Problem 71 - Chemistry Matter and Change

Question

Find the volume that 42 g of carbon monoxide gas occupies at STP.

Step-by-Step Solution

Answer

The volume is approximately 33.6 liters.

Step 1: Understand the Problem

We are tasked with finding the volume of 42 grams of carbon monoxide (CO) gas at Standard Temperature and Pressure (STP). STP conditions are defined as a temperature of 273.15 K and pressure of 1 atm.

Step 2: Determine the Molar Mass of CO

To find the volume using the Ideal Gas Law, we first need to calculate the molar mass of carbon monoxide. The atomic weight of carbon (C) is 12.01 g/mol and oxygen (O) is 16.00 g/mol. Hence, the molar mass of CO is 12.01 + 16.00 = 28.01 g/mol.

Step 3: Calculate the Number of Moles of CO

We use the formula for moles: \( n = \frac{\text{mass}}{\text{molar mass}} \). So, the number of moles of CO is \( n = \frac{42 \, \text{g}}{28.01 \, \text{g/mol}} \approx 1.50 \, \text{mol} \).

Step 4: Use the Ideal Gas Law to Find Volume

At STP, one mole of an ideal gas occupies 22.4 L. Since we have 1.50 moles of CO, the volume \( V \) is calculated as \( V = 1.50 \, \text{mol} \times 22.4 \, \text{L/mol} \approx 33.6 \, \text{L} \).

Key Concepts

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure, often abbreviated as STP, is a set of conditions used to simplify calculations involving gases. At STP, the temperature is defined as 273.15 Kelvin, equivalent to 0 degrees Celsius, and the pressure is 1 atmosphere (atm). These conditions are important because they provide a common reference that allows scientists and students to compare the properties of different gases.

• Temperature: 273.15 K (0°C)
• Pressure: 1 atm

Using STP, one can determine that one mole of an ideal gas occupies a fixed volume of 22.4 liters. This makes problem-solving with the Ideal Gas Law more straightforward, allowing quick calculations of gas volumes, moles, and other related properties under these conditions.

Molar Mass Calculation

Calculating the molar mass of a gas is an essential step when using the Ideal Gas Law. The molar mass is the sum of the atomic weights of all atoms in a molecule of the gas. For carbon monoxide (CO), the molar mass can be calculated by adding the atomic masses of carbon (C) and oxygen (O):

• Carbon (C): 12.01 g/mol
• Oxygen (O): 16.00 g/mol

Thus, the molar mass of CO is given by:\[ 12.01 ext{ g/mol (C)} + 16.00 ext{ g/mol (O)} = 28.01 ext{ g/mol} \]Understanding the molar mass is crucial because it allows us to convert between grams and moles, which is a necessary step in applying the Ideal Gas Law. It's a handy tool for calculating how much of the gas is present in a given mass.

Volume of Gas

The volume occupied by a gas is directly related to the number of moles when using the Ideal Gas Law and considering STP. At standard temperature and pressure, one mole of any ideal gas occupies exactly 22.4 liters. This relationship is handy for quickly determining the volume without needing to perform extensive calculations.

For our exercise, we calculated that 1.50 moles of carbon monoxide would occupy a space of:\[ V = n imes ext{molar volume at STP} \]\[ V = 1.50 ext{ mol} imes 22.4 ext{ L/mol} = 33.6 ext{ L} \]Knowing how to find the volume of gas under these standard conditions can significantly ease understanding and solving exercises related to the behavior of gases.

Mole Concept

The mole is a key concept in chemistry that helps in quantifying the amount of substance. It represents Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) entities (atoms, molecules, etc.). This concept bridges the atomic and macroscopic scales.

• One mole equals \( 6.022 \times 10^{23} \) entities.
• Allows conversion between grams and the number of particles.

By using the mole, calculations in chemistry become more manageable. In the context of gases, knowing the number of moles allows us to use the Ideal Gas Law reliably. In our example, we used the formula \( n = \frac{\text{mass}}{\text{molar mass}} \) to find the amount of CO. This gives us the ability to proceed with further calculations related to the physical properties of gases.