Question

What volume in litres will be occupied by \(4.4 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) at STP? (a) \(22.4 \mathrm{~L}\) (b) \(44.8 \mathrm{~L}\) (c) \(12.2 \mathrm{~L}\) (d) \(2.24 \mathrm{~L}\)

Short answer

2.24 liters

Step-by-step solution

Identify the molar mass of CO2

To find the volume of a gas at STP, we need to calculate the amount in moles. The molar mass of CO2 is given by the sum of the atomic masses of carbon (C) and oxygen (O). Since CO2 has one carbon atom (approximately 12.01 g/mol) and two oxygen atoms (approximately 16.00 g/mol each), the molar mass is 12.01 g/mol + 2(16.00 g/mol) = 44.01 g/mol.

Convert the mass of CO2 to moles

Using the molar mass of CO2, convert the given mass of CO2 to moles. Using the formula: moles = mass / molar mass. For 4.4 g of CO2, the calculation is: moles = 4.4 g / 44.01 g/mol.

Calculate the moles of CO2

Perform the calculation from Step 2 to find the moles: moles = 4.4 g / 44.01 g/mol = 0.1 moles.

Use the molar volume of a gas at STP

At STP (standard temperature and pressure), one mole of any gas occupies 22.4 liters. Since we have calculated the moles of CO2, we can now find the volume by multiplying the moles by the molar volume at STP.

Calculate the volume of CO2

The volume occupied by the CO2 at STP can be calculated by multiplying the number of moles of CO2 by the molar volume at STP (22.4 L/mol). So, the volume is 0.1 moles * 22.4 L/mol.

Solve for the volume

Carry out the multiplication: 0.1 moles * 22.4 L/mol = 2.24 L. This is the volume of 4.4 g of CO2 at STP.

Key concepts

Molar Mass Calculation

Understanding the molar mass of a compound is integral to solving many chemistry problems, particularly those involving gas laws. The molar mass, often measured in grams per mole (g/mol), is the weight of one mole of a substance. To calculate it, we add up the atomic masses of each atom in the molecule.

For carbon dioxide (CO_2), it contains one carbon atom and two oxygen atoms. Using the periodic table, we find that carbon's atomic mass is approximately 12.01 g/mol, and oxygen's is about 16.00 g/mol. We then calculate the molar mass by multiplying each atom's atomic mass by the number of times it occurs in the molecule and summing these values: 12.01 g/mol for carbon plus 2 * 16.00 g/mol for the two oxygen atoms. This gives us a molar mass of 44.01 g/mol for CO_2.

Knowing this molar mass allows us to convert between mass and moles, key for problems regarding reactions and gas volumes. The molar mass serves as a conversion factor, bridging the microscopic scale of atoms and molecules to the macroscopic world we can measure.

Moles to Volume Conversion

Once we have the quantity of a substance in moles, converting it to volume at standard temperature and pressure (STP) is the next step. This is based on the principle that under STP, which is defined as 0°C (273 K) and 1 atm pressure, one mole of any ideal gas occupies a volume of 22.4 liters.

To convert moles to volume, the following formula is used: Volume = moles * molar volume at STPwhere the molar volume at STP is 22.4 L/mol. Let's take our example of carbon dioxide; given 0.1 moles of CO_2, we multiply this by the molar volume to find the occupied volume. 0.1 moles * 22.4 L/mol gives us 2.24 liters.

This calculation is straightforward when conditions are at STP. However, variations in temperature and pressure require adjustments using the ideal gas law. This conversion is essential in stoichiometry for predicting product volumes in gaseous reactions.

Standard Temperature and Pressure

Standard temperature and pressure, commonly abbreviated as STP, are conditions of 0°C (273.15 K) and 1 atmosphere pressure, a standard set for comparing measurements. At STP, gases exhibit ideal behavior, which greatly simplifies calculations such as moles to volume conversions.

STP allows scientists and students to have a common reference for gas volumes, as the volume directly relates to the number of moles present. The molar volume of an ideal gas at STP is 22.4 L/mol, a figure derived from the ideal gas law. Due to this consistency, we can use it to calculate volumes of gases from the moles or reverse-engineer the number of moles from a known volume.

It's important to note that real gases might deviate slightly from ideal behavior at STP. Nevertheless, the variance is often negligible for educational purposes. Practically, the concept of STP provides a foundational understanding for students, easing the transition to more complex gas laws and thermodynamic concepts.