Calculating the Volume of SO2 Gas at STP Containing a Given Number of Oxygen Atoms
Calculating the Volume of SO2 Gas at STP Containing a Given Number of Oxygen Atoms
In this article, we address a specific scientific calculation aimed at determining the volume of sulfur dioxide (SO2) gas at standard temperature and pressure (STP) containing a specific number of oxygen atoms. The steps involved in this calculation are detailed below:
The Problem Statement
Given that 1 mole of SO2 contains 2 moles of oxygen atoms, and at STP (Standard Temperature and Pressure), 2 moles of oxygen atoms occupy 22,400 cm3 (L), our goal is to calculate the volume of SO2 gas at STP that contains 3.011 x 1020 atoms of oxygen.
Step-by-Step Solution
Here are the detailed steps to solve this problem:
Step 1: Calculate the Number of Moles of Oxygen Atoms
The number of moles of oxygen atoms in the given quantity can be calculated using Avogadro’s number, which is 6.022 x 1023 atoms per mole.
[ text{Number of moles of oxygen} frac{3.011 times 10^{20}}{6.022 times 10^{23}} ]Simplifying the above expression:
[ text{Number of moles of oxygen} approx 0.05 text{ moles} ]Step 2: Determine the Number of Moles of SO2 Gas Produced
From the balanced chemical equation for the formation of SO2 from its elements: S O2 → SO2. According to this equation, 2 moles of oxygen atoms are required to produce 1 mole of SO2 gas. Hence, the number of moles of SO2 gas produced is half the number of moles of oxygen atoms.
[ text{Number of moles of SO}_2 text{ gas} frac{0.05}{2} 0.025 text{ moles} ]Step 3: Apply the Ideal Gas Law to Find the Volume of SO2 Gas at STP
At STP, the temperature (T) is 273.15 K and the pressure (P) is 1 atm. The molar volume of any gas at STP is 22.4 L/mol.
Using the ideal gas law:
[ V frac{n cdot R cdot T}{P} ]Where n is the number of moles, R is the ideal gas constant (0.0821 L?atm/(mol?K)), T is the temperature, and P is the pressure.
[ V frac{0.025 text{ moles} cdot 0.0821 text{ L?atm/(mol?K)} cdot 273.15 text{ K}}{1 text{ atm}} ]Calculating the above expression:
[ V approx 0.549 text{ L} ]Conclusion
The volume of SO2 gas at STP that contains 3.011 x 1020 atoms of oxygen is approximately 0.549 L. This calculation demonstrates the application of the ideal gas law and stoichiometry in chemical problem-solving.