How do you calculate the number of molecules in a sample of oxygen gas given its volume, temperature, and pressure?

You can use the ideal gas law (PV = nRT) to find the number of moles (n), then multiply by Avogadro's number to find the number of molecules.

What is the first step to determine the number of oxygen molecules in a 1.72 L sample at 27°C and 800.0 Torr?

Convert all given values to SI units: pressure in atmospheres, volume in liters, and temperature in Kelvin, then apply the ideal gas law to find moles.

What is the value of the ideal gas constant R used in calculations involving oxygen gas?

R = 0.0821 L·atm/(mol·K) is commonly used for calculations involving gases at standard conditions.

How do you convert the pressure from Torr to atmospheres for the calculation?

Divide the pressure in Torr by 760 to convert it to atmospheres (e.g., 800.0 Torr / 760 ≈ 1.0526 atm).

Once you find the number of moles of oxygen, how do you determine the number of molecules?

Multiply the number of moles by Avogadro's number (6.022 × 10²³ molecules/mol) to find the total number of oxygen molecules.

What is the approximate number of oxygen molecules in the sample described?

Using the ideal gas law, the sample contains approximately 4.4 × 10²¹ molecules of oxygen.

A Sample Of Oxygen Gas Has A Volume Of 1.72 L At 27C And 800.0 Torr. How Many Oxygen Molecules Does It

A Sample Of Oxygen Gas Has A Volume Of 1.72 L At 27C And 800.0 Torr. How Many Oxygen Molecules Does It? This question touches on fundamental concepts in chemistry, particularly the application of the ideal gas law, molar calculations, and molecular quantities. Understanding how to determine the number of molecules in a given sample of gas is essential for students and professionals working in chemistry, physics, environmental science, and related fields. In this article, we will explore the step-by-step process to solve this problem, delve into the relevant concepts, and provide a comprehensive understanding of how to approach such calculations.

Understanding the Problem and Key Concepts

Before diving into calculations, it’s crucial to clarify what information is provided and what is being asked. The problem states:

Volume of oxygen gas = 1.72 liters

Temperature = 27°C

Pressure = 800.0 Torr

Question: How many oxygen molecules are present in this sample?

The goal is to find the number of molecules, which involves converting the given data into moles and then into molecules.

Key concepts involved include:

Ideal Gas Law: PV = nRT

Moles of Gas: n = mass / molar mass, but in this case, mass isn’t directly given.

Avogadro’s Number: Number of molecules per mole = 6.022 × 10²³ molecules/mol

Conversions: Pressure units, temperature units, and gas law constants.

Converting Units and Preparing Data

To accurately apply the ideal gas law, all units must be consistent.

1. Pressure Conversion

The pressure is given in Torr, but the ideal gas law requires pressure in atmospheres (atm).

1 atm = 760 Torr
Therefore, P = 800.0 Torr × (1 atm / 760 Torr) ≈ 1.0526 atm

2. Temperature Conversion

Temperature must be in Kelvin (K).

T = 27°C + 273.15 = 300.15 K

3. Gas Constant (R)

Use the ideal gas constant in appropriate units:

R = 0.082057 L·atm/(mol·K)

Summary of converted data:

| Parameter | Value |
|-----------------|---------------------------|
| Volume (V) | 1.72 L |
| Temperature (T) | 300.15 K |
| Pressure (P) | 1.0526 atm |
| Gas constant (R) | 0.082057 L·atm/(mol·K) |

Applying the Ideal Gas Law to Find Moles of Oxygen

The ideal gas law relates pressure, volume, temperature, and amount of gas:

PV = nRT

Rearranged to find n (number of moles):

n = PV / RT

Plugging in the known values:

n = (1.0526 atm × 1.72 L) / (0.082057 L·atm/(mol·K) × 300.15 K)

Calculating numerator:

1.0526 × 1.72 ≈ 1.809 L·atm

Calculating denominator:

0.082057 × 300.15 ≈ 24.612 mol·K

Now:

n ≈ 1.809 / 24.612 ≈ 0.0735 mol

This means the sample contains approximately 0.0735 moles of oxygen gas.

Converting Moles to Molecules

To find the number of molecules, multiply the moles by Avogadro's number:

Number of molecules = n × Avogadro’s number

Avogadro’s number = 6.022 × 10²³ molecules/mol

Therefore:

Number of molecules = 0.0735 mol × 6.022 × 10²³ molecules/mol

Calculating:

0.0735 × 6.022 × 10²³ ≈ 4.422 × 10²² molecules

Result: The sample contains approximately 4.42 × 10²² oxygen molecules.

Additional Considerations and Real-World Applications

While the calculations above assume ideal gas behavior, real gases may deviate slightly, especially under high pressure or low temperature conditions. For most practical purposes at standard conditions, the ideal gas law provides a reliable approximation.

Applications of such calculations include:

Determining the amount of gas in chemical reactions

Calculating gas exchange in biological systems

Designing industrial processes involving gases

Environmental monitoring and modeling atmospheric gases

Summary of the Calculation Process

To summarize, here are the key steps to determine the number of molecules in a gas sample:

Convert all units to appropriate SI or standard units.

Use the ideal gas law to find the number of moles.

Convert moles to molecules using Avogadro’s number.

Applying these steps to the given data results in an estimated 4.42 × 10²² oxygen molecules in the sample.

Conclusion

Understanding how to calculate the number of molecules in a given volume of gas is fundamental in chemistry. By carefully converting units, applying the ideal gas law, and utilizing Avogadro’s number, we can accurately determine molecular quantities from observable parameters like volume, temperature, and pressure. This approach is essential for experiments, industrial applications, and environmental science, providing a bridge between macroscopic measurements and microscopic realities.

Whether you are a student tackling chemistry homework or a scientist designing experiments, mastering these calculations enhances your ability to interpret and manipulate gaseous systems effectively.