Question

What is the mass of 1 liter of carbon monoxide (CO) at standard temperature and pressure (STP).

Short answer

The mass of 1 liter of carbon monoxide (CO) at standard temperature and pressure (STP) is approximately 1.14 g.

Step-by-step solution

Identify the given values and constants

Here, we are given the volume of the carbon monoxide (V) as 1 liter, and we know that at STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K (0°C) and the pressure (P) is 100 kPa (1 atm). We also need to know the molar mass of carbon monoxide, which is the sum of the molar masses of carbon (C) and oxygen (O): M = M_C + M_O

Convert the volume from liters to cubic meters

We need the volume in cubic meters (m^3) for our calculations, so we will convert the given volume from liters to cubic meters by using the following conversion factor: 1 L = 0.001 m^3 V = 1 L × 0.001 = 0.001 m^3

Calculate the molar mass of carbon monoxide (CO)

The molar mass of carbon monoxide (CO) is the sum of the molar masses of carbon (C) and oxygen (O). The molar mass of C is 12.01 g/mol, and the molar mass of O is 16 g/mol. Therefore, the molar mass of CO is: M = M_C + M_O = 12.01 g/mol + 16 g/mol = 28.01 g/mol

Use the ideal gas law to find the number of moles of CO

The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. We rearrange the equation to find the number of moles (n): n = PV / RT We use the values of P, V, and T at STP and the value of the ideal gas constant R = 8.314 J/(mol·K) to calculate the number of moles of CO: n = (100 × 10^3 Pa × 0.001 m^3) / (8.314 J/(mol·K) × 273.15 K) ≈ 0.0408 mol

Calculate the mass of carbon monoxide (CO)

Now that we have the number of moles of CO, we can calculate the mass of CO by multiplying the number of moles by the molar mass: mass = n × M = 0.0408 mol × 28.01 g/mol ≈ 1.14 g The mass of 1 liter of carbon monoxide (CO) at standard temperature and pressure (STP) is approximately 1.14 g.

Key concepts

Ideal Gas Law

Understanding the ideal gas law is crucial for solving problems involving the properties of gases under certain conditions. It is a cornerstone of chemical and physical gas calculations. The relationship represented by the ideal gas law is encapsulated in the equation \( PV = nRT \). Here, \(P\) stands for pressure in pascals, \(V\) for volume in cubic meters, \(n\) for moles of gas, \(R\) for the ideal gas constant with a value of 8.314 J/(mol·K), and \(T\) for temperature in kelvin. At a foundational level, this equation tells us how these variables are interdependent. In the context of our carbon monoxide problem, by knowing the volume, standard temperature and pressure, and the ideal gas constant, we can use the ideal gas law to determine how many moles of carbon monoxide are present in a given volume.

Molar Mass

When working with gases, calculating the molar mass is essential for converting between mass and moles, allowing us to use the ideal gas law effectively. The molar mass is the mass of one mole of a substance and is measured in grams per mole (g/mol). For compounds like carbon monoxide (CO), you'll need to know the molar mass of each element (carbon and oxygen in this case) and sum these to find the molar mass of the compound. Carbon has a molar mass of 12.01 g/mol, and oxygen has a molar mass of 16.00 g/mol.
Thus, the molar mass of CO is \( 12.01 g/mol + 16.00 g/mol = 28.01 g/mol \). Knowing the molar mass lets you convert the number of moles of gas calculated using the ideal gas law into the actual mass of the gas in grams.

Standard Temperature and Pressure (STP)

Standard temperature and pressure (STP) refer to a set of conditions used as a reference point in gas calculations. At STP, the temperature is 0°C, equivalent to 273.15 K, and the pressure is 1 atm, or approximately 100 kPa. Why are these particular conditions so important? They allow scientists and engineers to compare different gas behaviors in a uniform manner and provide a baseline for calculation constants like the ideal gas constant. In our exercise, knowing that our carbon monoxide gas sample is at STP simplifies the use of the ideal gas law significantly because we can use these defined temperature and pressure values directly in our calculation without having to convert them from other units or conditions.

Moles of Gas

The concept of 'moles of gas' relates to the measurement of the quantity of gas present. One mole is defined as the amount of substance that contains as many particles (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12. This amounts to Avogadro's number, which is approximately \(6.022 × 10^{23}\) particles.
In gas-related problems, moles provide a bridge between the macroscopic world we can measure (like volume and pressure) and the microscopic world of atoms and molecules. By using the ideal gas law, we can calculate the number of moles in a given volume of gas at a known pressure and temperature. When we calculated the moles of carbon monoxide in our exercise, we're finding out the number of CO molecules there are in 1 liter of space at STP, which helps us then figure out the mass of this given volume of gas.