Problem 41 - Chemistry: An Atoms-Focused Approach

Question

Convert the following pressures into atmospheres: (a) \(2.0 \mathrm{kPa} ;\) (b) \(562 \mathrm{mmHg}\)

Step-by-Step Solution

Answer

Question: Convert the given pressures into atmospheres: 2.0 kPa and 562 mmHg. Answer: 2.0 kPa is equal to 0.0197 atm, and 562 mmHg is equal to 0.7395 atm.

Step 1: Conversion of pressure in kPa to atm

To convert the pressure from kPa to atm, we simply need to divide the given pressure by the conversion factor. In this case, we are given a pressure of \(2.0 \mathrm{kPa}\). Using the conversion factor mentioned above, we can write: \(2.0 \mathrm{kPa} \times \frac{1 \mathrm{atm}}{101.325 \mathrm{kPa}}\) Now, cancel out the units of kPa to obtain the pressure in atm: \(2.0 \times \frac{1 \mathrm{atm}}{101.325} = 0.0197 \mathrm{atm}\) (rounded to 4 decimal places) So, \(2.0 \mathrm{kPa}\) is equal to \(0.0197 \mathrm{atm}\).

Step 2: Conversion of pressure in mmHg to atm

To convert the pressure from mmHg to atm, we again need to divide the given pressure by the conversion factor. In this case, we are given a pressure of \(562 \mathrm{mmHg}\). Using the conversion factor mentioned above, we can write: \(562 \mathrm{mmHg} \times \frac{1 \mathrm{atm}}{760 \mathrm{mmHg}}\) Now, cancel out the units of mmHg to obtain the pressure in atm: \(562 \times \frac{1 \mathrm{atm}}{760} = 0.7395 \mathrm{atm}\) (rounded to 4 decimal places) So, \(562 \mathrm{mmHg}\) is equal to \(0.7395 \mathrm{atm}\).

Key Concepts

kPa to atm

To convert kilopascals (kPa) to atmospheres (atm), you use a specific conversion factor. This conversion is crucial in understanding how pressure units relate to each other in different contexts, particularly in chemistry and physics. The standard conversion factor is that 1 atmosphere is equal to 101.325 kPa.

For example, if you have a pressure reading of 2.0 kPa and you want to express it in atm, you would divide 2.0 by 101.325. This division gives you the equivalent pressure in atm.

• The formula to convert from kPa to atm is: \[\text{Pressure in atm} = \frac{\text{Pressure in kPa}}{101.325}\]
• Substitute 2.0 for the pressure in kPa: \[\frac{2.0}{101.325} \approx 0.0197 \text{ atm}\]

The result tells us that 2.0 kPa is equivalent to approximately 0.0197 atm. Always remember to use the conversion factor correctly and to round off your answer appropriately.

mmHg to atm

Converting millimeters of mercury (mmHg) to atmospheres (atm) is another common pressure conversion used in chemistry. The reference point for this conversion is based on standard atmospheric pressure, where 1 atm is equal to 760 mmHg.

Let's say you're given a pressure of 562 mmHg and need to convert it to atm. You would divide 562 by 760 to get the equivalent pressure in atm.

• To convert mmHg to atm, use the formula: \[\text{Pressure in atm} = \frac{\text{Pressure in mmHg}}{760}\]
• Substitute 562 for the pressure in mmHg: \[\frac{562}{760} \approx 0.7395 \text{ atm}\]

So, 562 mmHg is approximately 0.7395 atm. This conversion is particularly useful for comparing pressure readings in lab experiments or understanding gas laws.

Unit Conversion in Chemistry

Unit conversion is a fundamental skill in chemistry, as it allows you to interpret and manipulate data easily across different measurements. In chemistry, dealing with units like pressure, volume, and temperature often requires conversions to analyze results or to perform calculations accurately.

An understanding of how to convert units allows chemists to communicate data clearly and to use universal standards in their work. For pressures, for example, knowing how to convert between kPa, mmHg, and atm can help in various applications, such as gas law problems or laboratory measurements.

• Identify the conversion factor needed for the units in question.
• Apply the conversion factor by either multiplying or dividing, depending on the relationship.
• Always check to make sure the units cancel out correctly, resulting in the desired units.
• Round to appropriate significant figures based on the precision of the initial data.

Appropriately using unit conversion supports accuracy and understanding in scientific investigations, ensuring that results are both valid and comparable.