Problem 1 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

0.5789 atm, 0.5866 bar, 58.6621 kPa

Step 1 - Convert mm Hg to Atmospheres

To convert from mm Hg to atmospheres, use the conversion factor: 1 atm = 760 mm Hg. \[ \text{Pressure in atm} = \frac{440}{760} = 0.5789 \space \text{atm} \]

Step 2 - Convert mm Hg to Bars

To convert from mm Hg to bars, use the conversion factor: 1 mm Hg = 0.00133322 bars. \[ \text{Pressure in bars} = 440 \times 0.00133322 = 0.5866 \space \text{bar} \]

Step 3 - Convert mm Hg to Kilopascals

To convert from mm Hg to kilopascals, use the conversion factor: 1 mm Hg = 0.133322 kPa. \[ \text{Pressure in kPa} = 440 \times 0.133322 = 58.6621 \space \text{kPa} \]

Key Concepts

Atmospheres Conversion

Atmospheric pressure is a key metric for understanding how the weight of air impacts our environment. When you are converting pressure from millimeters of mercury (mm Hg) to atmospheres (atm), you are shifting from a localized measurement to a universal standard. For this process, the conversion factor is critical: 1 atmosphere equals 760 mm Hg.

• To make the conversion, simply divide the given mm Hg value by 760.
• For example, if the pressure is 440 mm Hg, you calculate the atmospheres by \( \frac{440}{760} = 0.5789 \space \text{atm} \).

Using atmospheres as a unit can simplify the comparison of pressures and is common in many scientific calculations. Remember, this conversion gives you an understanding of how the pressure compares to the standard atmospheric level at sea level.

Bars Conversion

The bar is another unit of pressure commonly used in meteorology and various applications requiring precise measurement, especially in Europe. To convert from mm Hg to bars, know that 1 mm Hg corresponds to 0.00133322 bars.

• Start by multiplying the mm Hg value by this bar conversion factor.
• If you have 440 mm Hg, multiply to find out \( 440 \times 0.00133322 = 0.5866 \space \text{bar} \).

Bars are widely used because the value closely approximates standard atmospheric pressure and is easy to work with, particularly in weather forecasts and for tire pressures.

Kilopascals Conversion

The kilopascal (kPa) is part of the International System of Units (SI) and is frequently used in scientific and engineering contexts. To shift from mm Hg to kPa, use the conversion factor: 1 mm Hg equates to 0.133322 kPa.

• Calculate the kilopascals by multiplying the mm Hg value by 0.133322.
• For instance, starting with 440 mm Hg, you'll get \( 440 \times 0.133322 = 58.6621 \space \text{kPa} \).

Kilopascals are particularly convenient for understanding pressures in contexts like gas laws and physical sciences because they directly relate to the metric system, making it easier to integrate into international discussions and applications.