Problem 63 - Chemistry Matter and Change

Question

What volume is occupied by 1 \(\mathrm{mol}\) of a gas at STP? What volume does 2 mol occupy at STP?

Step-by-Step Solution

Answer

At STP, 1 mol occupies 22.4 liters; 2 mol occupies 44.8 liters.

Step 1: Understanding STP

STP, or Standard Temperature and Pressure, is defined as a temperature of 273.15 Kelvin (0°C) and a pressure of 1 atmosphere. It is a standard set of conditions for which the ideal gas laws are often applied.

Step 2: Gas Law at STP

According to the ideal gas law, 1 mole of an ideal gas occupies a volume of 22.4 liters at standard temperature and pressure (STP). This is derived from the equation for the ideal gas law, but specifically, at STP this quantity is recognized as a standard.

Step 3: Calculating Volume for 1 mole

Since 1 mole of an ideal gas occupies 22.4 liters at STP, the volume of 1 mole of gas at STP is clearly 22.4 liters.

Step 4: Calculating Volume for 2 moles

Using the same relationship, the volume occupied by 2 moles of gas at STP can be calculated. Since the volume is directly proportional to the amount of substance (number of moles), 2 moles of gas will occupy 2 times 22.4 liters. Thus, the volume is:\[ 2 imes 22.4 ext{ liters} = 44.8 ext{ liters} \]

Key Concepts

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure, often abbreviated as STP, is a concept used in chemistry and physics to set uniform conditions for the measurement of gas properties. At STP, the temperature is set at 273.15 Kelvin, which is equivalent to 0°C or the freezing point of water. The pressure is standardized at 1 atmosphere, equivalent to 101.325 kPa. These conditions are chosen because they make it easier to compare the behavior of gases in different experiments and calculations. By ensuring all experiments are conducted under these same conditions, scientists can avoid variations that might occur if temperature and pressure were allowed to fluctuate. Understanding STP is vital when working with the ideal gas law, as it provides a clear and consistent basis for calculations.

Moles and Volume Relationship

The relationship between moles and volume for gases is elegantly simple, thanks to the ideal gas law. This law states that the volume of a gas (V) is directly proportional to the number of moles (n), provided the temperature and pressure remain constant. This proportionality is expressed as:

• For 1 mole of any ideal gas at STP, it occupies a volume of 22.4 liters.
• For 2 moles of the same gas at STP, the volume will be 44.8 liters, as volume is directly proportional to the amount of gas (2 × 22.4 liters).

This direct relationship becomes invaluable when predicting how a gas will behave under different circumstances, such as reactions or changes in state. It simplifies the calculations since you just need to know the number of moles to find the volume, or vice versa. This proportional relationship is an important tool in both theoretical and practical chemistry.

Gas Volume Calculation

Calculating the volume of a gas involves applying the principles of the ideal gas law, which is typically expressed as:\[ PV = nRT \]where:

• P is the pressure,
• V is the volume,
• n is the number of moles,
• R is the ideal gas constant (approximately \(8.314 \text{ J/(mol·K)}\), though it can vary slightly based on the units used),
• T is the temperature in Kelvin.

At STP, you don't need the full ideal gas equation for simple mole-volume calculations because the volume for 1 mole of gas is universally accepted as 22.4 liters. This means the calculation can be simplified for multiple moles of a gas. For example, if you are dealing with 2 moles of gas at STP, the calculation is straightforward: simply multiply the 22.4 liters by the number of moles. This understanding allows for quick and effective solutions to many problems involving gases, making it an essential skill in chemistry.