Question

What is the volume (in litres) of oxygen at STP required for complete combustion of \(32 \mathrm{~g}\) of \(\mathrm{CH}_{4}\) ? (mol. wt. of \(\mathrm{CH}_{4}=16\) ) (a) \(89.6\) (b) \(189.6\) (c) \(98.4\) (d) \(169.5\)

Short answer

89.6 litres at STP.

Step-by-step solution

Write the Balanced Chemical Equation

The combustion of methane (\(\text{CH}_4\)) in the presence of oxygen (\(\text{O}_2\)) produces carbon dioxide (\(\text{CO}_2\)) and water (\(\text{H}_2\text{O}\)). The balanced chemical equation is:\[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \]

Key concepts

Balanced Chemical Equation

A balanced chemical equation is a crucial part of studying chemical reactions. It represents the substances going into a reaction (reactants) and the substances coming out of the reaction (products) while ensuring that the number of atoms stays the same on both sides. This reflects the law of conservation of mass, which states that mass cannot be created or destroyed in a chemical reaction. A balanced equation shows the precise proportion of molecules or moles of each substance involved, which is imperative for making calculations in chemistry.

• For instance, in the combustion of methane, the balanced equation is: \[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \]
• Here, one molecule of methane reacts with two molecules of oxygen to produce one molecule of carbon dioxide and two molecules of water.
• This balanced state is necessary to predict how much reactant is needed and how much product will be formed in a given reaction.

Balancing the equation ensures you use correct molar ratios, which are necessary for calculating volumes and masses in chemical reactions.

Combustion of Methane

Combustion reactions involve a substance reacting with oxygen to produce heat and usually light. The combustion of methane is an example of a hydrocarbon combustion process, where methane (\( \text{CH}_4 \)) burns in the presence of oxygen (\( \text{O}_2 \)) to form carbon dioxide (\( \text{CO}_2 \)) and water (\( \text{H}_2\text{O} \)). This reaction is highly exothermic, releasing a significant amount of energy.

• Methane is a simple hydrocarbon and one of the primary components of natural gas.
• The balanced equation is \( \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \).
• In terms of energy, the combustion of methane releases around 890 kJ/mol of energy.

Complete combustion occurs when there is a sufficient supply of oxygen, resulting in only carbon dioxide and water as products, with no leftover unburned fuel or partial oxidized products.

Molar Volume at STP

In chemistry, the concept of molar volume is used to describe the volume occupied by one mole of any gas at standard temperature and pressure (STP). STP is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (atm). Under these conditions, one mole of an ideal gas occupies 22.4 liters.

• Molar volume allows chemists to easily transition between moles and liters when dealing with gas substances.
• When applying these calculations to reactions like the combustion of methane, it's essential to use the balanced equation to determine the number of moles of gas involved.
• In our methane combustion example, for every mole of methane combusted, two moles of oxygen are required, producing a total volume of 44.8 liters of oxygen gas at STP (since each mole is 22.4 liters).

Understanding molar volume at STP is fundamental when you need to calculate the volume of gases produced or consumed in chemical reactions.