Question

\(2 \mathrm{~g}\) of \(\mathrm{O}_{2}\) at NTP occupies the volume: (a) \(1.4 \mathrm{~L}\) (b) \(2.8 \mathrm{~L}\) (c) \(11.4 \mathrm{~L}\) (d) \(3.2 \mathrm{~L}\)

Short answer

The volume is (a) 1.4 L.

Step-by-step solution

Recall the Mole Concept

At Normal Temperature and Pressure (NTP), one mole of any ideal gas occupies a volume of 22.4 liters. This is a foundational concept in chemistry that allows us to calculate the volume of a gas based on its quantity in moles.

Determine Molar Mass of Oxygen

The molecule \(\text{O}_2\) consists of two oxygen atoms. The atomic mass of oxygen is approximately \( 16 \) amu. Thus, the molar mass of \(\text{O}_2\) is \( 16 + 16 = 32 \) g/mol.

Calculate the Number of Moles

To find the number of moles in the given \( 2 \) grams of \(\text{O}_2\), use the formula: \(\text{Number of moles} = \frac{\text{Mass}}{\text{Molar Mass}}\). Substituting in the values gives \( \frac{2}{32} \) moles.

Calculate the Volume at NTP

Given that \( 1\) mole of \(\text{O}_2\) occupies \( 22.4\) liters at NTP, the volume for \( \frac{2}{32}\) moles is calculated by: \( \frac{2}{32} \times 22.4 \) liters. Evaluating this gives \( 1.4\) liters.

Identify the Correct Option

Compare the calculated volume (1.4 liters) with the given options. The correct answer is option (a) \( 1.4 \) liters.

Key concepts

Molar Mass

Understanding molar mass is key when dealing with chemical reactions and calculations. It represents the mass of one mole of a given substance, typically expressed in grams per mole (g/mol). For molecular substances, molar mass is calculated by summing the atomic masses of all atoms within a molecule. For example, the molecule of \(\text{O}_2\) comprises two oxygen atoms. Given that each oxygen atom has an atomic mass of about \(16\) amu, the molar mass for \(\text{O}_2\) is calculated as follows: \[\text{Molar Mass of } \text{O}_2 = 16 + 16 = 32\; \text{g/mol.}\] This means that one mole of \(\text{O}_2\) weighs \(32\) grams. Calculating molar mass is fundamental in converting quantities from grams to moles and allows scientists to predict how substances will react in a chemical equation.

Volume of Gases

The volume of gases is a crucial concept in chemistry, especially when using the mole concept. At normal temperature and pressure (NTP), one mole of any ideal gas occupies a fixed volume. This is known as the molar volume, and it is typically \(22.4\) liters per mole. The concept is beneficial because it establishes a predictable behavior in ideal gases. To determine the volume a certain mass of gas occupies, you first need to convert the mass to moles using molar mass. Then, multiply the number of moles by the molar volume. For example, with \(2\) grams of \(\text{O}_2\): \[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{2}{32}, \] and then, \[ \text{Volume} = \text{Number of moles} \times \text{Molar Volume} = \frac{2}{32} \times 22.4, \] results in approximately \(1.4\) liters of volume. This versatility is what makes understanding gas volume so valuable.

Normal Temperature and Pressure (NTP)

Normal temperature and pressure (NTP) refers to standard conditions set for experiments and calculations in chemistry. These conditions are defined as:

• Temperature: \(0\;\text{°C}\) or \(273.15\; \text{K}\) (Kelvin),
• Pressure: \(1\;\text{atm}\) (atmosphere).

Under these conditions, gases behave in predictable ways, allowing scientists to reliably perform calculations and comparisons. NTP is particularly relevant when applying the Ideal Gas Law, which is an equation of state of a hypothetical ideal gas. At NTP, familiar properties such as the molar volume of \(22.4\) liters per mole for an ideal gas allow for easy transitions between calculations involving pressure, volume, temperature, and the amount of gas in moles. This predictability at NTP is valuable for accurate scientific experiments and provides a baseline for understanding gas behavior.