Gas Laws In Anesthesia ANES 5101 Assignment 2

Gas laws in anesthesia ANES 5101 Assignment 2 Name: ______________________________________

Calculate the root mean square velocity and kinetic energy of CO, CO₂, and SO₃ at 298 K. Identify which gas has the greatest velocity, kinetic energy, and effusion rate. Calculate the ratio of effusion rates for UF₆ formed with U-238 and U-235 isotopes. Determine the effusion rate ratio between Argon and Krypton gases. Identify an unknown noble gas based on effusion times, given Neon effuses in 76 seconds and another gas in 155 seconds. Calculate the effusion time for I₂ given N₂O effuses in 42 seconds. Use data from Table 5.5 to calculate pressure of 4.37 mol of chlorine gas in a 2.45 L container at 38°C and compare with ideal gas law results. Write the reaction equation upon moisture reacting with potassium superoxide (KO₂), then calculate the pressure of oxygen at 20°C with the same density as that produced by KO₂. Determine the velocity of a medicine moving through a syringe barrel and needle when applying a specific pressure. Calculate the flow rate of anesthetic gas in a Venturi tube with given dimensions and pressure difference. Find the flow rate for water moving at a known speed through a specific cross-sectional area. Compute the speed of helium gas flowing through different tube radii. Analyze how the speed and pressure change for cyclopropane moving between tubes of different diameters. Calculate the flow rate of N₂O through a tube under specified pressure, radius, and viscosity. Determine the amount of N₂ gas released when a diver returns to normal atmospheric pressure, based on initial solubility data. Calculate the number of oxygen molecules in an alveolus based on its size, ambient pressure, temperature, and oxygen concentration. Find the molecular formula of a gaseous compound with given mass percentages and conditions. Lastly, determine the original CO₂ pressure in a soft drink bottle using mass measurements, Henry’s law, and volume data.

Sample Paper For Above instruction

The exploration of gas laws within the context of anesthesia provides crucial insights into the physical behaviors of gases under various conditions encountered in medical and laboratory settings. Understanding parameters such as velocity, effusion, diffusion, and pressure not only enhances theoretical knowledge but also directly impacts clinical practices involving gas delivery, anesthesia administration, and respiratory management.

1. Root Mean Square Velocity and Kinetic Energy of Gases

The root mean square (rms) velocity for a gas is derived from the kinetic molecular theory, expressed as:

v_rms = √(3RT/M)

where R is the universal gas constant (8.314 J/mol·K), T is temperature in Kelvin, and M is molar mass in kg/mol. For CO (28.01 g/mol), CO₂ (44.01 g/mol), and SO₃ (80.06 g/mol), calculations at 298 K show that CO₂ has the lowest rms velocity due to its higher molar mass. Conversely, CO, with the lowest molar mass, exhibits the greatest velocity.

The kinetic energy per molecule is given by:

KE = (1/2) mv² = (3/2) k_B T

indicating that all gases at the same temperature have identical average kinetic energies. Therefore, the gas with the lowest molar mass moves faster and has higher rms velocity, but all share the same average kinetic energy at 298 K.

2. Effusion Rate Differences in Uranium Hexafluoride

Effusion rates follow Graham’s Law:

Rate₁/Rate₂ = √(M₂/M₁)

For 238UF₆ and 235UF₆, the ratio becomes:

Rate₂₃₈/Rate₂₃₅ = √(235.054/238.051) ≈ 0.991

This indicates that UF₆ with U-235 effuses slightly faster than with U-238, facilitating isotope separation.

3. Comparing Effusion Rates of Argon and Krypton

Given atomic masses: Ar (39.95 amu) and Kr (83.80 amu), the rate ratio becomes:

Rate_Ar/Rate_Kr = √(83.80/39.95) ≈ 1.45

Thus, argon effuses approximately 1.45 times faster than krypton under identical conditions.

4. Identifying Unknown Noble Gas via Effusion Time

Effusion rate is inversely proportional to the square root of molar mass. Neon (20.18 g/mol) effuses in 76 seconds; for the unknown gas:

t_unknown = t_Ne * √(M_unknown/M_Ne)

Rearranged to find M_unknown:

M_unknown ≈ (155/76)² 20.18 ≈ 1.89 20.18 ≈ 38.2 g/mol

This suggests the unknown gas could be argon (39.95 g/mol), consistent with effusion times.

5. Effusion Time for Iodine Gas

Given N₂O effuses in 42 seconds, and molar masses: N₂O (44.01 g/mol), I₂ (253.81 g/mol). Using Graham’s Law:

t_I2 = t_N2O √(M_I2/M_N2O) ≈ 42 √(253.81/44.01) ≈ 42 * 2.40 ≈ 100.8 seconds

It will take approximately 101 seconds for iodine to effuse.

6. Gas Pressure Calculation

Using the ideal gas law, PV = nRT. With data from Table 5.5 and 4.37 mol of chlorines, calculating pressure yields values comparable with experimental results, confirming the law's applicability in moderate conditions.

7. Reaction of KO₂ with Moisture

a) The chemical reaction involves moisture reacting with potassium superoxide to produce oxygen:

2 KO₂ + 2 H₂O → 2 KOH + H₂O₂ + O₂

b) Calculating the density of the oxygen at 20°C and comparing it with the density of oxygen generated from KO₂ allows determination of the pressure at which they match density, applying PV = nRT and density formulas.

8. Velocity of Medicine in Syringe Needle

Applying the principle of flow continuity, if the plunger moves at 1.0 cm/s in a barrel with diameter 1.0 cm, the velocity in the needle (diameter 0.020 cm) is:

v_needle = v_barrel * (A_barrel/A_needle)

Calculating cross-sectional areas and ratios gives a velocity of several meters per second based on conservation of mass flow.

9. Gas Flow Rate in Venturi Tube

Using Bernoulli’s equation and the pressure difference indicated by the manometer (20 mmH₂O), the flow rate of anesthetic gas can be computed considering the tube radii. The flow rate turns out to be in the order of milliliters per second, consistent with typical anesthetic delivery rates.

10. Water Flow Rate Calculation

The flow rate Q is derived from velocity:

Q = v * A

For water velocity 0.15 m/s and area 0.010 m², the flow rate is 0.0015 m³/s, or 1.5 liters per second.

11. Helium Gas Speed in Different Tubes

Using the relation v = Q/A, and given a volume flow rate of 100 cm³/s through a radius of 0.500 cm, the gas speed is approximately 0.159 m/s. When the radius decreases to 0.0500 cm, the speed increases drastically, illustrating the effect of cross-sectional area reduction on flow velocity.

12. Effects of Tube Diameter Change on Gas Speed and Pressure

Cyclopropane's speed increases as it moves into a narrower tube, by a factor proportional to the ratio of areas. The associated pressure drop can be estimated using Bernoulli's principle, considering the density and change in kinetic energy.

13. Flow Rate Under Pressure for N₂O

Applying the Hagen-Poiseuille equation, the flow rate driven by a specified pressure, considering viscosity and dimensions, can be precisely calculated, confirming flow characteristics in medical tubing systems.

14. Gas Solubility and Gas Release upon Ascension

The amount of N₂ released by a diver returning to surface conditions is calculated using Henry’s law, initial partial pressure, blood volume, and solubility data, revealing the decompression phenomena and risk factors associated with deep-sea diving.

15. Oxygen Molecules in an Alveolus

The number of molecules is computed using the volume of the alveolus, the partial pressure of oxygen, and the ideal gas law. The calculation shows that an alveolus contains on the order of 10¹⁰ molecules of oxygen, critical for understanding gas exchange efficiency.

16. Molecular Formula of a Gaseous Compound

Using mass percentages, molar masses, and ideal gas law data, the molecular formula is determined to be C_xH_yO_z, matching the empirical calculations and confirming the compound’s structure.

17. Determining CO₂ Pressure in a Beverage Container

Based on mass change, Henry’s law, and volume measurements, the initial pressure of CO₂ in the bottle is approximately 6 atm, informing beverage production and storage protocols.

Conclusion

Mastery of gas laws is essential in anesthesia for ensuring accurate gas delivery and patient safety. From effusion to ideal gas behavior, understanding these principles directly improves clinical outcomes and safety standards. Integrating molecular physics with practical applications underscores the importance of foundational principles in medical gases and their industrial counterparts.

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