Problem 71 - Chemistry The Science in Context

Question

What is meant by standard temperature and pressure (STP)? What is the volume of 1 mole of an ideal gas at STP?

Step-by-Step Solution

Answer

Answer: The volume of 1 mole of an ideal gas at STP is 22.41 liters.

Step 1: Definition of Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) are defined as the conditions of 0 degrees Celsius (273.15 Kelvin) for temperature and 1 atmosphere (101.325 kPa) for pressure. These standard conditions are used as a reference for performing experiments and making calculations related to gases.

Step 2: Ideal Gas Law

In order to find the volume of 1 mole of an ideal gas at STP, we need to recall the Ideal Gas Law, which relates the pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas. The Ideal Gas Law is given by: PV = nRT, where R is the ideal gas constant. For this problem, n = 1 mole, T = 273.15 K, and P = 1 atm. We can use these values to calculate the volume of the gas at STP.

Step 3: Calculate the Volume of 1 Mole of an Ideal Gas at STP

Using the Ideal Gas Law, we can calculate the volume (V) of 1 mole of an ideal gas at STP: PV = nRT V = (nRT) / P A unit conversion might be necessary, based on the units desired for the final answer and the unit for the ideal gas constant (R). In this case, let's use the value for R = 0.08206 L atm/(K mol). V = ((1 mol) * (0.08206 L atm/(K mol)) * (273.15 K)) / (1 atm)

Step 4: Final Result

After performing the calculation, we obtain: V = 22.41 L So, the volume of 1 mole of an ideal gas at STP is 22.41 liters.

Key Concepts

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) are commonly used reference conditions in the study of gases. At STP, the temperature is maintained at 0 degrees Celsius, which is equivalent to 273.15 Kelvin. The pressure is set at 1 atmosphere, or 101.325 kilopascals (kPa).
These conditions provide a baseline that makes it easier to compare and predict the behavior of gases in a standard way.
Many scientific experiments and gas-related calculations rely on STP because they simplify the variables involved, making it more straightforward to predict how gases will behave under these standardized conditions.

• Temperature at STP: 0°C (273.15 K)
• Pressure at STP: 1 atm (101.325 kPa)

Overall, using STP conditions creates a consistent framework for scientists to evaluate and share their findings effectively.

Molar Volume

Molar volume is the volume occupied by one mole of a substance, typically gas, under specified conditions of temperature and pressure. At STP, the molar volume of an ideal gas is an important benchmark.
For one mole of an ideal gas at Standard Temperature and Pressure, the molar volume is 22.41 liters. This value is significant in chemistry because it helps to quantify the amount of space a specific quantity of gas occupies under standard conditions.
It serves as a dependable figure, particularly in calculations involving the Ideal Gas Law, because it provides a consistent point of reference for comparing gases.

• 1 mole of an ideal gas at STP occupies 22.41 liters
• Molar volume allows for practical applications in stoichiometry and gaseous reactions

Recognizing the molar volume at STP is crucial for accurately predicting the outcomes in experiments and industrial applications.

Gas Constant

The gas constant, often denoted as \( R \), is a key component in the Ideal Gas Law equation. It's a proportionality constant that relates pressure (\( P \)), volume (\( V \)), temperature (\( T \)), and the number of moles (\( n \)) of a gas:
\[ PV = nRT \]
The ideal gas constant allows these variables to be reliably unified into one comprehensible formula.
Different units of measurement exist for \( R \), depending on the context of the problem. For calculations involving liters, atmospheres, moles, and Kelvin, \( R \) is typically 0.08206 L atm/(K mol).

• Used in the equation \( PV = nRT \)
• Value of \( R \) in L atm/(K mol) is 0.08206

Choosing the correct \( R \) value is critical depending on the units of the other variables in the equation, as this ensures accuracy in applying the Ideal Gas Law across various scenarios.