Question

Calculate the volume (in liters) of \(124.3 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) at \(\mathrm{STP}\).

Short answer

The volume of 124.3 g of CO2 at STP is approximately 63.33 liters.

Step-by-step solution

Understand STP Conditions

Standard Temperature and Pressure (STP) refers to a temperature of 273.15 K (0 °C) and a pressure of 1 atm. At these conditions, one mole of any ideal gas occupies 22.414 liters.

Determine Molar Mass of CO2

The molar mass of CO2 is calculated by summing the atomic masses of its constituent atoms. Carbon (C) has a molar mass of approximately 12.01 g/mol, and Oxygen (O) has a molar mass of approximately 16.00 g/mol. Therefore, the molar mass of CO2 is: \[ 12.01 + 2(16.00) = 44.01 \text{ g/mol} \]

Calculate Moles of CO2

To find out how many moles are present in 124.3 g of CO2, use the formula for moles: \[ \text{Moles of } CO_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{124.3}{44.01} \approx 2.826 \text{ moles} \]

Calculate Volume at STP

Since one mole of gas occupies 22.414 liters at STP, the volume of 2.826 moles of CO2 is calculated as follows: \[ \text{Volume} = \text{Moles} \times 22.414 \text{ L/mol} = 2.826 \times 22.414 \approx 63.33 \text{ L} \]

Key concepts

STP (Standard Temperature and Pressure)

Standard Temperature and Pressure, often abbreviated as STP, is a set of agreed-upon conditions for measuring gases. These conditions include a temperature of 273.15 Kelvin, equivalent to 0 degrees Celsius, and a pressure of 1 atmosphere. Understanding these conditions is crucial because they provide a standard reference point that allows scientists and students to compare the properties of gases consistently. At STP, one mole of an ideal gas occupies exactly 22.414 liters. This constant volume serves as a benchmark in many calculations involving gases, including conversions between volume, pressure, and temperature.

Molar Mass Calculation

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a given substance. For gases like carbon dioxide (CO₂), you'll want to calculate the molar mass by summing the atomic masses of its component elements. A molecule of CO₂ consists of one carbon (C) atom and two oxygen (O) atoms. Carbon has an atomic mass of approximately 12.01 g/mol, while each oxygen atom has an atomic mass of about 16.00 g/mol. Therefore, the molar mass of CO₂ is calculated as follows:

• Add the atomic mass of carbon: 12.01 g/mol.
• Multiply the atomic mass of oxygen by two, as there are two oxygen atoms: 2 x 16.00 g/mol = 32.00 g/mol.
• Sum these values to find the molar mass of CO₂: 12.01 + 32.00 = 44.01 g/mol.

Understanding molar mass is essential for converting between mass, moles, and volume.

Ideal Gas Law

The ideal gas law is expressed in the equation PV = nRT, where P stands for pressure, V for volume, n for the number of moles, R for the gas constant, and T for temperature. This law provides a relationship among the four variables that describe a gaseous system, allowing you to calculate any one of them if the others are known. At STP, things are simplified because you can directly relate the volume to the number of moles, as one mole of any ideal gas will occupy 22.414 liters. Although the ideal gas law doesn’t directly figure in this calculation at STP, understanding it can help you handle gas calculations under various conditions by rearranging the equation to solve for different variables.

Chemical Calculations

Chemical calculations often require the conversion between different units to solve complex problems involving substances, like finding the volume of a gas given its mass. To perform such calculations:

• First, determine the molar mass of the substance, which is crucial for converting mass to moles.
• Next, calculate the number of moles from the given mass using the formula: Moles = Mass / Molar Mass.
• Finally, calculate the volume by multiplying the number of moles by the molar volume at STP (22.414 L/mol for gases).

For our specific example of CO₂, we calculated the volume using the number of moles derived from its given mass at STP. Such step-by-step calculations are vital for accurately determining properties of substances under standard conditions, which can be extended to various practical applications in science and engineering.