Question

What is the volume (in litre) of oxygen required at STP to completely convert \(1.5\) moles of sulphur to sulphur dioxide? (a) \(33.6\) (b) \(43.6\) (c) \(11.2\) (d) \(23.6\)

Short answer

The volume of oxygen required is 33.6 liters at STP.

Step-by-step solution

Identify the Reaction

The chemical reaction for converting sulphur to sulphur dioxide is: \[ S + O_2 \rightarrow SO_2 \]This indicates that 1 mole of sulphur reacts with 1 mole of oxygen to produce 1 mole of sulphur dioxide.

Calculate Oxygen Moles Required

As per the stoichiometry of the reaction, it requires 1 mole of oxygen to react with 1 mole of sulphur. Given the problem, there are 1.5 moles of sulphur, so it requires 1.5 moles of oxygen.

Determine Volume at STP

At Standard Temperature and Pressure (STP), 1 mole of gas occupies 22.4 liters. Therefore, the volume of oxygen needed is:\[ 1.5 \text{ moles} \times 22.4 \text{ L/mole} = 33.6 \text{ liters} \]

Key concepts

Understanding Chemical Reactions

Chemical reactions describe the process where substances, known as reactants, undergo a transformation to become different substances, called products. In a chemical reaction, you can think of molecules as groups of atoms rearranging like puzzle pieces to form something new.
In the context of our exercise, sulfur (\(S\)) is the reactant that will be transformed into sulfur dioxide (\(SO_2\)) through its interaction with oxygen (\(O_2\)). The chemical equation for this transformation is:

• \[ S + O_2 \rightarrow SO_2 \]

This equation shows that one sulfur atom reacts with one molecule of oxygen gas to create one molecule of sulfur dioxide.
The balancing of a chemical equation is vital as it shows the ratio of reactants used and products formed, maintaining the principle of conservation of mass. Hence, for our reaction, 1 mole of sulfur reacts with 1 mole of oxygen to produce 1 mole of sulfur dioxide.

Moles to Volume Conversion

Converting moles to volume is an essential part of stoichiometry, especially when dealing with gases. In stoichiometric calculations, you'll often need to convert the amount of a substance from moles to volume or vice versa based on the context and available data.
To convert moles to volume, you'll rely on the molar volume of a gas, which is typically 22.4 liters per mole under Standard Temperature and Pressure (STP).

• Molecular gases behave predictably when under these standard conditions, allowing you to use this conversion factor.
• For example, in the previous step, we determined that we require 1.5 moles of oxygen to react with 1.5 moles of sulfur.

To find out the volume that these moles of oxygen will occupy at STP, you simply multiply the number of moles by the molar volume:

• \(\text{Volume} = 1.5 \text{ moles} \times 22.4 \text{ L/mole} = 33.6 \text{ liters}\)

This calculation shows that for the reaction, 33.6 liters of oxygen are necessary to completely react with the sulfur.

STP Gas Calculations

Standard Temperature and Pressure (STP) is a set of conditions for measuring gases, defined as 0°C (273.15 K) temperature and 1 atm pressure.
Under these conditions, gases exhibit predictable behavior, which simplifies the calculation of their volumes. At STP, 1 mole of an ideal gas occupies 22.4 liters. This is known as the molar volume of a gas.

• Using these convenient units, calculations involving gas volumes become much more straightforward.

In our exercise, using the stoichiometry of the reaction \(S + O_2 \rightarrow SO_2\) and knowing we need 1.5 moles of oxygen, the calculation is simplified:

• The volume of 1.5 moles of \(O_2\) at STP is \(1.5 \times 22.4 \text{ L} = 33.6 \text{ L}\).

Thus, you can always rely on STP conditions to provide a reliable baseline for gas law calculations, making complex chemical problems more approachable.