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

The volume of oxygen required is 89.6 liters.

Step-by-step solution

Understand the Reaction

Methane (\(\mathrm{CH}_4\) combusts with oxygen (\(\mathrm{O}_2\)), forming carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\)). The balanced chemical equation for this reaction is: \[\mathrm{CH}_4 + 2\, \mathrm{O}_2 \rightarrow \mathrm{CO}_2 + 2\, \mathrm{H}_2\mathrm{O}\]This tells us that one mole of methane reacts with two moles of oxygen.

Calculate Moles of CH4

We are given 32 grams of methane (\(\mathrm{CH}_4\)) and the molecular weight of \(\mathrm{CH}_4\) is 16 g/mol. Calculate the moles of methane using the formula: \[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]\[ \text{Number of moles} = \frac{32}{16} = 2 \text{ moles} \]

Determine Moles of O2 Needed

According to the balanced equation, 1 mole of \(\mathrm{CH}_4\) requires 2 moles of \(\mathrm{O}_2\) for complete combustion. Therefore, 2 moles of \(\mathrm{CH}_4\) will need: \[ 2 \times 2 = 4 \text{ moles of } \mathrm{O}_2 \]

Convert Moles of O2 to Volume

At Standard Temperature and Pressure (STP), 1 mole of any gas occupies 22.4 liters. To find the volume of oxygen needed, multiply the moles of \(\mathrm{O}_2\) by 22.4: \[ 4 \times 22.4 = 89.6 \text{ liters} \]

Key concepts

Combustion Reactions

Combustion reactions are chemical processes where a substance rapidly reacts with oxygen, releasing energy in the form of heat and light. Let's focus on the combustion of oxygen with hydrocarbons like methane (\(CH_4\)) as it is quite common. In these reactions, the hydrocarbon combines with oxygen to produce carbon dioxide (\(CO_2\)) and water (\(H_2O\)).
These reactions are exothermic, which means they release energy. That's why combustion is used in heating systems and engines. Understanding the balanced equation for combustion reactions is essential because it shows the ratio in which reactants combine. For example, in our exercise, 1 mole of methane reacts with 2 moles of oxygen to produce 1 mole of carbon dioxide and 2 moles of water. This relationship helps us figure out how much of each substance is needed or produced in a reaction.

Mole Calculations

The mole is a fundamental unit in chemistry used to express amounts of a chemical substance. It allows chemists to convert between atoms/molecules and grams, making it easier to deal with large quantities that are part of chemical reactions. When calculating moles, we use the formula: \( \text{Number of moles} = \frac{\text{Mass}}{\text{Molar Mass}} \).
In our problem, we began with 32 grams of methane with a molar mass of 16 g/mol. By applying the formula, we calculated that there are 2 moles of \(CH_4\). This is a critical step as it lays the groundwork for determining how much oxygen is needed for combustion.

Stoichiometry

Stoichiometry derives from Greek words meaning "element" and "measure." It refers to the calculation of reactants and products in chemical reactions. It involves using a balanced chemical equation to determine the relative quantities of substances needed or produced.
By understanding stoichiometry, you can scale chemical reactions up or down. In our example, the balanced reaction tells us that 1 mole of \(CH_4\) needs 2 moles of \(O_2\). Therefore, naturally, 2 moles of \(CH_4\) will need 4 moles of \(O_2\). This showed us exactly how much oxygen is required for complete combustion, demonstrating the power and necessity of stoichiometric calculations.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is a highly useful concept in chemistry, providing a reference point for measuring gases. At STP, the temperature is 273 K (0°C) and the pressure is 1 atm. Under these conditions, one mole of gas occupies a volume of 22.4 liters.
This standardization simplifies the conversion between moles and volume for gases, vital for problems like the one we tackled. By knowing that 4 moles of \(O_2\) are needed for complete combustion, we multiplied it by 22.4 liters per mole, giving us 89.6 liters. Understanding and applying STP conditions allow chemists to make accurate predictions about gas quantities in reactions.