Problem 15 - Chemistry The Central Science

Question

The average concentration of carbon monoxide in air in an Ohio city in 2006 was 3.5 ppm. Calculate the number of CO molecules in \(1.0 \mathrm{~L}\) of this air at a pressure of 759 torr and a temperature of \(22^{\circ} \mathrm{C}\).

Step-by-Step Solution

Answer

There are approximately \(8.61 \times 10^{16}\) CO molecules in 1.0 L of the air sample in this Ohio city.

Step 1: Convert temperature to Kelvin

First, we need to convert the given temperature of 22°C to Kelvin since all calculations in gas laws are done in Kelvin. To convert from Celsius to Kelvin, we add 273.15. Temperature in Kelvin = Temperature in Celsius + 273.15 Temperature in Kelvin = 22 + 273.15 Temperature in Kelvin = 295.15 K

Step 2: Convert pressure to atm

Next, we need to convert the given pressure of 759 torr to atmospheres (atm) since the Ideal Gas Law uses pressures in atm. We can do this using the conversion factor 1 atm = 760 torr. Pressure in atm = Pressure in torr / (760 torr/atm) = 759 torr / 760 torr/atm = 0.9987 atm

Step 3: Calculate the moles of air

We will use the Ideal Gas Law (PV=nRT) to calculate the moles of air (n_air) in the given volume, pressure, and temperature. The gas constant (R) is 0.08206 L*atm/mol*K. n_air = PV / RT n_air = (0.9987 atm)(1.0 L) / (0.08206 L*atm/mol*K)(295.15 K) n_air = 0.04090 mol

Step 4: Calculate the moles of CO

Now that we have the moles of air, we can use the ppm concentration to determine the moles of CO (n_CO). n_CO = 3.5 ppm * n_air = (3.5 * 10^(-6)) * 0.04090 mol n_CO = 1.4315 * 10^(-7) mol

Step 5: Calculate the number of CO molecules

Finally, we can calculate the number of CO molecules by multiplying the moles of CO by Avogadro's number (6.022 × 10^23 molecules/mol). CO molecules = n_CO * Avogadro's number CO molecules = (1.4315 * 10^(-7) mol)(6.022 × 10^23 molecules/mol) CO molecules ≈ 8.61 × 10^16 There are approximately \(8.61 \times 10^{16}\) CO molecules in 1.0 L of the air sample in this Ohio city.

Key Concepts

ppm concentration

PPM stands for 'parts per million,' which is a way of expressing the concentration of one substance in a mixture. This unit is widely used when dealing with dilute concentrations of pollutants or chemical substances, similar to how we see with the concentration of carbon monoxide (CO) in the air.
To understand ppm, imagine a million tiny parts of air and what percentage out of that million consists of a particular gas. In the context of the exercise, a concentration of 3.5 ppm means there are 3.5 parts of carbon monoxide for every million parts of air. This measurement helps scientists and decision-makers quantify pollution levels and assess air quality standards.
The conversion from ppm to moles of a substance involved using the definition where 1 ppm equals one part of substance per million parts of the total mixture. It gets converted to moles by multiplying the ppm value by the total moles of the air present.

molecular conversion

Molecular conversion is a step that translates from the moles of a substance to the individual molecules of it. In chemistry, it's crucial for understanding how small-scale molecular interactions translate to larger-scale physical quantities.
The conversion begins, in our case, by determining the number of moles of carbon monoxide using its concentration in ppm as detailed in the previous section. By calculating how many moles are available, we can then find out how many molecules we’re dealing with.
Using the proper conversion factor (ppm to moles), we determine the number of moles and then use Avogadro’s number (which will be discussed next) to convert moles directly into molecules. This conversion is a foundational chemistry technique for quantifying chemical reactions on a microscopic scale.

Avogadro's number

Avogadro's number is an essential constant in chemistry for molecular conversion. This number is approximately \(6.022 \times 10^{23}\) entities per mole, allowing chemists to convert between the macroscopic amount of a substance, measured in moles, and the microscopic entities like atoms or molecules.
This huge number helps bridge the gap between lab-scale quantities and molecular-scale quantities. In the given exercise, once the number of moles of CO is calculated, Avogadro’s number is used to move from moles to the actual number of carbon monoxide molecules.
Understanding and utilizing Avogadro's number lets you see the true scale of chemical quantities, shifting from a broad "amount of substance" to counting the individual molecules, making it a pivotal tool in chemistry calculations.