Breathing air that contains 4.0 % by volume CO2 over time causes rapid breathing, throbbing headache, and nausea, among other symptoms. What is the concentration of CO2 in such air in terms of (b) molarity, assuming 1 atm pressure and a body temperature of 37 °C?

Verified step by step guidance

1. insert step 1: Start by understanding that the problem requires converting a volume percentage of CO2 to molarity. Molarity is defined as moles of solute per liter of solution.
2. insert step 2: Use the ideal gas law, PV = nRT, to find the number of moles of CO2. Here, P is the pressure (1 atm), V is the volume (assume 1 L for simplicity), R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin (37 °C + 273.15 = 310.15 K).
3. insert step 3: Calculate the volume of CO2 in liters using the given percentage. Since the air contains 4.0% CO2 by volume, in 1 L of air, the volume of CO2 is 0.04 L.
4. insert step 4: Substitute the values into the ideal gas law to solve for n, the number of moles of CO2: n = PV / RT. Use P = 1 atm, V = 0.04 L, R = 0.0821 L·atm/mol·K, and T = 310.15 K.
5. insert step 5: Finally, calculate the molarity of CO2 by dividing the number of moles of CO2 by the total volume of the solution in liters (1 L in this case).

Key Concepts

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is commonly used in chemistry to express the concentration of a substance in a solution. To calculate molarity, one must know the amount of solute (in moles) and the volume of the solution (in liters). In this context, we will convert the percentage of CO2 in air to moles and then to molarity.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under different conditions. In this scenario, we will use the Ideal Gas Law to determine the number of moles of CO2 in a given volume of air at a specified temperature and pressure, which is crucial for calculating molarity.

Volume of Gas at Standard Conditions

At standard temperature and pressure (STP), one mole of an ideal gas occupies approximately 22.4 liters. However, in this question, we are considering body temperature (37 °C) and 1 atm pressure, which slightly alters the volume occupied by a mole of gas. Understanding how to adjust for these conditions is important for accurately calculating the molarity of CO2 in the air.