How many moles of \(\mathrm{CO}_{2}\) are contained in \(9.55 \mathrm{~L}\) at \(45^{\circ} \mathrm{C}\) and 752 torr?

Understanding the concept of moles is fundamental in chemistry, especially when working with gases. A mole is a unit that represents a quantity of particles, usually atoms or molecules, and is defined as the number of carbon atoms in exactly 12 grams of carbon-12, which is approximately 6.022 x 10²³ particles - a value known as Avogadro's number.

When you're given a volume of gas under certain conditions of temperature and pressure, as in the exercise, you can calculate the number of moles of the gas present using the Ideal Gas Law. This law is a reliable approximation for most gases under standard conditions. The challenge here often comes with the manipulation of this law to solve for the desired quantity; the number of moles, denoted by 'n'. In our exercise, with the volume, temperature, and pressure known, the mole calculation simply involves using the formula after converting all the measurements into the correct units.

The behavior of gases is predictable and is explained by several fundamental laws, collectively known as the Gas Laws. One of these, the Ideal Gas Law, combines the relationships outlined in Boyle's Law, Charles's Law, and Avogadro's Law. It is expressed mathematically as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature in Kelvin.

The Ideal Gas Law assumes that the gas particles are point particles that interact with each other only through elastic collisions. This is an approximation, but it holds true for many conditions and allows us to solve for unknown variables, assuming the others are known. In the context of the provided exercise, by rearranging the Ideal Gas Law equation, we isolate and calculate the quantity 'n,' which is essential for understanding how much of a gas is present.

One critical skill in mastering chemistry problems, such as those involving the Ideal Gas Law, is the conversion of units. This step is necessary because the law only applies when the units used are consistent, specifically the volume in liters, pressure in atmospheres, temperature in Kelvin, and the number of moles.

Starting with temperature, converting from degrees Celsius to Kelvin is a straightforward addition of 273.15 to the Celsius temperature. This is vital because the Kelvin scale establishes absolute zero as its zero point. Next, pressures often need to be converted to atmospheres from other measurements like torr or mmHg. Recognizing conversion factors such as 1 atm equals 760 torr ensures calculations use the right units. Finally, volumes should be expressed in liters rather than milliliters or cubic centimeters for the Ideal Gas Law. These conversions are essential to successfully solving gas law problems and to avoid errors in calculations.