Calculating Moles of ( text{CO}_2 ) and ( text{SO}_2 ) at STP Using the Ideal Gas Law

When dealing with gases at standard temperature and pressure (STP, 0°C and 1 atm), the ideal gas law can be simplified to relate the volume of a gas to the number of moles, making mole calculations straightforward. This article will guide you through the process of determining the moles of ( text{CO}_2 ) and ( text{SO}_2 ) given specific volumes at STP.

Understanding the Ideal Gas Law at STP

The ideal gas law states that ( PV nRT ), where ( P ) is the pressure, ( V ) is the volume, ( n ) is the number of moles, ( R ) is the universal gas constant, and ( T ) is the temperature. At STP, the conditions are fixed as 0°C (273.15 K) and 1 atm, and the molar volume of an ideal gas is 22.4 dm(^3) (or 22400 cm(^3)). Therefore, ( n ) can be determined using the formula:

[n frac{V}{text{molar volume at STP}}]

Given that the molar volume of an ideal gas at STP is 22.4 dm(^3), the number of moles can be calculated if the volume in dm(^3) is known.

Steps to Calculate Moles

Let's consider two scenarios where 50 cm(^3) of ( text{CO}_2 ) and 50 cm(^3) of ( text{SO}_2 ) are measured. We'll convert these volumes to dm(^3) first and then determine the number of moles using the ideal gas law.

Step 1: Convert Volume from cm(^3) to dm(^3)

[50 text{ cm}^3 frac{50}{1000} 0.05 text{ dm}^3]

Converting cm(^3) to dm(^3) using the conversion factor 1 dm(^3) 1000 cm(^3).

Step 2: Calculate Moles Using the Ideal Gas Law

Using the simplified relationship at STP, where 1 mole of gas occupies 22.4 dm(^3):

[text{moles} frac{text{volume in dm}^3}{text{molar volume at STP}}]

For 50 cm(^3),

[text{moles} frac{0.05 text{ dm}^3}{22.4 text{ dm}^3/text{mol}} approx 0.00223 text{ mol}]

Therefore, the number of moles of ( text{CO}_2 ) and ( text{SO}_2 ) is approximately 0.00223 mol each, assuming ideal behavior of the gases.

Conclusion

Both ( text{CO}_2 ) and ( text{SO}_2 ), when measured in 50 cm(^3) volumes at STP, will have the same number of moles. This is because the molar volume of all ideal gases at STP is the same, leading to an equal number of moles for equal volumes of different gases under these conditions.

Additional Insights

By using this formula, one can easily calculate the moles of any gas given its volume at STP, as long as the volume is expressed in dm(^3). The relationship between volume and moles is a fundamental concept in chemistry, particularly important in gas law applications and stoichiometry.

Frequently Asked Questions (FAQs)

1. What is STP in chemistry? Standard Temperature and Pressure (STP) refers to the conditions of 0°C (273.15 K) and 1 atm pressure, which are used as standard conditions for measurement and calculation in chemistry.

2. Why is the molar volume of an ideal gas at STP The molar volume of an ideal gas at STP is

3. How accurate are the calculations for real gases at STP? While the ideal gas law is a useful approximation, real gases may deviate from these calculations due to intermolecular forces and compression, which affects their behavior at STP.