Question

How many number of moles of nitrogen will be present in \(2.24\) L of nitrogen gas at STP? (a) \(9.9\) (b) \(0.099\) (c) \(0.001\) (d) \(1.00\)

Short answer

The number of moles of nitrogen gas present in 2.24 L at STP is 0.10.

Step-by-step solution

Understand the Concept of Molar Volume at STP

At Standard Temperature and Pressure (STP), one mole of any gas occupies 22.4 liters of volume. Knowing this, we can calculate the number of moles of a gas if we have its volume at STP.

Calculate the Number of Moles

To calculate the number of moles of nitrogen gas, use the formula: Number of moles = Volume of gas at STP / Molar volume at STP (22.4 L/mol).

Apply the Values to the Formula

Substitute the given volume (2.24 L) into the formula: Number of moles = 2.24 L / 22.4 L/mol.

Perform the Division

Divide the volume by the molar volume to get the number of moles: Number of moles = 2.24 L / 22.4 L/mol = 0.1 moles.

Round off the Answer

Since the options provided are in decimal form, round the answer to two decimal places: Number of moles = 0.1 moles ≈ 0.10 moles.

Key concepts

Molar Volume at STP

When we talk about molar volume at STP, we are referring to the volume that one mole of any gas occupies when it is at Standard Temperature and Pressure. By definition, the molar volume of a gas at STP is 22.4 liters. This comes from the ideal gas law, which states that the volume occupied by a gas is directly proportional to the number of moles when the temperature and pressure are held constant.

Understanding the concept of molar volume is crucial for solving problems involving the quantification of gases. In the case of our nitrogen gas exercise, knowing the molar volume value allows us to directly find the number of moles present in any given volume of gas at STP through a simple division. This concept is not difficult to grasp but requires remembering the standard value of 22.4 liters per mole, which is an essential figure in many chemistry problems.

Standard Temperature and Pressure

The terms 'Standard Temperature and Pressure', commonly abbreviated as STP, refer to the conditions under which scientists and engineers have agreed to perform measurements to maintain consistency across experiments. At STP, the temperature is set at 0 degrees Celsius (273.15 Kelvin), and the pressure is 1 atmosphere (101.325 kPa).

The importance of STP comes from its role in replicability and comparability of results. In the educational context, when students are solving problems involving gases, they often use STP conditions to make accurate predictions about gas behavior. For our nitrogen gas problem, the volume measurement would be significantly different if the conditions were not at STP. Therefore, it’s important for students to always verify if the conditions given are STP to avoid calculation errors.

Avogadro's Law

Avogadro's Law provides another cornerstone of understanding in our explorations of gaseous substances. The law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. This is foundational because it introduces the idea of the mole, which is a unit representing a certain quantity of particles, specifically, Avogadro's number (\(6.022 \times 10^{23}\) particles).

Avogadro's Law is intrinsically linked to the concept of molar volume at STP. It reinforces that 22.4 liters of any gas at STP will contain Avogadro's number of particles, assuming ideal gas behavior. This universality allows students to approach problems like our nitrogen gas example with confidence, knowing that if they are dealing with STP conditions, the mole-to-volume ratio is constant.