Question

Convert the following pressures into pascals. a. 774 torr b. 0.965 atm c. \(112.5 \mathrm{kPa}\) d. \(801 \mathrm{~mm} \mathrm{Hg}\)

Short answer

The converted pressure values are: a. \(103,142.42 \,\mathrm{Pa}\), b. \(97,749.225 \,\mathrm{Pa}\), c. \(112,500 \,\mathrm{Pa}\), and d. \(106,809.42 \,\mathrm{Pa}\).

Step-by-step solution

Determine the conversion factors for each pressure unit

Before we can begin converting the given pressure values to pascals, we need to know the conversion factors for each unit. - 1 torr = 133.322 Pa - 1 atm = 101,325 Pa - 1 kPa = 1000 Pa - 1 mm Hg = 133.322 Pa

Convert 774 torr to pascals

Now that we have the conversion factor for torr, we can convert 774 torr to pascals: \(774 \mathrm{~torr} * \frac{133.322 \mathrm{~Pa}}{1 \mathrm{~torr}} = 103142.42\,\mathrm{Pa}\)

Convert 0.965 atm to pascals

Using the conversion factor for atm, we can convert 0.965 atm to pascals: \(0.965 \mathrm{~atm} * \frac{101325 \mathrm{~Pa}}{1 \mathrm{~atm}} = 97749.225 \,\mathrm{Pa}\)

Convert 112.5 kPa to pascals

To convert 112.5 kPa to pascals, we must use the kPa to Pa conversion factor: \(112.5 \mathrm{~kPa} * \frac{1000 \mathrm{~Pa}}{1 \mathrm{~kPa}} = 112500 \,\mathrm{Pa}\)

Convert 801 mm Hg to pascals

Finally, using the conversion factor for mm Hg, we can convert 801 mm Hg to pascals: \(801 \mathrm{~mm\, Hg} * \frac{133.322 \mathrm{~Pa}}{1 \mathrm{~mm\, Hg}} = 106809.42\,\mathrm{Pa}\) In summary, the pressure values converted to pascals are: a. 774 torr = 103,142.42 Pa b. 0.965 atm = 97,749.225 Pa c. 112.5 kPa = 112,500 Pa d. 801 mm Hg = 106,809.42 Pa

Key concepts

Pascals

The pascal (Pa) is the SI unit for measuring pressure. It is named after Blaise Pascal, a renowned French mathematician and physicist. A pascal is defined as one newton per square meter, which provides a clear way to gauge pressure force over an area.
Pressure, in general, is the force applied perpendicular to the surface of an object over a specific area.
Using pascals helps standardize pressure calculations in science and engineering. It's widely used because it simplifies the integration and comparison of data.
The formulas involved are straightforward, making calculations manageable. Understanding the pascal is critical in fields such as engineering, meteorology, and medicine.

• 1 Pa = 1 N/m²
• Commonly used in scientific research
• Part of the International System of Units (SI)

Pressure Units

There are various units to express pressure, which differ based on context and geographical preference.
Some of the most common pressure units include pascals, atmospheres (atm), torrs, and millimeters of mercury (mm Hg).
Each unit originates from a different scientific background or application, which can make direct comparisons tricky without conversion factors.
For instance, torrs and mm Hg are often used in practices like meteorology or aviation. Understanding these units allows you to accurately assess different pressure forms, contributing to better problem-solving skills in scientific fields.

• Pascals (Pa): The standard unit in scientific contexts
• Atmospheres (atm): Mostly used in chemistry to describe ocean and air pressure
• Torr: Named after Evangelista Torricelli, commonly used in vacuum measurements
• mm Hg: Historical use for barometric readings

Conversion Factors

Conversion factors allow translation between differing pressure units. These are essential for solving chemistry and physics problems as they help bridge varying measurement systems.
To convert from one pressure unit to another, you multiply the value by a conversion factor, which is specific to each unit pair. For example, converting atmospheres to pascals involves using the factor 101,325 Pa/atm.
Here are the key conversion factors used for converting to pascals from other pressure units:

• 1 torr = 133.322 Pa
• 1 atm = 101,325 Pa
• 1 kPa = 1,000 Pa
• 1 mm Hg = 133.322 Pa

By consistently using these factors, you ensure that your calculations are accurate. Converting pressures is a foundational skill in scientific calculations and helps ensure that all standards align across different practices.

Chemistry Problem Solving

Chemistry problem solving often involves the conversion of pressure units, because reactions can vary under different conditions of pressure.
When solving chemistry problems, it's critical to carefully convert units to ensure that all values are in a consistent format.
This method allows chemists to determine reactant/product quantities or assess conditional changes like temperature and volume shifts.
Using the correct units and conversion factors ensures that equations used in chemistry, such as the ideal gas law or reaction rate calculations, yield valid results.
When presented with a problem involving pressures given in various units, follow these steps:

• Identify the given units and relevant conversion factors
• Apply the conversion factors to unify pressure values
• Use converted values in the chemical equations required for the problem

By practicing these steps, students can enhance their skills and confidence in tackling chemistry problems involving pressure.