What is the total pressure, in millimeters of mercury, of a gas mixture containing argon gas at 0.25 atm, helium gas at 350 mmHg, and nitrogen gas at 360 Torr? (8.7)

Verified step by step guidance

1. Convert the pressure of argon gas from atmospheres to millimeters of mercury using the conversion factor: 1 atm = 760 mmHg.
2. Add the converted pressure of argon gas to the given pressure of helium gas, which is already in mmHg.
3. Add the pressure of nitrogen gas, given in Torr, to the sum of the pressures of argon and helium gases. Note that 1 Torr is equivalent to 1 mmHg, so no conversion is needed for nitrogen gas.
4. The sum of these pressures will give you the total pressure of the gas mixture in millimeters of mercury.
5. Ensure all units are consistent and verify the calculations to ensure accuracy.

Key Concepts

Gas Pressure Units

Gas pressure can be measured in various units, including atmospheres (atm), millimeters of mercury (mmHg), and torr. Understanding these units is crucial for converting pressures to a common unit for calculations. Notably, 1 atm is equivalent to 760 mmHg and 760 torr, allowing for straightforward conversions between these measurements.

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. This principle is essential for calculating the total pressure of a gas mixture, as it allows us to add the pressures of argon, helium, and nitrogen to find the overall pressure in the system.

Pressure Conversion

To accurately calculate the total pressure of the gas mixture, it is necessary to convert all pressures to the same unit. For instance, converting helium's pressure from mmHg to atm or nitrogen's pressure from torr to mmHg ensures consistency. This step is vital for applying Dalton's Law effectively and obtaining the correct total pressure.