A sample of nitrogen gas kept in a container of volume \(2.3 \mathrm{~L}\) and at a temperature of \(32^{\circ} \mathrm{C}\) exerts a pressure of 4.7 atm. Calculate the number of moles of gas present.

Understanding moles of gas is crucial in chemistry, as it represents the amount of substance present. A mole is a unit that measures the number of particles, similar to how a dozen represents twelve items. For gases, the mole concept is often linked with the volume, pressure, and temperature that the gas occupies.

In the context of the provided exercise, the number of moles of nitrogen gas was determined using the ideal gas law—a fundamental equation in chemistry that relates these variables. When we talk about moles in relation to gases, we typically use the volume in liters, the pressure in atmospheres, and the temperature in Kelvin—a standard format for these calculations.

It’s important to highlight that standard temperature and pressure conditions (STP) are normally set at 0°C (273.15 K) and 1 atm. These conditions allow scientists to compare the behavior of gases under universally accepted benchmarks. However, the number of moles can be calculated under any other condition as well, as demonstrated in our textbook exercise.

The gas laws are a series of principles that describe the behavior of gases and how various properties are interrelated. The ideal gas law, used in our exercise, encompasses several of these gas laws, incorporating Boyle’s law, Charles's law, and Avogadro’s law into a single equation: \( PV = nRT \), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the universal gas constant, and \(T\) is temperature.

Understanding each variable in the equation is key for proper calculations. The pressure exerted by the gas is affected by the number of gas particles colliding with container walls. The volume is the space the gas occupies and impacts pressure inversely per Boyle’s law. The number of moles represents the amount of gas present. The universal gas constant provides the necessary proportionality to balance the units involved in the equation. Finally, the temperature needs to be in Kelvin, as it is an absolute scale that starts at absolute zero—the point where no molecular motion exists.

Temperature plays a pivotal role in the behavior of gases, and for gas law calculations, it must be in the Kelvin scale. Unlike Celsius or Fahrenheit, Kelvin is an absolute temperature scale, with 0 K marking the point of absolute zero.

Converting from Celsius to Kelvin is straightforward: simply add 273.15 to the Celsius temperature. Thus, a temperature of \(32^\circ C\) becomes \(305.15 K\). The Kelvin scale's importance lies in its direct relationship with energy—it reflects the absolute energy in particles. Moreover, because the Kelvin scale does not deal with negative numbers, it simplifies mathematical calculations involving temperature.

In practice, as shown in the exercise, the correct Kelvin conversion ensures the accuracy of the ideal gas law calculation. The solution already provided demonstrates this step as integral, and without it, the calculation of moles could result in a significantly different, and incorrect, value.