Problem 1 - Chemical Principles in the Laboratory

Question

The atmospheric pressure on a spring day in Minnesota was found to be \(726 \mathrm{mm}\) 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? _______________\({m} \mathbf{H}_{2} \mathbf{O}\)

Step-by-Step Solution

Answer

a. 987.36 cm H₂O b. 9.8736 m H₂O

Step 1: Convert mm Hg to cm H₂O

To convert the atmospheric pressure from millimeters of mercury to centimeters of water, use the conversion factor where 1 mm Hg is equivalent to 1.36 cm H₂O. Therefore, calculate:\[726 \text{ mm Hg} \times 1.36 \text{ cm H}_{2}\text{O/mm Hg}\]

Step 2: Perform the Calculation for Pressure in cm H₂O

Carry out the multiplication:\[726 \times 1.36 = 987.36\]Thus, the atmospheric pressure is approximately 987.36 cm H₂O.

Step 3: Convert cm H₂O to m H₂O

Since 1 meter equals 100 centimeters, convert the pressure to meters of water by dividing the pressure in cm H₂O by 100:\[\frac{987.36}{100} = 9.8736\]Therefore, the atmospheric pressure is approximately 9.8736 meters of water.

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted onto a surface by the weight of the air above it. This weight of air is due to the gravitational pull of the Earth. On a typical day, atmospheric pressure can vary based on geographic location and weather conditions, among other factors. Understanding atmospheric pressure is crucial for various scientific and engineering fields, such as meteorology and aviation. It is commonly measured in units like millimeters of mercury (mm Hg) or inches of mercury (in Hg).

• Atmospheric pressure is usually around 760 mm Hg at sea level under standard conditions.
• Weather changes and altitude can greatly affect atmospheric pressure measurements.
• Units like mm Hg give a tangible way to communicate air pressure based on the height of a mercury column supported by air pressure.

In specific science exercises, we often convert pressure measurements into different units, which brings us to our next topic.

Unit Conversion

Unit conversion is a process that involves changing a physical quantity from one unit to another using conversion factors. In scientific calculations, it's essential to use the proper conversion factor to ensure accurate results. For the problem at hand, the conversion from millimeters of mercury (mm Hg) to centimeters of water (cm H₂O) employs the factor where 1 mm Hg is equivalent to 1.36 cm H₂O.
Why do we convert units? Different units can offer more clarity or relevance depending on the context. For example, pressure can be expressed in already familiar terms such as water columns, making it easier to visualize than if it were described in mm Hg.

• Determine the relevant units for your calculation (e.g., mm Hg to cm H₂O).
• Use the correct conversion factor to translate those units (1 mm Hg = 1.36 cm H₂O).
• Complete the mathematical operation to find the outcome in the desired units.

In our case, converting 726 mm Hg to cm H₂O involves multiplying by 1.36, resulting in 987.36 cm H₂O.

Scientific Calculation

Scientific calculation involves using mathematics and logic to solve scientific problems effectively. In exercises like the one we've discussed, calculations help quantify phenomena that are not directly observable, turning abstract data into understandable, usable information.

• First, identify what the problem is asking for—the target unit of measurement.
• Perform mathematical operations to convert units and solve for the desired result.
• Keep track of units throughout to ensure consistency and accuracy.

In the given problem, the scientific calculation starts with multiplication to switch from mm Hg to cm H₂O, followed by division to convert to meters of water. Ensuring each step maintains scientific precision is critical for achieving valid results. The final solutions, approximately 987.36 cm H₂O and 9.8736 m H₂O, showcase the powerful role calculations play in transforming theoretical challenges into practical outcomes.