Question

The number of moles of oxygen in one litre of air containing \(21 \%\) oxygen by volume, in standard conditions, is: (a) \(0.176 \mathrm{~mol}\) (b) \(0.32 \mathrm{~mol}\) (c) \(0.0093 \mathrm{~mol}\) (d) \(2.20 \mathrm{~mol}\)

Short answer

The number of moles of oxygen is \(0.0093 \mathrm{~mol}\) (Option c).

Step-by-step solution

Identify the given data

We are given that air contains \(21\%\) oxygen by volume. We need to find the number of moles of oxygen in 1 litre of air under standard conditions (0 °C and 1 atm).

Calculate the volume of oxygen

Under standard conditions, we assume the air's density is such that 1 litre of air contains 0.21 litres of oxygen because air contains \(21\%\) oxygen by volume.

Use the ideal gas law to find moles

At standard temperature and pressure (STP), 1 mole of any gas occupies \(22.4\, \text{litres}\). Using this, we can calculate the number of moles of oxygen: \[ n = \frac{0.21}{22.4} \]

Calculate the result

Compute the moles of oxygen using the formula from Step 3: \[ n = \frac{0.21}{22.4} \approx 0.00938 \]

Comparison with options

Compare the calculated moles (\(0.00938\)) with the given options. It matches closest with option (c) \(0.0093 \mathrm{~mol}\).

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry. It helps to describe how gases behave under different conditions. The formula is given by: \[ PV = nRT \] where:

• **P** stands for pressure
• **V** represents volume
• **n** is the number of moles of the gas
• **R** is the universal gas constant
• **T** is the temperature in Kelvin

This equation lets us relate these properties of a gas. When you know any three of them, you can easily calculate the fourth.
The **Ideal Gas Law** is useful because it describes how gases behave under normal conditions. It simplifies understanding the physical behavior of gases.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It's like the mathematical backbone of chemistry that tells you how much of each substance you'll need or produce.
Consider a recipe for making cookies. If you have a recipe that makes 10 cookies, stoichiometry would help you adjust, say, if you want to make 20 cookies instead.
In the context of gases, stoichiometry becomes a tool to predict the volume or moles of a gas involved in a chemical equation.

• Here, we can understand how the volume of a gas relates to the number of moles using **molar volume** under STP.
• In simpler terms, stoichiometry helps you make those conversions when dealing with chemical equations.

It ensures everything is balanced and that no reactants go to waste.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure, or **STP**, define a set condition for experiments. It allows scientists to have a baseline to compare results. The standard measure is:

• **Temperature:** 0 °C or 273.15 K
• **Pressure:** 1 atm or 101.325 kPa

Using these conditions, one mole of a gas occupies **22.4 liters** of volume. This is handy for quick calculations in chemical reactions and experiments. It provides uniformity for calculating gas volumes and moles. In our exercise, it lets us find out how the volume of oxygen gas translates into moles at these standard conditions.

Volume-Volume Relationships

Volume-Volume Relationships describe how the volumes of gases relate to each other in a chemical reaction. Since gases behave predictably under set conditions, volumes of gases can relate directly to the coefficients in a balanced chemical equation.
Let's imagine a situation where if 1 liter of gas A reacts to produce 2 liters of gas B, we can predict these outcomes using proportional relationships.

• This is possible because all gases, at the same temperature and pressure, occupy volumes proportional to the number of moles of gas.
• In our problem, we calculate the oxygen volume as part of the whole air, using its percentage by volume.

The **Volume-Volume Relationships** simplify such calculations because each volume ratio is equal to the mole ratio in gas reactions. It helps because you gain insights into how changes in one reactant or product affect others in a balanced way.