Question

The pressure of a gas is \(440 \mathrm{mm}\) Hg. Express this pressure in units of (a) atmospheres, (b) bars, and (c) kilopascals.

Short answer

0.5789 atm; 0.5866 bars; 58.66 kPa.

Step-by-step solution

Understand Conversion Units

Before converting the pressure, let's understand the conversion units. 1 atmosphere (atm) is equal to 760 mm Hg, 1 bar is equal to 750.062 mm Hg, and 1 kilopascal (kPa) is equal to 7.50062 mm Hg.

Convert mm Hg to Atmospheres

To convert 440 mm Hg to atmospheres, use the conversion factor: \(1 \text{ atm} = 760\, \text{mm Hg}\). Divide the given pressure by this factor: \[\frac{440}{760} \approx 0.5789 \text{ atm}.\]

Convert mm Hg to Bars

To convert 440 mm Hg to bars, use the conversion factor: \(1 \text{ bar} = 750.062\, \text{mm Hg}\). Divide the given pressure by this factor: \[\frac{440}{750.062} \approx 0.5866 \text{ bars}.\]

Convert mm Hg to Kilopascals

To convert 440 mm Hg to kilopascals, use the conversion factor: \(1\, \text{kPa} = 7.50062\, \text{mm Hg}\). Divide the given pressure by this factor: \[\frac{440}{7.50062} \approx 58.66 \text{ kPa}.\]

Key concepts

Atmospheres

Pressure is often measured using different units depending on the context. One such unit is the atmosphere, abbreviated as atm. The atmosphere is a unit of pressure that is based on the average atmospheric pressure at sea level on Earth. It provides a handy way to think about pressure in terms of the natural environment.

When converting pressure measurements to atmospheres, it's important to know the conversion factor. For atmospheric pressure, the key number to remember is that 1 atm equals 760 mm Hg. To convert a pressure measured in millimeters of mercury (mm Hg) to atmospheres, simply divide your pressure value by this factor.

• For example, if you have a pressure of 440 mm Hg, you convert it by calculating \( \frac{440}{760} \approx 0.5789 \text{ atm}\).

Thus, 440 mm Hg is approximately 0.579 atmospheres. This is useful when comparing other pressures to typical conditions at sea level.

Bars

The bar is another unit for measuring pressure and is commonly used in many scientific and engineering applications. It is especially prevalent in Europe. When dealing with bar as a unit of pressure, it's important to remember its specific conversion value.

The conversion factor for bars is that 1 bar equals approximately 750.062 mm Hg. This precision helps in achieving accurate conversions, crucial in scientific work.

• To convert 440 mm Hg to bars, you can use the formula: \( \frac{440}{750.062} \approx 0.5866 \text{ bars} \).

Hence, a pressure of 440 mm Hg is about 0.587 bars. Using bars can help simplify certain calculations, especially when working within the international metric system.

Kilopascals

Kilopascals, with the abbreviation kPa, are another common unit of pressure favored in scientific measurements due to their base metric system relationship. It belongs to the pascal family of units, the pascal being the standard unit of pressure in the International System of Units (SI).

Kilopascals provide a convenient way to express pressure in larger values. Converting from mm Hg to kilopascals requires understanding that 1 kPa equals approximately 7.50062 mm Hg. The conversion reflects the need for precision in measurements.

• For 440 mm Hg, this converts to: \( \frac{440}{7.50062} \approx 58.66 \text{ kPa} \).

This means 440 mm Hg equates to approximately 58.66 kilopascals. The kilopascal offers a clear and straightforward metric measure, making it a favorable choice in many scientific settings.