An automobile tire is filled with \(\mathrm{O}_{2}\) gas to a total pressure of \(40.0 \mathrm{lb} / \mathrm{in} .^{2}\). The temperature is \(22.5^{\circ} \mathrm{C}\). The inside volume of the inflated tire is \(10.5\) gallons. How many grams of \(\mathrm{O}_{2}\) are in the tire? \(\left(760 \mathrm{~mm} \mathrm{Hg}=14.696 \mathrm{lb} / \mathrm{in} .^{2} ; 1\right.\) gallon \(=3.785 \mathrm{~L}\). (Hint: Your first step should be solving the ideal gas equation for \(n\).)

Understanding SI units conversion is fundamental in the sciences, as it allows for standardization in measurements worldwide. In the context of the Ideal Gas Law, proper conversion is crucial since this law relies on specific units for pressure (P), volume (V), and temperature (T).

Pressure is typically measured in pascals (Pa) in the metric system, while in other systems, it may be presented in pounds per square inch (lb/in²). To convert from lb/in² to pascals, you multiply by a conversion factor that equates the two units. In this case, 1 lb/in² equals 6894.76 Pa.

Volume, often given in gallons for everyday applications, must be converted to cubic meters (m³) for scientific calculations. Since 1 gallon is equivalent to 3.785 liters, and there are 1000 liters in a cubic meter, you would multiply the volume in gallons by 3.785 and then by 10^-3 to convert to m³.

Temperature is converted from degrees Celsius to Kelvin because the Kelvin scale is the SI unit for thermodynamic temperature. This scale starts at absolute zero, so to convert Celsius to Kelvin, you add 273.15 to the Celsius temperature.

The mole is a unit of measurement for amount of substance in the International System of Units (SI). One mole corresponds to the quantity of substance that contains as many elementary entities as there are atoms in 12 grams of carbon-12. It's essential for understanding chemical reactions and properties of gases.

To calculate moles (n) using the Ideal Gas Law, you rearrange the law to solve for n: \[n = \frac{PV}{RT}\] Here, R is the Ideal Gas Constant in the units of Joules per mole per Kelvin (J/(mol·K)). Substituting the converted values of P, V, and T will yield the number of moles. It's important to ensure that all units match, otherwise, you risk obtaining an incorrect value for n. This step establishes a bridge between the macroscopic properties of gases that we can measure, like pressure and volume, and the microscopic property, which is the amount of substance measured in moles.

Gas laws describe how gases behave under various conditions of pressure, volume, and temperature. The Ideal Gas Law is a fundamental equation that encompasses all the individual gas laws, representing the relationship between these variables.

The Ideal Gas Law equation is \[PV = nRT\] in which P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. This equation presumes gases behave ideally, meaning gas particles do not attract or repel each other and occupy no volume. While no gas is truly ideal, many gases behave nearly ideally under a range of conditions.

Through the use of the Ideal Gas Law, one can deduce information about the amount of gas (in moles), necessary to achieve a certain pressure and temperature in a known volume, empowering students and scientists to predict the behavior of gases in closed systems and application in real-world scenarios like filling an automobile tire with gas.