamental in chemistry. The mole is a unit that represents \( 6.022 \times 10^{23} \) particles of a substance, also known as Avogadro's number. This helps chemists count tiny particles like atoms and molecules by weighing them.
To illustrate, let's calculate the moles of ammonium nitrate. First, find its molar mass: \[ \text{NH}_4\text{NO}_3 = 14 + (4 \times 1) + 14 + (3 \times 16) = 80 \text{ g/mol} \].
Next, convert the given mass to moles: \[ \text{mass} / \text{molar mass} = 15,000 \text{ g} / 80 \text{ g/mol} = 187.5 \text{ mol} \].
With 187.5 moles of \( \text{NH}_4\text{NO}_3 \), we use stoichiometry to find the moles of gas produced. The balanced equation shows that 2 moles of \( \text{NH}_4\text{NO}_3 \) produce 7 moles of gas. Thus,
\( 187.5 \text{ mol NH}_4\text{NO}_3 * \frac{7 \text{ mol gas}}{2 \text{ mol NH}_4\text{NO}_3} = 656.25 \text{ mol gas} \).
Understanding mole calculations makes solving chemical problems easier! Learning to convert masses to moles and using mole ratios is key for mastering chemistry.