Question

the chemical composition of air that is exhaled (expired) is different from ordinary air. A typical analysis of expired air at 37∘C and 1.00 atm, expressed as percent by volume, is 74.2% N₂, 15.2% O₂, 3.8% CO₂, 5.9% H₂O and 0.9% Ar. The composition of ordinary air is 78.08% N₂, 20.95% O₂, 0.93% Ar, and 0.036% CO₂. You may want to reference (Page) Section 6.1 while completing this problem. Part A What is the ratio of the partial pressure of CO₂(g) in expired air to that in ordinary air? Express your answer to two significant figures.

Answer 1

The ratio of the partial pressure of CO₂ in expired air to that in ordinary air, when rounded to two significant figures, is 1.1 x 10².

Step-by-step explanation:

The ratio of the partial pressure of CO₂ in expired air to that in ordinary air can be calculated using the formula P = (Patm) X (percent content in mixture).

Given that the atmospheric pressure (Patm) is the same for both expired and ordinary air (1.00 atm), we can calculate the partial pressures directly based on their respective percentages.

For expired air, the partial pressure of CO₂ (Pᵢₓ₂ expired) would be:
1.00 atm × (3.8/100) = 0.038 atm.

For ordinary air, the partial pressure of CO₂ (Pᵢₓ₂ ordinary) would be:
1.00 atm × (0.036/100) = 0.00036 atm.

Now, the ratio of partial pressure of CO₂ in expired air to that in ordinary air is:
(Pᵢₓ₂ expired) / (Pᵢₓ₂ ordinary) = 0.038 atm / 0.00036 atm = 105.≈55 (to multiple significant figures)

Expressed to two significant figures, the ratio is 1.1 x 10².

Answer 2

The ratio of the partial pressure of CO₂ in expired air to that in ordinary air is 95, when considering a typical atmospheric pressure of 1.00 atm and expressing gas compositions in percent by volume.

Step-by-step explanation:

To calculate the ratio of the partial pressure of CO₂ in expired air to that in ordinary air, we use the formula:

P = (Patm) X (percent content in mixture).

For expired air, CO₂ makes up 3.8% of the mixture. Therefore, the partial pressure of CO₂ in expired air (Pexp) is:

Pexp = 1.00 atm X 0.038 = 0.038 atm.

For ordinary air, CO₂ is 0.04% of the mixture. The partial pressure of CO₂ in ordinary air (Pord) is:

Pord = 1.00 atm X 0.0004 = 0.0004 atm.

To find the ratio (R) of the partial pressures, we divide the partial pressure in expired air by that in ordinary air:

R = Pexp / Pord = 0.038 atm / 0.0004 atm = 95.

Therefore, to two significant figures, the ratio is 95.