Problem 1 - Chemical Principles in the Laboratory

Question

Verifying the Absolute Zero of Temperature Determination of the Atmospheric Pressure. The atmospheric pressure on a spring day in Minnesota was found to be \(762 \mathrm{mm} \mathrm{Hg}\). a. What would the pressure be in \(\mathrm{cm} \mathrm{H}_{2} \mathrm{O} ?\) _______\(\mathrm{cm} \mathrm{H}_{2} \mathrm{O}\) b. About how many meters of water would it take to exert that pressure?

Step-by-Step Solution

Answer

a. 1035.12 cm H₂O; b. 10.35 m of water.

Step 1: Understand the Units

The problem involves converting pressure from millimeters of mercury (mm Hg) to centimeters of water (cm H₂O) and then to the height of water in meters. The conversion factors needed are: 1 mm Hg = 1.36 cm H₂O.

Step 2: Convert mm Hg to cm H₂O

Use the conversion factor 1 mm Hg = 1.36 cm H₂O. Multiply the given pressure in mm Hg by this factor to find the pressure in cm H₂O. \[ 762 \text{ mm Hg} \times 1.36 \text{ cm H₂O/mm Hg} = 1035.12 \text{ cm H₂O} \]

Step 3: Convert cm H₂O to m of Water

To convert the pressure from centimeters of water to meters of water, divide the pressure in cm H₂O by 100 (since 100 cm = 1 m). \[ \frac{1035.12 \text{ cm H₂O}}{100} = 10.3512 \text{ m} \]

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air above us. It is often measured in units like millimeters of mercury (mm Hg) or pascals (Pa). This pressure is vital for various physical and chemical processes on Earth.

• This pressure can change with altitude and weather conditions.
• At sea level, standard atmospheric pressure is approximately 1013.25 hPa or 760 mm Hg.

At different locations and times, atmospheric pressure can vary. In Minnesota, as in the exercise example, the pressure was found to be 762 mm Hg during a spring day. Understanding atmospheric pressure is key to studying weather patterns and the behavior of gases.

Absolute Zero

Absolute zero represents the theoretical lowest temperature possible, where substances contain no thermal energy. It is a fundamental concept in physical chemistry and thermodynamics.

• At absolute zero, a system would have minimal internal energy.
• Absolute zero is 0 Kelvin, equivalent to -273.15°C or -459.67°F.

Scientists cannot reach absolute zero, but they can approach it in laboratory conditions to study the properties of matter at extremely low temperatures. This concept also highlights the behavior of gases, predicting they would exert zero pressure and cease to move at this temperature.

Unit Conversion

Unit conversion plays a crucial role in science, especially in experiments like the given exercise. Converting units allows scientists to standardize measurements and compare results accurately. Different substances and scenarios might call for distinct units. For instance:

• Pressure can be measured in mm Hg, cm H₂O, or pascals (Pa).
• Length might be in centimeters, meters, or inches.

In the provided exercise, we utilized the fact that 1 mm Hg is equivalent to 1.36 cm H₂O for converting atmospheric pressure from one unit to another. This step-by-step conversion is essential for consistent and clear scientific communication.

Physical Chemistry

Physical chemistry focuses on understanding the physical properties and behaviors of chemical systems, providing a bridge between physics and chemistry. It investigates concepts such as:

• Thermodynamics, which studies energy changes within chemical reactions.
• Kinetics, which looks at the speed and rate of reactions.

Understanding these principles helps in explaining how and why reactions happen and how temperature, pressure, and other conditions can affect a chemical system. The exploration of topics like absolute zero and how gases behave at different conditions reflects the depth of physical chemistry. These studies lead to innovations and have practical applications in fields like medicine, environmental science, and engineering.