Problem 35 - Chemistry The Molecular Nature of Matter

Question

Carry out the following unit conversions: (a) 1.26 atm to torr, (b) 740 torr to atm, (c) 738 torr to \(\mathrm{mm} \mathrm{Hg}\), (d) \(1.45 \times 10^{3} \mathrm{~Pa}\) to torr.

Step-by-Step Solution

Answer

a) 1.26 atm to torr is 1.26 x 760 = 957.6 torr; b) 740 torr to atm is 740 / 760 = 0.974 atm; c) 738 torr to mmHg is 738 mmHg (same units); d) \(1.45 \times 10^3\) Pa to torr is $1.45 \times 10^3 / 133.322 = 10.88 torr.

Step 1: Convert atm to torr

To convert atmospheres (atm) to torr, use the conversion factor that 1 atm is equivalent to 760 torr. Multiply the value in atm by 760 to get the value in torr.

Step 2: Convert torr to atm

To convert torr to atmospheres (atm), use the conversion factor that 1 atm is equivalent to 760 torr. Divide the value in torr by 760 to obtain the value in atm.

Step 3: Recognize torr and mmHg as equivalent units

Torr and millimeters of mercury (mmHg) are equivalent units of pressure. Therefore, to convert torr to mmHg, the value remains the same. No calculation is necessary.

Step 4: Convert Pa to torr

To convert pascals (Pa) to torr, use the conversion factor that 1 torr is equivalent to 133.322 Pa. Divide the value in pascals by 133.322 to get the value in torr.

Key Concepts

Atmospheres to Torr

Understanding how to convert atmospheres (atm) to torr is a common requirement in chemistry, particularly in studies involving gas laws and atmospheric science. To convert from atmospheres to torr, we utilize the fact that 1 atmosphere is equal to 760 torr. This conversion factor is based on the historical definition of pressure where 1 torr was roughly the pressure exerted by a millimeter column of mercury.To convert 1.26 atm to torr for example, multiply 1.26 by 760, resulting in 957.6 torr. This allows students to easily convert between these two units of measurement by using a simple multiplication.

Practical Application

Understanding this conversion is essential for accurately measuring pressure in various scientific contexts and applying the ideal gas law in practical situations.

Torr to Atmospheres

Alternatively, converting torr to atmospheres (atm) is just as critical when dealing with pressure measurements. The inverse of the atm to torr conversion factor is used. As we know 1 atm is equivalent to 760 torr, to convert from torr to atm, we divide the number of torr by 760.

For instance, to convert 740 torr to atm, we perform the following calculation: 740 ÷ 760, which equals approximately 0.974 atm. This illustrates how students can transition from the more granular torr unit to the broader atmosphere unit, which can be useful when comparing local atmospheric pressure with standardized measurements.

Common Pitfalls

One typical error to avoid is failing to remember that we must divide and not multiply when converting torr to atm, which can lead to incorrect results and misconceptions in pressure-related calculations.

Pascals to Torr

The conversion from pascals (Pa) to torr is a bit more complex due to the difference in magnitude between these units. Pascals are part of the International System of Units (SI) and are widely used in science and engineering. Torr, on the other hand, are a non-SI unit that is derived from the physical pressure of a column of mercury.The conversion factor is 1 torr is equivalent to 133.322 pascals.To convert from pascals to torr, you divide the number of pascals by 133.322. For example, to convert 1,450 Pa to torr, the calculation would be 1,450 ÷ 133.322, which results in approximately 10.878 torr.

It's beneficial to understand this conversion for activities such as calibrating instruments or when interfacing with international systems where SI units are the standard.

Pressure Units Conversion

Having a solid grasp of pressure units conversion is crucial for a variety of chemical and physical applications. Pressure, which is a measurement of force applied per unit area, can be expressed in multiple units, including atmospheres (atm), torr (mmHg), and pascals (Pa). The ability to convert between these units is essential for understanding and communicating scientific data.Both atm and torr are commonly used in the study of gases, while Pa is typically used in a broader range of physics applications. Knowing the conversions:

• 1 atm = 760 torr or mmHg
• 1 torr = 133.322 Pa

allows for fluid translation between the different scales of measurement and helps prevent any misunderstanding or errors in pressure readings, be it for academic assignments or professional practices.

Consistency is Key

Being consistent with units throughout scientific investigation ensures clarity and reliability of results, making conversions between units a fundamental skill in the sciences.