Question

Given the following amounts of gases, calculate the number of moles of each gas. Calculate the volume each amount of gas would occupy at STP. (a) \(2.2 \mathrm{~g} \mathrm{CO}_{2}\) (b) \(5.6 \mathrm{~g} \mathrm{~N}_{2}\) (c) \(145 \mathrm{~g} \mathrm{Ar}\)

Short answer

The number of moles and their respective volumes at STP are: (a) \(CO_{2}\): 0.05 mol, 1.12 L (b) \(N_{2}\): 0.2 mol, 4.48 L (c) \(Ar\): 3.63 mol, 81.31 L.

Step-by-step solution

Calculate the Number of Moles

This is done by dividing the given mass of the gas by its molar mass. The molar masses of \(CO_{2}\), \(N_{2}\) and \(Ar\) is approximately 44 g/mol, 28 g/mol and 40 g/mol respectively. So, for \(CO_{2}\), \(N_{2}\), and \(Ar\) the calculations are: (a) Number of moles of \(CO_{2}\) = \(2.2 g / 44 g/mol = 0.05 mol\) (b) Number of moles of \(N_{2}\) = \(5.6 g / 28 g/mol = 0.2 mol\) (c) Number of moles of \(Ar\) = \(145 g / 40 g/mol = 3.63 mol\)

Calculate the Volume at STP

At Standard Temperature and Pressure (STP), 1 mole of any gas will occupy a volume of 22.4 liters. Therefore, the volume can be calculated as follows: (a) Volume of \(CO_{2}\) at STP = \(0.05 mol * 22.4 L/mol = 1.12 L\) (b) Volume of \(N_{2}\) at STP = \(0.2 mol * 22.4 L/mol = 4.48 L\) (c) Volume of \(Ar\) at STP = \(3.63 mol * 22.4 L/mol = 81.31 L\)

Key concepts

Moles Calculation

When calculating the moles, you are working in the world of chemistry to convert mass into a number of particles. A mole provides a bridge between the atomic world and our macroscopic world. To find out how many moles are contained in a given mass of a substance, we use the formula:

• Number of moles = \( \frac{\text{mass of the substance}}{\text{molar mass of the substance}} \)

This calculation is essential because it tells you how many units (or atoms, molecules) are in the substance. For example, if you have 2.2 g of \( \text{CO}_{2} \), you'd divide by its molar mass—44 g/mol—to find the moles. So, \( \frac{2.2}{44} = 0.05 \text{mol} \). This same principle is applied to any substance to determine its number of moles by dividing its given mass by its respective molar mass.

Molar Mass

Molar mass is crucial in chemistry as it links a substance's weight to its chemical properties. Defined as the mass of one mole of a given substance (usually grams per mole), it reflects the mass of all the atoms present in a molecular formula. Understanding molar mass is imperative for moles calculation. For instance:

• The molar mass of \( \text{CO}_{2} \) (carbon dioxide) can be calculated by adding the atomic masses of one carbon atom (12 g/mol) and two oxygen atoms (16 g/mol each). Therefore, the molar mass is 44 g/mol.
• \( \text{N}_{2} \) has a molar mass of 28 g/mol as each nitrogen atom is 14 g/mol.
• Finally, Argon's (\( \text{Ar} \)) molar mass is 40 g/mol, as it is a noble gas with a single atomic form.

These molar masses are used in conjunction with the mass of a substance to calculate the number of moles it contains.

STP (Standard Temperature and Pressure)

Standard Temperature and Pressure (STP) is a set of conditions used as a reference point for gas calculations. It helps in making consistent and standardized comparisons between different gas substances.

• STP is defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere.
• Under STP, one mole of any gas occupies a volume of 22.4 liters.

This means that regardless of what gas you're dealing with—be it oxygen, nitrogen, or argon—a mole will occupy 22.4 liters at STP. This standardization is immensely helpful for chemists in predicting how gases will behave under certain conditions, enabling easy volume and moles calculations.

Volume Calculation

Volume calculation at STP turns the number of moles into a tangible measure we can visualize, like liters. To find the volume that a gas occupies at STP, you use the number of moles and multiply by the volume of one mole at STP.

• Volume at STP = \( \text{moles} \times 22.4 \text{ L/mol} \)

For example, if we consider \( \text{N}_{2} \), where the number of moles is 0.2 mol (previously calculated), you determine that it occupies \( 0.2 \times 22.4 = 4.48 \text{ L} \) at STP. This simple formula provides a quick way to calculate how much space a gas will fill, a necessary step in many chemical processes and experiments involving gases.