Carry out the following conversions: (b) 0.255 atm to mm Hg

Verified step by step guidance

1. Identify the conversion factor between atmospheres (atm) and millimeters of mercury (mm Hg). The conversion factor is 1 atm = 760 mm Hg.
2. Set up the conversion equation using the given value and the conversion factor. This involves multiplying the given pressure in atmospheres by the conversion factor to convert it to mm Hg.
3. Write the equation: \(0.255 \, \text{atm} \times 760 \, \text{mm Hg/atm}\).
4. Perform the multiplication to convert the pressure from atmospheres to millimeters of mercury.
5. Ensure the units are correctly canceled out and only mm Hg remains as the unit in your final answer.

Key Concepts

Gas Pressure Units

Gas pressure can be measured in various units, including atmospheres (atm), millimeters of mercury (mm Hg), and pascals (Pa). Understanding these units is essential for converting between them, as they represent the same physical quantity but are expressed differently. For example, 1 atm is defined as the pressure exerted by a column of mercury 760 mm high at sea level.

Conversion Factors

Conversion factors are ratios used to convert a quantity from one unit to another. In the case of pressure, the conversion factor between atm and mm Hg is 760 mm Hg/1 atm. By multiplying the pressure in atm by this conversion factor, one can easily find the equivalent pressure in mm Hg, ensuring accurate calculations in various scientific contexts.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert units by canceling out dimensions. It involves multiplying the quantity by conversion factors that have the desired units in the numerator and the original units in the denominator. This method not only simplifies calculations but also helps verify that the final answer is in the correct units, which is crucial in chemistry for maintaining consistency.